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  • Articles  (161,092)
  • Springer  (139,698)
  • American Institute of Physics  (21,394)
  • 1995-1999  (161,092)
  • 1980-1984
  • 1955-1959
  • 1998  (76,319)
  • 1996  (84,773)
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  • 1995-1999  (161,092)
  • 1980-1984
  • 1955-1959
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  • 1
    Electronic Resource
    Electronic Resource
    Extending the quasi-steady state approximation by changing variables (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 43-63 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The parameter domain for which the quasi-steady state assumption is valid can be considerably extended merely by a simple change of variable. This is demonstrated for a variety of biologically significant examples taken from enzyme kinetics, immunology and ecology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458281
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  • 2
    Electronic Resource
    Electronic Resource
    Environmental fluctuations and the maintenance of genetic diversity in age or stage-structured populations (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 103-127 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The ability of random fluctuations in selection to maintain genetic diversity is greatly increased when generations overlap. This result has been derived previously using genetic models with very special assumptions about the population age structure. Here we explore its robustness in more realistic population models, with very general age structure or physiological structure. For a range of genetic models (haploid, diploid, single and multilocus) we find that the condition for maintaining genetic diversity generalizes almost without change. Genetic diversity is maintained by selection if a product of the form (generation overlap)×(selection intensity)×(variability in the selection regime) is sufficiently large, where the generation overlap is measured in units of Fisher's reproductive value. This conclusion is based on a local evolutionary stability analysis, which differs from the standard “protected polymorphism” criterion for the maintenance of genetic diversity. Simulation results match the predictions from the local stability analysis, but not those from the protected polymorphism criterion. The condition obtained here for maintaining genetic diversity requires fitness fluctuations that are substantial but well within the range observed in many studies of natural populations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458284
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  • 3
    Electronic Resource
    Electronic Resource
    Book reviews (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 203-206 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458288
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  • 4
    Electronic Resource
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    A community model of ciliateTetrahymena and bacteriaE. coli: Part II. Interactions in a batch system (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 265-283 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of aTetrahymena pyriformis-Escherichia coli community. In this study an alternative approach, an individual-based model, is employed to investigate the growth and interactions ofTetrahymena pyriformis andE. coli in a batch culture. Due to improved representation of physiological processes, the model provides a better agreement with experimental data of bacterial density and ciliate biomass than previous modeling studies. It predicts a much larger coexistence domain than rudimentary models, dependence of biomass dynamics on initial conditions (bacteria to ciliate biomasses ratio) and appropriate timing of minimal bacteria density. Moreover, it is found that accumulation ofE. coli sized particles andE. coli toxic metabolites has a stabilizing effect on the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458309
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  • 5
    Electronic Resource
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    Biometrics, biomathematics and the morphometric synthesis (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 313-365 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract At the core of contemporarymorphometrics—the quantitative study of biological shape variation—is a synthesis of two originally divergent methodological styles. One contributory tradition is the multivariate analysis of covariance matrices originally developed as biometrics and now dominant across a broad expanse of applied statistics. This approach, couched solely in the linear geometry of covariance structures, ignores biomathematical aspects of the original measurements. The other tributary emphasizes the direct visualization of changes in biological form. However, making objective the biological meaning of the features seen in those diagrams was always problematical; also, the representation of variation, as distinct from pairwise difference, proved infeasible. To combine these two variants of biomathematical modeling into a valid praxis for quantitative studies of biological shape was a goal earnestly sought though most of this century. That goal was finally achieved in the 1980s when techniques from mathematical statistics, multivariate biometrics, non-Euclidean geometry and computer graphics were combined in a coherent new system of tools for the complete regionalized quantitative analysis oflandmark points together with the biomedical images in which they are seen. In this morphometric synthesis, correspondence of landmarks (biologically labeled geometric points, like “bridge of the nose”) across specimens is taken as a biomathematical primitive. The shapes of configurations of landmarks are defined as equivalence classes with respect to the Euclidean similarity group and then represented as single points in David Kendall'sshape space, a Riemannian manifold with Procrustes distance as metric. All conventional multivariate strategies carry over to the study of shape variation and covariation when shapes are interpreted in the tangent space to the shape manifold at an average shape. For biomathematical interpretation of such analyses, one needs a basis for the tangent space compatible with the reality of local biotheoretical processes and explanations at many different geometric scales, and one needs graphics for visualizing average shape differences and other statistical contrasts there. Both of these needs are managed by thethin-plate spline, a deformation function that has an unusually helpful linear algebra. The spline also links the biometrics of landmarks to deformation analysis of the images from which the landmarks originally arose. This article reviews the history and principal tools of this synthesis in their biomathematical and biometrical context and demonstrates their usefulness in a study of focal neuroanatomical anomalies in schizophrenia.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458311
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  • 6
    Electronic Resource
    Electronic Resource
    A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competitive environment (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 425-447 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A competition model describing tumor-normal cell interaction with the added effects of periodically pulsed chemotherapy is discussed. The model describes parameter conditions needed to prevent relapse following attempts to remove the tumor or tumor metastasis. The effects of resistant tumor subpopulations are also investigated and recurrence prevention strategies are explored.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460591
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  • 7
    Electronic Resource
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    A model of growing vascular structures (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 409-424 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Increasing attention is being paid to the configuration and development of vascular structures and their possible correlations with physiological events. The study of angiogenesis in normal and pathological states as well as in the embryo and adult has provided new insights into the mechanism of vessel growth and organization of the vasculature. Various mathematical branching models have been developed. These constructions are mainly geometrical and only involve a branching phenomenon. We propose the use of a deterministic non-linear model based on physiological laws and hydrodynamics. Growth, branching and anastomosis, the three actual main events occurring in vascular growth, are included in this model. Space growth, including cells and vessels, is defined by a decreasing transformation. Space density and the length of new sprouts are controlled by a set of parameters. The conditions on these parameters are well established, which allows the production of realistic patterns.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460590
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  • 8
    Electronic Resource
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    The expected extinction time of a population within a system of interacting biological populations (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 555-568 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The quasi-stationary distribution of a population within a system of interacting populations is approximated by a stochastic logistic process. The parameters of this process can be expressed in the parameters of the full system. Using the diffusion approximation, an expression for the expected extinction time is derived from this logistic process. Since the expected extinction time is expressed in the parameters of the full system, the effect of these parameters on the extinction risk can be easily evaluated, which may be of use for studies in ecology, conservation biology and epidemiology. The outcome is compared with simulation results for the case of a prey-predator system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460596
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  • 9
    Electronic Resource
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    Making sense of the combined effect of interleukin-2 and interleukin-4 on lymphocytes using a mathematical model (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 569-594 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The cytokines are the information superhighway of the immune system. They are an important component of the integrated behavior of the system. In order to be able to have a good understanding of the immune system, we must be able to model the effect of cytokines and their combined effect. This work is a step in that direction. We study the combined effect of two cytokines: interleukin-2 (IL-2) and interleukin-4 (IL-4) on some cells of the immune system. Interleukin-2 and interleukin-4 are important growth and differentiation factors for B and T cells. Interleukin-4 antagonizes the effect of interleukin-2 on B cells and some T cells while it synergizes with interleukin-2 on other T cells. We build a mathematical model of the interaction of both cytokines on T and B cells as a building block toward a model of the Th1/Th2 cross-regulation. The response of a given cell to the combination of interleukin-2 and interleukin-4 is shown to involve competing dynamical effects which can lead to either antagnostic or synergistic combined effect.
