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  • Springer  (140,705)
  • 1995-1999  (140,705)
  • 1925-1929
  • 1999  (66,910)
  • 1996  (73,795)
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  • 1995-1999  (140,705)
  • 1925-1929
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  • 1
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    Bulletin of mathematical biology 58 (1996), S. 43-63 
    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.
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  • 2
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    Bulletin of mathematical biology 58 (1996), S. 103-127 
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    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.
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  • 3
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    Bulletin of mathematical biology 58 (1996), S. 203-206 
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  • 4
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    Bulletin of mathematical biology 58 (1996), S. 265-283 
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    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.
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    Bulletin of mathematical biology 58 (1996), S. 313-365 
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    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.
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    Bulletin of mathematical biology 58 (1996), S. 425-447 
    ISSN: 1522-9602
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    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.
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  • 7
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    Bulletin of mathematical biology 58 (1996), S. 409-424 
    ISSN: 1522-9602
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    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.
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    Bulletin of mathematical biology 58 (1996), S. 555-568 
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    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.
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  • 9
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    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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    Bulletin of mathematical biology 58 (1996), S. 661-717 
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    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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  • 11
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    Bulletin of mathematical biology 58 (1996), S. 809-810 
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    Bulletin of mathematical biology 58 (1996), S. 787-808 
    ISSN: 1522-9602
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    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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    Bulletin of mathematical biology 58 (1996), S. 907-922 
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    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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  • 14
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    Bulletin of mathematical biology 58 (1996), S. 1019-1022 
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  • 15
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    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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    Bulletin of mathematical biology 58 (1996), S. 1075-1097 
    ISSN: 1522-9602
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    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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    Bulletin of mathematical biology 58 (1996), S. 1099-1121 
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    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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    Bulletin of mathematical biology 58 (1996), S. 835-859 
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    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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    Bulletin of mathematical biology 58 (1996), S. 923-938 
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    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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    Bulletin of mathematical biology 58 (1996), S. 1001-1018 
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    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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    Bulletin of mathematical biology 58 (1996), S. 1023-1046 
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    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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    Bulletin of mathematical biology 58 (1996), S. 1155-1170 
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    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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    Bulletin of mathematical biology 58 (1996), S. 1187-1207 
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    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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    Bulletin of mathematical biology 61 (1999), S. 1-17 
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    Notes: Abstract An equivalent electrical circuit is given for a branch of an amphibian motor-nerve terminal in a volume conductor. The circuit allows for longitudinal current flow inside the axon as well as between the axon and its Schwann cell sheath, and also for the radial leakage of current through the Schwann cell sheath. Analytical and numerical solutions are found for the spatial and time dependence of the membrane potential resulting from the injection of depolarizing current pulses by external electrodes at one or two separate locations on the terminal. These solutions show that the depolarization at an injection site can cause a hyperpolarization at sites a short distance away. This effect becomes more pronounced in a short terminal with sealed-end boundary conditions. The hyperpolarization provides a possible explanation for recent experimental results, which show that the average quantal release due to a test depolarizing current pulse delivered by an electrode at one site on a nerve terminal is reduced by the application of an identical conditioning pulse at a neighbouring site.
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    Bulletin of mathematical biology 61 (1999), S. 113-140 
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    Notes: Abstract Synthetic barriers such as gloves, condoms and masks are widely used in efforts to prevent disease transmission. Due to manufacturing defects, tears arising during use, or material porosity, there is inevitably a risk associated with use of these barriers. An understanding of virus transport through the relevant passageways would be valuable in quantifying the risk. However, experimental investigations involving such passageways are difficult to perform, owing to the small dimensions involved. This paper presents a mathematical model for analyzing and predicting virus transport through barriers. The model incorporates a mathematical description of the mechanisms of virus transport, which include carrier-fluid flow, Brownian motion, and attraction or repulsion via virus-barrier interaction forces. The critical element of the model is the empirically determined rate constant characterizing the interaction force between the virus and the barrier. Once the model has been calibrated through specification of the rate constant, it can predict virus concentration under a wide variety of conditions. The experiments used to calibrate the model are described, and the rate constants are given for four bacterial viruses interacting with a latex membrane in saline. Rate constants were also determined for different carrier-fluid salinities, and the salt concentration was found to have a pronounced effect. Validation experiments employing laser-drilled pores in condoms were also performed to test the calibrated model. Model predictions of amount of transmitted virus through the drilled holes agreed well with measured values. Calculations using determined rate constants show that the model can help identify situations where barrier-integrity tests could significantly underestimate the risk associated with barrier use.
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    Bulletin of mathematical biology 61 (1999), S. 221-238 
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    Notes: Abstract Evaluation of the fluid flow pattern in a non-pregnant uterus is important for understanding embryo transport in the uterus. Fertilization occurs in the fallopian tube and the embryo (fertilized ovum) enters the uterine cavity within 3 days of ovulation. In the uterus, the embryo is conveyed by the uterine fluid for another 3 to 4 days to a successful implantation site at the upper part of the uterus. Fluid movements within the uterus may be induced by several mechanisms, but they seem to be dominated by myometrial contractions. Intra-uterine fluid transport in a sagittal cross-section of the uterus was simulated by a model of wall-induced fluid motion within a two-dimensional channel. The time-dependent fluid pattern was studied by employing the lubrication theory. A comprehensive analysis of peristaltic transport resulting from symmetric and asymmetric contractions is presented for various displacement waves on the channel walls. The results provide information on the flow field and possible trajectories by which an embryo may be transported before implantation at the uterine wall.
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    Bulletin of mathematical biology 61 (1999), S. 379-398 
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    Notes: Abstract A mechanistically based mathematical model is used to investigate some of the important factors in priming hepatocytes to enter the G1 phase of the cell cycle. The model considers all of the relevant biochemical mechanisms from signal-receptor binding to the elevation of AP-1(activation protein transcription factor) levels. Focus is centered on the chain of biochemical events governing the sequential activation of protein kinase C (PKC), mitogen-activated protein kinase (MAPK) and AP-1. Factors such as amplitude and duration of growth factors signals, the kinetics of guanosine diphosphate (GDP) to guanosine triphosphate (GTP) conversion, and the negative feedback control mechanisms governing initial steps in cellular replication were theoretically examined. The results of our theoretical assessments support the finding that specific mutations along the PKC-AP1 pathways can have a critical effect on the rate at which cells enter the division cycle.
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    Bulletin of mathematical biology 61 (1999), S. 273-301 
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