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    URL: http://dx.doi.org/10.1007/BF02460597
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  • 10
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    Mathematical model of self-organizing hierarchies in animal societies (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 661-717 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We propose a mathematical approach to the modelling of self-organizing hierarchies in animal societies. This approach relies on a basic positive feedback mechanism that reinforces the ability of a given individual to win or to lose in a hierarchical interaction, depending on how many times it won or lost in previous interactions. Motivated by experiments carried out on primitively eusocial waspsPolistes, the model, is based on coupled differential equations supplemented with a small stochastic term. Numerical integrations allow many different hierarchical profiles to be obtained depending on the model parameters: (1) the particular form of the probability for an individual to win or lose a fight given its history, (2) the probability of interaction between two individuals, (3) the forgetting strength, which determines the rate at which events in the past are forgotten and no longer influence the force of an individual and (4) two individual recognition parameters, which set the contribution of individual recognition in the process of hierarchical genesis. We compare the results, expressed in terms of a hierarchical index or of the Landau number that describes the degree of linearity of the hierarchy, with various experimental results.
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    URL: http://dx.doi.org/10.1007/BF02459478
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  • 11
    Electronic Resource
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    Melanin granule model for laser-induced thermal damage in the retina (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 809-810 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02459483
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  • 12
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    A mathematical model for fibro-proliferative wound healing disorders (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 787-808 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsenet al., J. theor. Biol. 177, 113–128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states—a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.
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    URL: http://dx.doi.org/10.1007/BF02459482
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  • 13
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    Abrupt population changes along smooth environmental gradients (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 907-922 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Populations often exhibit abrupt changes in abundance associated with a smooth, continuous change in some component of their environment, with the abruptness usually attributed to inter-specific interactions or physical extremes. This paper presents a spatially explicit single-species population model in which intra-specific interactions alone are responsible for such an abrupt change. The essential mechanism involves cooperation in both colonization (through enhanced recruitment near other individuals) and mortality (protection through a “safety-in-numbers” interaction). Large fluctuations in population density would likely be observable near the transition region.
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    URL: http://dx.doi.org/10.1007/BF02459489
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  • 14
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    Epidemic models: Their structure and relation to data (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1019-1022 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459495
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  • 15
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    Material recycling in a closed aquatic ecosystem. I. Nitrogen transformation cycle and preferential utilization of ammonium to nitrate by phytoplankton as an optimal control problem (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 957-982 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model of the nitrogen transformation cycle in an aquatic environment is studied. Using Pontryagin's maximum principle, a preferential utilization of ammonium to nitrate by phytoplankton is explained and verified by experimental data. A multiparameter bifurcation is given. The model was found to have four types of equilibrium sets. It is shown that a Hopf bifurcation may occur.
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    URL: http://dx.doi.org/10.1007/BF02459492
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  • 16
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    Parallel computation enables precise description of Ca2+ distribution in nerve terminals (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1075-1097 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Parallel computation employing a domain decomposition method was used to calculate precisely without approximations the spatio-temporal distribution of Ca2+ in nerve terminals. The results showed, contrary to expectations, that for equal admitted Ca2+ currents at low (one channel open) and high (four channels open) depolarization, the average Ca2+ concentration at the release area is higher at the low depolarization. These calculations provide additional support for the Ca2+-voltage hypothesis for neurotransmitter release.
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    URL: http://dx.doi.org/10.1007/BF02458384
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  • 17
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    Modeling immunotherapy for allergy (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1099-1121 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Type I hypersensitivity, which functions to protect the organism from parasites, is caused by binding of antigen to IgE antibodies pre-attached to the cell surface of tissue mast cells and their circulating counterparts, the basophils. In “allergy,” type I hypersensitivity is inappropriately induced by protein-based foreign substances (such as pollen) or protein components of insect stings, which in the normal course of events would be cleared from the organism without causing any damage. Paradoxically, a successful clinical treatment of allergy involves repeated immunization of allergic persons with low doses of the allergen—immunotherapy. Investigation of the available experimental evidence leads to the conclusion that the phenomena of immunotherapy are best addressed in terms of the interplay among the mechanism(s) of immune memory—Th1/Th2 cross-regulation—and the physical compart-mentalization of the immune system. These conclusions are illustrated with a numerical simulation.
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    URL: http://dx.doi.org/10.1007/BF02458385
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  • 18
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    Weakly dissipative predator-prey systems (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 835-859 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the presence of seasonal forcing, predator-prey models with quadratic interaction terms and weak dissipation can exhibit infinite numbers of coexisting periodic attractors corresponding to cycles of different magnitude and frequency. These motions are best understood with reference to the conservative case, for which the degree of dissipation is, by definition, zero. Here one observes the familiar mix of “regular” (neutrally stable orbits and tori) and chaotic motion typical of non-integrable Hamiltonian systems. Perturbing away from the conservative limit, the chaos becomes transitory. In addition, the invariant tori are destroyed and the neutrally stable periodic orbits becomes stable limit cycles, the basins of attraction of which are intertwined in a complicated fashion. As a result, stochastic perturbations can bounce the system from one basin to another with consequent changes in system behavior. Biologically, weak dissipation corresponds to the case in which predators are able to regulate the density of their prey well below carrying capacity.
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    URL: http://dx.doi.org/10.1007/BF02459486
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  • 19
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    A pharmacodynamic model for the action of the antibiotic imipenem onPseudomonas aeruginosa populationsin vitro (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 923-938 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The standard method for measuringin vitro antibiotic efficacy is based on a point observation of bacterial activity 18 hours after inoculation. The method, while simple, forgoes significant information by ignoring the dynamics of the interations between antibiotic and bacteria. This paper proposes a simple dynamic model describing these interactions. The model consists of two non-linear differential equations of the S-system type. Its parameter values are estimated, through the minimization of residual errors, from data on the effect of the carbapenem antibiotic imipenem onPseudomonas aeruginosa. The model adequately describes the dynamic behavior of the bacterial populations in the presence of the antibiotic: beginning with drug administration, then through the decline of the bacterial population and possibly ending with bacterial resurgence.
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    URL: http://dx.doi.org/10.1007/BF02459490
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  • 20
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    Persistence of the weaker species in a non-homogeneous competitive system: Exact result through a quantum mechanical analogy (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1001-1018 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We have studied an ecological system of two species, which we denotestrong andweak, respectively, that compete for a single food resource. This system is modelled as a three component reaction-diffusion process. In the presence of a solitary pulse of increased resources, the weaker competitor can diffuse toward this surplus, gaining a competitive advantage and hence persisting in contraposition with the classical Lotka-Volterra result. An exact analytical solution has been found through a quantum mechanical analogy. A stability analysis of this solution against changes in different parameters has been carried out.
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    URL: http://dx.doi.org/10.1007/BF02459494
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  • 21
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    Numerical simulation of collapsible-tube flows with sinusoidal forced oscillations (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1023-1046 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Collapsible-tube flow with self-excited oscillations has been extensively investigated. Though physiologically relevant, forced oscillation coupled with self-excited oscillation has received little attention in this context. Based on an ODE model of collapsible-tube flow, the present study applies modern dynamics methods to investigate numerically the responses of forced oscillation to a limit-cycle oscillation which has topological characteristics discovered in previous unforced experiments. A devil's staircase and period-doubling cascades are presented with forcing frequency and amplitude as control parameters. In both cases, details are provided in a bifurcation diagram. Poincaré sections, a frequency spectrum and the largest Lyapunov exponents verify the existence of chaos in some circumstances. The thin fractal structure found in the strange attractors is believed to be a result of high damping and low stiffness in such systems.
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    URL: http://dx.doi.org/10.1007/BF02458382
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  • 22
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    Determination of pulmonary mean transit time and cardiac output using a one-dimensional model (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1155-1170 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this work, we show that a one-dimensional model of the blood flow across the lungs can reproduce the evolution of a bolus versus the time. Solving the differential equation governing the bolus concentration in the framework of this model, we determine the solution which fulfills Gaussian initial boundary conditions. An effective parameter related to the ratio of a diffusion coefficient to the square of the mean speed of the flow is defined. The determination of its numerical values following a semi-empirical approach enables us to know accurately the mean transit time and the cardiac output. The results have been compared to other methods, and were found in good agreement. Such an approach could be of interest in all studies where the knowledge of flow—including micro-circulation—is needed.
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    URL: http://dx.doi.org/10.1007/BF02458387
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  • 23
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    Competition during colonization vs competition after colonization in disturbed environments: A metapopulation approach (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 1187-1207 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract How two species interact during and after colonization influences which of them will be present in each stage of succession. In the tolerance model of ecological succession in a patchy environment, empty patches can be colonized by any species, but the ability to tolerate reduced resource levels determines which species will exclude the other. Here, we analyze a meta-population model of the possible roles of competition in colonization and succession, using non-linear Markov chains as a mathematical framework. Different kinds of competition affect the final equilibrial, abundances of the species involved in qualitatively different ways. An explicit criterion is given to determine which interactions have stronger effects on the final equilibrial levels of the weaker, species. Precise conditions are stated for the co-existence of both species. Both species are more likely to co-exist in the presence of an intermediate disturbance frequency.
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    URL: http://dx.doi.org/10.1007/BF02458389
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  • 24
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    Book review (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 195-196 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1006/bulm.1997.0018
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  • 25
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    A mathematical model for fibroblast and collagen orientation (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 101-129 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1006/bulm.1997.0027
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  • 26
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    Extinction times and phase transitions for spatially structured closed epidemics (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 215-230 
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    ISSN: 1522-9602
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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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    Book reviews (1998)
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    Bulletin of mathematical biology 60 (1998), S. 409-415 
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    URL: http://dx.doi.org/10.1006/bulm.1997.0019
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    The loss of immunity in directly transmitted infections modeling: Effects on the epidemiological parameters (1998)
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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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    Models for the length distributions of actin filaments: I. Simple polymerization and fragmentation (1998)
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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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    Parallel dose-response curves in combination experiments (1998)
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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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    Pattern formation in a generalized chemotactic model (1998)
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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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    A continuum mechanics approach to determining the cellular velocity field within a wool follicle (1998)
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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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    Modelling the metabolic versatility of a microbial trichome (1998)
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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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    Optimal harvesting for a predator-prey metapopulation (1998)
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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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    Wavelet-based analysis of human blood-flow dynamics (1998)
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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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    Diffusively coupled bursters: Effects of cell heterogeneity (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1167-1200 
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    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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    Modeling actin filament reorganization in endothelial cells subjected to cyclic stretch (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1017-1037 
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    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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    Emergence of donor control in patchy predator—prey systems (1998)
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    Bulletin of mathematical biology 60 (1998), S. 1149-1166 
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    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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    Frequency domain design of FIR and IIR Laplacian of Gaussian filters for edge detection (1996)
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    Circuits, systems and signal processing 15 (1996), S. 555-572 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This work addresses the design of LoG filters in the frequency domain within a structure formed by the cascade of quasi-Gaussian and discrete Laplacian filters. The main feature of such a structure is that it requires half the number of convolutions of the classical structure in which the LoG transfer function is expressed as the sum of two separable transfer functions of 1-D Gaussian and LoG type. Such a perspective allows one to rephrase the design of IIR and FIR filters for edge detection as a frequency domain approximation problem solvable by standard digital filter design tools. The zero-phase IIR solutions have a good performance at low orders and approximation errors practically independent of the aperture parameter. The characteristics of the nearly linear-phase IIR filters solving the problem suggest the consideration of linear-phase FIR filters with zeros constrained on the unit circle. The use of such filters leads to remarkable computational savings with respect to the filters designed by impulse response sampling. The agreement between the edge values obtained by the filters designed according to the scheme proposed in this work and those obtained by standard techniques is very good.
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    Mean oscillation of functions and the Paley-Wiener space (1998)
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    The journal of Fourier analysis and applications 4 (1998), S. 283-297 
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    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
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    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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    Wavelets on fractals and besov spaces (1998)
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    The journal of Fourier analysis and applications 4 (1998), S. 329-340 
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    ISSN: 1531-5851
    Keywords: 42C15 ; 46E35 ; Wavelets ; function spaces ; fractals
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    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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    Gibbs' phenomenon for sampling series and what to do about it (1998)
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    The journal of Fourier analysis and applications 4 (1998), S. 357-375 
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    ISSN: 1531-5851
    Keywords: 42C15 ; 94A12 ; wavelets ; interpolation ; orthogonal expansions
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    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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    Vector Potential Theory on Nonsmooth Domains in R3 and Applications to Electromagnetic Scattering (1996)
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    The journal of Fourier analysis and applications 3 (1996), S. 131-192 
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    Notes: Abstract We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for Lp-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.
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    The Banach Algebra A* and Its Properties (1996)
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    The journal of Fourier analysis and applications 3 (1996), S. 103-129 
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    Notes: Abstract Beurling's algebra $A^*=\{f:\sum_{k=0}^{\infty} \sup_{k\le |m|} |\hat f (m)| 〈 \infty \}$ is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with $[-\pi,\pi],$ and its dual space is indicated. Analogs of Herz's and Wiener-Ditkin's theorems hold. Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis are presented. The paper ends with a summary of some open problems.
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    Pseudodifferential Operators on SU(2) (1996)
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    The journal of Fourier analysis and applications 3 (1996), S. 193-205 
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    Notes: Abstract We construct an algebra of left-invariant pseudodifferential operators on SU(2). We require only that the symbols be homogeneous and C2. For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory. Some remarks on applications to matrices of operators are made.
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    On the connection between state-space representation and generalized Bezout identity of multivariable systems (1996)
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    Circuits, systems and signal processing 15 (1996), S. 505-514 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A novel and complete method is presented for constructing the generalized Bezout identity in polynomial form of the transfer matrix from its state-space representation of a reachable and observable system. As a result, one can easily apply well-developed synthesis and analysis theories to systems described in the frequency domain.
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    Robustness analysis of polynomials with linearly correlated uncertain coefficients in lp-normed balls (1996)
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    Circuits, systems and signal processing 15 (1996), S. 543-554 
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    Notes: Abstract The aim of this paper is to obtain the uncertain value set in the complex plane for systems with real and complex parameters that are known to lie inside a ball in a weightedl p-norm. It generalizes previously available results and may be used to test the robust stability of polynomials whose coefficients lie in a weighted lp-ball.
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    Weighted mean squared error criterion with fixed-level modification for linear-phase fIR filter design (1996)
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    Circuits, systems and signal processing 15 (1996), S. 581-595 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper describes a new approach—a Fixed-Level Least Squares (FLLS) method for linear-phase FIR filter design. It is intended for rejection of the Gibbs phenomenon through the introduction of a set of equally spaced fixed levels in the transition band and subsequent redefinition of the approximated and weighted functions. Detailed mathematical solutions of the problem as well as many examples are given. The results in graphical form are shown as an output of the FLLS software model.
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    Finite modeling of parabolic equations using Galerkin methods and inverse matrix approximations (1996)
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    Circuits, systems and signal processing 15 (1996), S. 631-648 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we examine order reduction of parabolic systems using modal truncation. The parabolic distributed system is first approximated using the Galerkin method. The system matrices have a special structure that allows us to find the approximate spectrum of the parabolic system. To do this we compute approximate inverses of tridiagonal, diagonally dominant symmetric matrices. The approximation leads to algorithms of orderO(n), as opposed to traditional algorithms of orderO(n), wheren is the order of the system. Finally, an example is presented to illustrate the proposed algorithm.
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    Network approximation of input-output maps and functionals (1996)
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    Circuits, systems and signal processing 15 (1996), S. 711-725 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We give results concerning the problem of approximating the input-output maps of nonlinear discrete-time approximately finite-memory systems. Here the focus is on the linear dynamical parts of the approximating structures, and we give examples showing that these linear parts can be derived from asingle prespecified function that meets certain conditions. This is done in the context of an approximation theorem in which attention is focused on what we call “basic sets.” We also consider the related but very different problem of approximating nonlinear functionals using lattice operations or the usual linear ring operations. For this problem we give criteria, not just sufficient conditions, for approximation on compact subsets of reflexive Banach spaces (any Hilbert space is a reflexive Banach space).
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    Sensor location calibration for bearing estimation (1996)
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    Circuits, systems and signal processing 15 (1996), S. 763-770 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract New calibration methods are presented for bearing estimation with sensor location uncertainties, which are based on eigenvalue decomposition of the sample covariance matrix and three or more nondisjoint sources in known bearings. The methods can be applied to arbitrary arrays, including linear arrays, require fewer computations, and are suitable for low signal-to-noise ratio (SNR) cases. Computer simulations are given to illustrate the performance of the proposed methods.
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    A fast algorithm for FIR digital filtering with a sum-of-triangles weighting function (1996)
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    Circuits, systems and signal processing 15 (1996), S. 145-164 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A doubly recursive algorithm for time domain convolution with a piecewise linear weighting function is presented that combines the speed of a recursive (IIR) digital filter with the flexibility and ease of design of a nonrecursive (FIR) digital filter. The approach approximates the desired FIR weighting function by a sum-of-triangles weighting function. ForL triangles (or triangle pairs for a linear phase filter) the algorithm is of orderLN. The approximation improves with the number of triangles. A significant advantage of the algorithm compared to FFT filtering or direct convolution is that there is no necessity of a tradeoff between frequency response accuracy and computation time per output point as the data spacing decreases in the filtered signal. The computational complexity is dependent on the number of triangles chosen, not the width of the weighting function, so the algorithm is especially effective for filters with an inherently wide FIR weighting function.
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    Correlation analysis of stochastic amplitude-angle modulated signals (1996)
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    Circuits, systems and signal processing 15 (1996), S. 335-342 
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    Notes: Abstract A solution of the problem of correlation analysis of stochastic amplitude-angle modulated signals is presented. The solution is obtained on the basis of the theory of linear stochastic processes for the general case of nonstationary correlated Gaussian noises in both modulation channels. These noises are regarded as the results of a linear filtration of Gaussian white noise processes. As an example of the analysis a case of band-pass modulation noises is considered.
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    Analysis of 2-D state-space periodically shift-variant discrete systems (1996)
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    Circuits, systems and signal processing 15 (1996), S. 395-413 
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    Notes: Abstract Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.
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    A note on error bounds for approximation in inner product spaces (1996)
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    Circuits, systems and signal processing 15 (1996), S. 515-518 
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    Notes: Abstract In a recent paper a method is described for constructing certain approximations to a general element in the closure of the convex hull of a subset of an inner product space. This is of interest in connection with neural networks. Here we give an algorithm that generates simpler approximants with somewhat less computational cost.
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    Stability for composite singular systems of differential equations with a delay (1996)
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    Circuits, systems and signal processing 15 (1996), S. 573-580 
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    Notes: Abstract In this paper, we gave an exponential estimate for the solutions of singular systems of differential equations with a delay and establish a comparison inequality for the systems. Based on this we estabish the criteria for asymptotic stability for the composite singular systems.
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    New VLSI architectures for three-level correlators (1996)
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    Circuits, systems and signal processing 15 (1996), S. 685-693 
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    Notes: Abstract This paper presents the VLSI architectures for three-level correlator design based on 1-μm CMOS technology. The architecture performs very high speed, real-time, three-level cross-correlation of signals. Two architectures, one for serial incoming samples of signals (serial data) and the other for stored signal samples (parallel data), are described in the paper.
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    Infinite nonlinear resistive networks, after Minty (1996)
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    Circuits, systems and signal processing 15 (1996), S. 727-733 
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    Notes: Abstract This paper gives the existence of and bounds for the branch voltages and currents in a given infinite network, which on each branch are related by a maximal monotone resistance function. We give a simpler proof than that of Minty, with smaller bounds, in the finite network case.
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    Computation of the frequency response of interval systems (1996)
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    Circuits, systems and signal processing 15 (1996), S. 807-818 
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    Notes: Abstract An efficient procedure is presented for computing the frequency-response templates of uncertain rational transfer functions depending on two independent interval polynomials. It consists of a modified Cohen-Sutherland algorithm for the intersection test of two rectangles and a pivoting algorithm. Because the proposed procedure traces out the boundary of a frequency-response template directly, it is, in general, more efficient than the previously proposed algorithms.
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    A space-time-filtered Viterbi receiver for CCI/ISI reduction in TDMA systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 85-102 
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    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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    Sydney Richard Parker 1923–1996 (1998)
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    Circuits, systems and signal processing 17 (1998), S. i 
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    Parametric signal processing of anechoic data from prosthetic heart valve testing (1998)
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    Circuits, systems and signal processing 17 (1998), S. 123-136 
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    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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    On neural network design — Part I: Using the MVQ algorithm (1998)
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    Circuits, systems and signal processing 17 (1998), S. 195-218 
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    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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    A holographic transform domain image watermarking method (1998)
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    Circuits, systems and signal processing 17 (1998), S. 361-389 
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    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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    A sectoring algorithm for exact computation of the frequency response of linear interval systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 483-493 
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    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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    The fundamental subspace sequences of matrix pencils: A toeplitz matrix unified characterization (1998)
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    Circuits, systems and signal processing 17 (1998), S. 559-574 
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    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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    Active noise compression systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 667-682 
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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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    A note on representation theorems for linear discrete-space systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 703-708 
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    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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    Robust stabilization of singular systems withH ∞-bounded uncertainty (1998)
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    Circuits, systems and signal processing 17 (1998), S. 737-755 
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    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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    Concurrent computation of two-dimensional discrete cosine transform (1996)
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    Circuits, systems and signal processing 15 (1996), S. 597-607 
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    Notes: Abstract In this paper, a novel VLSI algorithm for the computation of a two-dimensional discrete cosine transform is proposed. The 2D-DCT equation can be expressed by the sum of high order cosine functions, and the algorithm can be realized by combining a highly efficient first order recursive structure with some simplified matrix multiplications, which results in highly regular hardware architecture and simple routing. The algorithm has temporal and spatial locality of connection and can be segmentized for pipeline operations, so the computation time is greatly reduced. Owing to the simplicity in hardware structure, it is especially good for VLSI implementation.
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    Time-varying matched filters (1996)
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    Circuits, systems and signal processing 15 (1996), S. 609-630 
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    Notes: Abstract We examine a generalized matched-filter problem in which the interference is a nonstationary process generated by passing white noise through a general linear time-varying filter. First a matched filter is constructed by transforming the problem into an equivalent formulation involving stationary interference and a time-varying propagation channel. Whereas the response of a time-invariant matched filter is sampled at its peak, the response of this time-varying matched filter is normalized before sampling to account for variations in the signal power. Next a matched filter is constructed using a spectral characterization of the nonstationary interference. This construction is then used to formulate a simplified solution for the case where the rate of variation in the nonstationary interference is sufficiently small. The different solutions are illustrated by a numerical example.
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    Universal approximation capability of EBF neural networks with arbitrary activation functions (1996)
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    Circuits, systems and signal processing 15 (1996), S. 671-683 
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    Notes: Abstract The purpose of this paper is to investigate the approximation capability of elliptic basis function (EBF) neural networks. The main results are: (1) A necessary and sufficient condition for a functionS′ (R 1) to be qualified as an activation function in the hidden layer of an EBF neural network is given. (2) Every nonzero functionG ε L 2(R n ) is qualified to be an activation function in the elliptic neural network to approximate any function in L2(Rn). (3) As applications, we give new proofs of the theorems concerning the approximation capability of affine basis function (ABF) neural networks and generalized radial basis function (GRBF) neural networks (including radial basis function neural networks) with arbitrary activation functions. In particular, we solve the problem of the approximation capability of sigma-pi neural networks.
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    Frequency response of PID-controlled linear interval systems (1996)
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    Circuits, systems and signal processing 15 (1996), S. 735-748 
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    Notes: Abstract The frequency response of linear interval systems under PID controllers is analyzed. A two-stage elimination algorithm is presented to describe the boundary of the response in the complex plane. Illustrative examples are included.
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    A formal language description and inference strategy for analog circuit design (1996)
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    Circuits, systems and signal processing 15 (1996), S. 771-805 
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    Notes: Abstract This article deals with a new intelligent analog circuit design system. Unlike previous design methods, this approach introduces a formal circuit representation for both the numerical and heuristic knowledge of the design system. The predicate logic circuit representation is proposed as a new formal analog circuit description language. The language's syntax and semantics provide a precise symbolic description of analog circuit functionality at higher levels of hierarchy and network component connectivities, together with CMOS transistor sizes as the lowest level of hierarchy. It is shown how sentence conversion rules of language grammer can be used to derive transistor level circuits from input performance specifications. Language sentences have the form of clauses. In addition to clause representation, a frame representation to reflect VLSI design hierarchy is also introduced. An original bidirectional inference mechanism with elements of hypothesis has been introduced to infer designs from the knowledge in clause and frame representations. The unique feature of this circuit knowledge representation is its ability to automate the analog CMOS circuit design process. The design methodology is described in detail. The proposed iterative closed loop design system adopts an expert system approach to provide topological synthesis, uses a SPICE circuit simulator to evaluate the circuit performance, and uses a new diagnostic expert system to provide advice on how to improve the design. The implementation of the methodology and associated experimental results for simple CMOS operational amplifier designs are also presented.
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    Design of sharp linear-phase FIR bandstop filters using the frequency-response-masking technique (1998)
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    Circuits, systems and signal processing 17 (1998), S. 1-27 
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    Notes: Abstract A novel computationally efficient realization of sharp linear-phase finite impulse response (FIR) bandstop filters is proposed. The synthesis scheme for the bandstop filters is derived from variations of the frequency-response-masking technique. Five realization structures are presented in this paper for the synthesis of five different classes of bandstop filters. Approximate expressions for the optimal value of the impulse response up-sampling ratio (M) and the corresponding number of multipliers are derived.
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    Capon estimation of covariance sequences (1998)
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    Circuits, systems and signal processing 17 (1998), S. 29-49 
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    Notes: Abstract Estimating the covariance sequence of a wide-sense stationary process is of fundamental importance in digital signal processing (DSP). A new method, which makes use of Fourier inversion of the Capon spectral estimates and is referred to as theCapon method, is presented in this paper. It is shown that the Capon power spectral density (PSD) estimator yields an equivalent autoregressive (AR) or autoregressive moving-average (ARMA) process; hence, theexact covariance sequence corresponsing to the Capon spectrum can be computed in a rather convenient way. Also, without much accuracy loss, the computation can be significantly reduced via an approximate Capon method that utilizes the fast Fourier transform (FFT). Using a variety of ARMA signals, we show that Capon covariance estimates are generally better than standard sample covariance estimates and can be used to improve performances in DSP applications that are critically dependent on the accuracy of the covariance sequence estimates.
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    Signal processing based on parameter structural modeling and separation of highly correlated signals of known structure (1998)
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    Circuits, systems and signal processing 17 (1998), S. 51-68 
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    Notes: Abstract Results in the study of signal processing based on the use of parameter structural modeling (PSM) are presented. First, we introduce a special form of time-series modeling based on signal-dependent building blocks. Such modeling is used in the design of a nestedform transversal structure, known as a composite filter, based on a shift-invariant finite impulse resonse (FIR) as well as infinite impulse response (IIR) building blocks. The newly proposed composite PSM model (CPSM) possesses a unique feature, namely, its ability to suppress one signal of a given structure, while at the same time being ideally transparent to another one. The intrinsic property of this proposed CPSM is its enhanced insensitivity with respect to noise as well as its ability to fast track, in contrast to the commonly used linear line-enhancer based on conventional autoregressive moving average (ARMA), thus leading to a more practically sound processing of short-duration signals. It is shown that the proposed time-series modeling based on CPSM can be effectively applied towards the separation of superimposed signals of heavily overlapping spectra. Next, the parameter-invariant nonlinear structural signal representation based on shift-invariant CPSM is presented. The use of this model in the design of annihilation operators (AO) is described, and composite parameter-free structural modeling (CPFSM) is developed. Based on this model, two canonical forms of the parameter-invariant null filters (PINF) are presented, and their use in the suppression of a given class of signals, independently of the values of theira priori unknown parameters, is illustrated. The paper also presents some simulation examples illustrating the application of the proposed CPSM and CPFSM in solving problems of detection and parameter estimation in the presence of highly non-Gaussian, mainly signal-like interferences.
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    Nonlinear digital filters mimicking cellular neural networks (1998)
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    Circuits, systems and signal processing 17 (1998), S. 69-83 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This work is motivated by the need forFaithful digital simulation of cellular neural networks (CNNs) that maintains most of their qualitative properties of stability and convergence. An interconnection of nonlinear digital filters mimicking behaviors of the analog CNNs is proposed, and the main properties are studied in detail. The discrete model obtained is proven to have the same convergence properties as the original analog network. The key to this development is the use of anAppropriate discretization scheme. Our discrete approximation to the nonlinear state-space representation of cellular neural networks is such that the Lyapunov function used to show convergence in analog cellular neural networks is still a Lyapunov function (when appropriately discretized) for our nonlinear digital filter network. This is in contrast to other digital simulations of CNNs, which have not been proven to preserve the convergence properties. The network of nonlinear digital filters so introduced thus adds another item to the catalog of digital filters obtained viaappropriate discretization of analog circuits, e.g., wave digital filters, orthogonal filters, and certain other of their more recently studied nonlinear counterparts.
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    Direct multiple-channel blind equalization (1998)
    Springer
    Circuits, systems and signal processing 17 (1998), S. 117-122 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, the problem of blind channel identification and equalization is reviewed, and some recent results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213973
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    Halfband filters and Hilbert transformers (1998)
    Springer
    Circuits, systems and signal processing 17 (1998), S. 137-164 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents in summarizing form a description of halfband filters and the related symmetrical Hilbert transformers. It starts with the two complemetary relations by which halfband filters are defined and the consequences for their impulse responses. The idealized versions of the frequency responses of halfband lowpasses and Hilbert transformers are introduced, and the related tolerance schemes that realized systems must satisfy are described. Using their frequency responses, the transformation of one filter type into the other is presented in general form. The design of finite impulse response (FIR)-halfband filters and their relation to corresponding Hilbert transformers are recalled, using maximally flat and Chebyshev approximations as examples. It is shown that the relation between both types of systems can be used for the infinite impulse response (IIR) case as well. The design of IIR-halfband filters is presented for systems with approximately linear phase and for those with minimum phase again for maximally flat and Chebyshev approximations. The design methods are partly new. The general procedure for the transformation into Hilbert transformers yields noncausal solutions, one of which is already known from the literature. By modifying this operation, phase-splitting systems are obtained, one of them related to corresponding continuous ones, discussed in papers published around 1950. Another system with approximately linear phase corresponds to a paper presented in 1987. Finally, the coupled form of these phase splitting allpasses is found to be a Hilbert transformer with precise phase difference, but with deviations of the magnitudes of the frequency responses.
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    URL: http://dx.doi.org/10.1007/BF01202851
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    Computationally efficient, robust algorithm for matched field processing (1998)
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    Circuits, systems and signal processing 17 (1998), S. 165-193 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The matched field processing (MFP) localization performance of very low frequency (VLF) arrays operated in the deep ocean basins appears to be limited more by uncertainty in the sound velocity profile (SVP) than by low signal-to-noise ratio (SNR). We present a new robust variation of MFP designed to be less sensitive to velocity error in weakly inhomogeneous environments. We analyze the computational requirements of this and other MFP algorithms. When either the search volume is large of the acoustic array is large, computational efficiency is an issue. We present an efficient MFP implementation for the conventional MFP algorithm and our robust algorithm. We show that parallel implementation of these algorithms may allow real-time performance.
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    URL: http://dx.doi.org/10.1007/BF01202852
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    Global asymptotic stability of a class of feedback neural networks with an application to optimization problems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 219-241 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract By applying results from homotopy theory, new conditions are obtained for the existence and uniqueness of an equilibrium for a class of continuous-time feedback neural networks which contains the Hopfield model as a special case. Next, new criteria are established for the global asymptotic stability of the unique equilibrium of this class of neural networks by utilizing Lur'e-type Lyapunov functions and the stability theory for systems of differential inequalities. Several practical stability testing conditions are given. As a special case, criteria are derived for the global asymptotic stability of Hopfield neural networks. This is followed by a robustness analysis of the class of neural networks considered. The results obtained are then applied to an optimization problem.
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    URL: http://dx.doi.org/10.1007/BF01202854
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    Optimal interpolating and smoothing functional artificial neural networks (FANNs) based on a generalized fock space framework (1998)
    Springer
    Circuits, systems and signal processing 17 (1998), S. 271-287 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Functional artificial neural networks (FANNs) are artificial neural networks (ANNs) in which the synaptic weights are “functions” rather than numbers. Thus the signals in such networks are analog, and the action of a synapse on a signal passing through it takes place in the form of a scalar product inL 2 between the functional weight and the signal. In this paper, four classes of FANNs are introduced. They result from the solution of a nonparametric optimization problem in a generalized Fock space (GFS) of abstract Volterra series under interpolating or smoothing input-output training data constraints. Two of these classes of FANNs correspond to the interpolating case and are represented by what we call the (two-layer)optimal interpolating (OI) FANN and theoptimal multilayer neural interpolating (OMNI) FANN. The remaining two classes correspond to the smoothing case. We name their representations as the (two-layer)optimal smoothing (OS) FANN and theoptimal smoothing multilayer artificial neural (OSMAN) FANN. In addition to providing the background and the derivation of these FANNs, this paper presents a novel approach to their implementation. This approach does away with the computationally cumbersome use of functional weights. Instead, the effect of these weights is provided by linear time-invariant differential equation models of which those weights are impulse responses. These are implemented by a linear filter bank. This approach thus leads to simple and meaningful causal realizations of FANNs which we call Dynamical FANNs or simply D-FANNs.
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    URL: http://dx.doi.org/10.1007/BF01202856
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    Are analog neural networks better than binary neural networks? (1998)
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    Circuits, systems and signal processing 17 (1998), S. 243-270 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we study the problem of maximizing an objective function over the discrete set {−1, 1} n using a neural network. It is now known that a binary (two-state) Hopfield network can take, in the worst case, an exponential number of time steps to find even a local maximum of the objective function. In this paper, we carry this argument further by studying theradius of attraction of the global maxima of the objective function. If a binary neural network is used, in general there is no guarantee that a global maximum has a nonzero radius of attraction. In other words, even if the optimization process is started off with the neural network in an initial state that isadjacent to the global maximum, the resulting trajectory of the network may not converge to the nearby maximum, but may instead go off to another maximum. At the same time, another set of recent results shows that, if ananalog neural network is used to optimize the same objective function, thenevery local maximum of the objective function has a nontrivial domain of attraction, and conversely, the only equilibria that are attractive are the local maxima of the objective function. This raises the question as to whether analog neural networks offer some advantages over binary neural networks for optimizing the same objective function. As a motivation for this line of inquiry, we study the problem of decoding an algebraic block code using a neural network. It is shown that the binary neural network implementation has the undesirable property thatall the global maxima of the objective function have azero radius of attraction. In contrast, if an analog neural network is used to maximize exactly the same objective function, the region of attraction of each maximum contains not only the associated “orthant” of the state space, but also some points not in this orthant. In other words, the analog implementation exhibits the desired tolerance to transmission errors, whereas the binary neural network does not have this property. With this motivation, two open questions are posed that provide a program of research for studying the possible superiority of analog neural networks over binary neural networks.
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    URL: http://dx.doi.org/10.1007/BF01202855
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    Average power analysis of sequential circuits using an autoregressive model (1998)
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    Circuits, systems and signal processing 17 (1998), S. 289-304 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We present a new statistical technique for average power estimation in sequential circuits. Because of the feedback loops, power dissipations of sequential circuits in consecutive clock cycles are temporally correlated. The existence of data correlation makes it unsuitable to apply conventional techniques to average power inference, because the sample variance is no longer a maximum likelihood estimator. The convergence criterion derived from the biased variance estimation will be overly optimistic, causing power simulation to stop prematurely at a lower-than-specified estimation accuracy. To overcome this problem, we propose a systematic approach for modeling the power dissipation behavior of sequential circuits as an autoregressive random process. An accurate process variance can be obtained by the model parameters, which enables the derivation of a robust confidence interval of the average power. The interval is checked for convergence against a user-specified accuracy criterion. An iterative procedure is developed to invoke these steps repeatedly until the convergence specification is met. For a set of benchmark sequential circuits, this technique yields high accuracy and efficiency.
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    URL: http://dx.doi.org/10.1007/BF01202857
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    An algebraic technique for designing active filters in the frequency domain for control and signal processing (1998)
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    Circuits, systems and signal processing 17 (1998), S. 391-400 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a straightforward algebraic method for designing feedback loops in the frequency domain. The emphasis here is on control system design, but the technique is applicable to active filter design as well. The object is to produce a practical analog filter with a minimum of design effort. The algebraic solution to the design problem is presented, and several examples are explored.
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    URL: http://dx.doi.org/10.1007/BF01202299
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    Parameter estimation using RELAX with a COLD array (1998)
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    Circuits, systems and signal processing 17 (1998), S. 471-481 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This correspondence presents a RELAX (RELAXation-based) algorithm for angle, polarization, and waveform estimation of completely polarized narrowband electromagnetic plane waves arriving at a uniform linear co-centered orthogonal loop and dipole (COLD) array. We use numerical examples to demonstrate the performance of the RELAX algorithm for parameter estimation with the COLD array and compare it with the performance of the MODE (Method of Direction Estimation) algorithm. We show that this RELAX algorithm can outperform MODE and yet be computationally faster than MODE.
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    URL: http://dx.doi.org/10.1007/BF01201503
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    Coordinate logic filters and their applications in image processing and pattern recognition (1998)
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    Circuits, systems and signal processing 17 (1998), S. 517-538 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we present a number of image processing applications using coordinate logic filters, which execute coordinate logic operations among the pixels of the image. These filters are very efficient in various 1D, 2D, or higher-dimensional digital signal processing applications, such as noise removal, magnification, opening, closing, skeletonization, and coding, as well as in edge detection, feature extraction, and fractal modeling. In this paper we present some typical image processing applications using coordinate logic filters. The key issue in the coordinate logic analysis of images is the method of fast successive filtering and managing of the residues. The desired processing is achieved by executing only direct logic operations among the pixels of the given image. Coordinate logic filters can be easily and quickly implemented using logic circuits or cellular automata; this is their primary advantage.
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    URL: http://dx.doi.org/10.1007/BF01201506
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    Discretization of cascaded continuous-time controllers and uncertain systems (1998)
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    Circuits, systems and signal processing 17 (1998), S. 591-611 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a new method for the digital modeling of a continuous-time uncertain system and a new method for the digital redesign of a sampled-data uncertain system. The system matrices characterizing the state-space representation of the original uncertain system are assumed to be interval matrices. The Chebyshev quadrature formula together with the interval arithmetic are used for the digital interval modeling, and a dual concept of digital interval modeling is utilized to discretize a predesigned cascaded analog controller for robust digital control of a continuous-time uncertain system. Using the newly developed digital interval models and digitally redesigned controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systemsare able to closely match those of the originally analogously controlled continuous-time uncertain systems for a relatively longer sampling period.
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    URL: http://dx.doi.org/10.1007/BF01203107
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    Eyes Closed: Simple, Intuitive, Statistically Sound, and Efficient Methods for Estimating Parameters of Clonal Growth Cancer Models (1998)
    Springer
    Risk analysis 18 (1998), S. 529-534 
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    ISSN: 1539-6924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:RIAN.0000006255.30436.ff
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    A Risk Assessment for Consumers of Mourning Doves (1998)
    Springer
    Risk analysis 18 (1998), S. 563-573 
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    ISSN: 1539-6924
    Keywords: Risk assessment ; mourning doves ; hunting ; radionuclides ; heavy metals ; lead shot ; cesium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Recreational and subsistence hunters and anglers consume a wide range of species, including birds, mammals, fish and shellfish, some of which represent significant exposure pathways for environmental toxic agents. This study focuses on the Department of Energy's (DOE's) Savannah River Site (SRS), a former nuclear weapons production facility in South Carolina. The potential risk of contaminant intake from consuming mourning doves (Zenaida macroura), the most popular United States game bird, was examined under various risk scenarios. For all of these scenarios we used the mean tissue concentration of six metals (lead, mercury, cadmium, selenium, chromium, manganese) and radiocesium, in doves collected on and near SRS. We also estimated risk to a child consuming doves that had the maximum contaminant level. We used the cancer slope factor for radiocesium, the Environmental Protection Agencies Uptake/Biokinetic model for lead, and published reference doses for the other metals. As a result of our risk assessments we recommend management of water levels in contaminated reservoirs so that lake bed sediments are not exposed to use by gamebirds and other terrestrial wildlife. Particularly, measures should be taken to insure that the hunting public does not have access to such a site. Our data also indicate that doves on popular hunting areas are exposed to excess lead, suggesting that banning lead shot for doves, as has been done for waterfowl, is desirable.
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    URL: http://dx.doi.org/10.1023/B:RIAN.0000005931.39844.35
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    An Empirical Approach for Deriving Information on Total Duration of Exposure from Information on Historical Exposure (1998)
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    Risk analysis 18 (1998), S. 611-619 
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    ISSN: 1539-6924
    Keywords: Exposure duration ; survey data ; longevity bias ; angler populations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Exposure duration is an important component in determining long-term dose rates associated with exposure to environmental contaminants. Surveys of exposed populations collect information on individuals' past behaviors, including the durations of a behavior up to the time of the survey. This paper presents an empirical approach for determining the distribution of total durations that is consistent with the distribution past durations obtained from surveys. This approach is appropriate where the rates of beginning and ending a behavior are relatively constant over time. The approach allows the incorporation of information on the distribution of age in a population into the determination of the distribution of durations. The paper also explores the impact of “longevity” bias on survey data. A case study of the application of this approach to two angler populations is also provided. The results of the case study have characteristics similar to the results reported by Israeli and Nelson (Risk Anal. 12, 65–72 (1992)) from their analytical model of residential duration. Specifically, the average period of time for the total duration in the entire population is shorter than the average period of time reported for historical duration in the surveyed individuals.
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    URL: http://dx.doi.org/10.1023/B:RIAN.0000005935.81670.61
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    A Quantitative Test of the Cultural Theory of Risk Perceptions: Comparison with the Psychometric Paradigm (1998)
    Springer
    Risk analysis 18 (1998), S. 635-647 
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    ISSN: 1539-6924
    Keywords: Risk perceptions ; cultural theory ; psychometric paradigm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper seeks to compare two frameworks which have been proposed to explain risk perceptions, namely, cultural theory and the psychometric paradigm. A structured questionnaire which incorporated elements from both approaches was administered to 129 residents of Norwich, England. The qualitative risk characteristics generated by the psychometric paradigm explained a far greater proportion of the variance in risk perceptions than cultural biases, though it should be borne in mind that the qualitative characteristics refer directly to risks whereas cultural biases are much more distant variables. Correlations between cultural biases and risk perceptions were very low, but the key point was that each cultural bias was associated with concern about distinct types of risks and that the pattern of responses was compatible with that predicted by cultural theory. The cultural approach also provided indicators for underlying beliefs regarding trust and the environment; beliefs which were consistent within each world view but divergent between them. An important drawback, however, was that the psychometric questionnaire could only allocate 32% of the respondents unequivocally to one of the four cultural types. The rest of the sample expressed several cultural biases simultaneously, or none at all. Cultural biases are therefore probably best interpreted as four extreme world views, and a mixture of qualitative and quantitative research methodologies would generate better insights into who might defend these views in what circumstances, whether there are only four mutually exclusive world views or not, and how these views are related to patterns of social solidarity, and judgments on institutional trust.
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    URL: http://dx.doi.org/10.1023/B:RIAN.0000005937.60969.32
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    Kinetics of an autocatalytic zymogen reaction in the presence of an inhibitor coupled to a monitoring reaction (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 19-41 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A global kinetic analysis of a model consisting of an autocatalytic zymogen-activation process, in which an irreversible inhibitor competes with the zymogen for the active site of the proteinase, and a monitoring coupled reaction, in which the enzyme acts upon one of its substrates, is presented. This analysis is based on the progress curves of any of the two products released in the monitoring reaction. The general solution is applied to an important particular case in which rapid equilibrium conditions prevail. Finally, we suggest a procedure to predict whether the inhibition or activation route dominates in the steady state of the system. These results generalize our previous analysis of simpler mechanisms.
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    URL: http://dx.doi.org/10.1007/BF02458280
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    An evolution of pulse speed in arteries (1996)
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    Bulletin of mathematical biology 58 (1996), S. 129-140 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this work, treating the artery as a thick-walled cylindrical shell made of an incompressible, isotropic and elastic solid, utilizing the large deformation theory and the stress-strain relation proposed by Demiray (1976b,Trans. ASME Ser. E, J. Appl. Mech.,98, 194–197), an explicit expression for the pulse speed is obtained and the effect of lumen pressure and the axial stretch on wave speed is discussed. Numerical results indicate that the wave speed increases with lumen pressure but decreases with the axial stretch. The results of the present model are compared with our previous work (Demiray, 1988,J. Biomech. 21, 55–58) on the same subject.
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    URL: http://dx.doi.org/10.1007/BF02458285
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    Variational principles in evolution (1996)
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    Bulletin of mathematical biology 58 (1996), S. 175-202 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.
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    URL: http://dx.doi.org/10.1007/BF02458287
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    A new bell-shaped function for idiotypic interactions based on cross-linking (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 285-312 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the “field”, which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network. The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field. When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higher-affinity interactions. We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.
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    URL: http://dx.doi.org/10.1007/BF02458310
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    A community model of ciliateTetrahymena and bacteriaE. coli: Part I. Individual-based models ofTetrahymena andE. coli populations (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 247-264 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dynamics of a microbial community consisting of a eucaryotic ciliateTetrahymena pyriformis and procaryoticEscherichia coli in a batch culture is explored by employing an individual-based approach. In this portion of the article, Part I, population models are presented. Because both models are individual-based, models of individual organisms are developed prior to construction of the population models. The individual models use an energy budget method in which growth depends on energy gain from feeding and energy sinks such as maintenance and reproduction. These models are not limited by simplifying assumptions about constant yield, constant energy sinks and Monod growth kinetics as are traditional models of microbal organisms. Population models are generated from individual models by creating distinct individual types and assigning to each type the number of real individuals they represent. A population is a compilation of individual types that vary in a phase of cell cycle and physiological parameters such as filtering rate for ciliates and maximum anabolic rate for bacteria. An advantage of the developed models is that they realistically describe the growth of the individual cells feeding on resource which varies in density and composition. Part II, the core of the project, integrates models into a dynamic microbial community and provides model analysis based upon available data.
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    URL: http://dx.doi.org/10.1007/BF02458308
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    A model for treatment strategy in the chemotherapy of AIDS (1996)
    Springer
    Bulletin of mathematical biology 58 (1996), S. 367-390 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mathematical models are developed for the chemotherapy of AIDS. The models are systems of differential equations describing the interaction of the HIV infected immune system with AZT chemotherapy. The models produce the three types of qualitative clinical behavior: anuninfected steady state, aninfected steady state (latency) and aprogression to AIDS state. The effect of treatment is to perturb the system from progression to AIDS back to latency. Simulation of treatment schedules is provided for the consideration of treatment regimes. The following issues of chemotherapy are addressed: (i) daily frequency of treatment, (ii) early versus late initiation of treatment and (iii) intermittent treatment with intervals of no treatment. The simulations suggest the following properties of AZT chemotherapy: (i) the daily period of treatment does not affect the outcome of the treatment, (ii) treatment should not begin until after the final decline of T cells begins (not until the T cell population falls below approximately 300 mm−3) and then, it should be administered immediately and (iii) a possible strategy for treatment which may cope with side effects and/or resistance, is to treat intermittently with chemotherapy followed by interruptions in the treatment during which either a different drug or no treatment is administered. These properties are revealed in the simulations, as the model equations incorporate AZT chemotherapy as a weakly effective treatment process. We incorporate into the model the fact that AZT treatment does not eliminate HIV, but only restrains its progress. The mathematical model, although greatly simplified as a description of an extremely complex process, offers a means to pose hypotheses concerning treatment protocols, simulate alternative strategies and guide the qualitative understanding of AIDS chemotherapy.
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    URL: http://dx.doi.org/10.1007/BF02458312
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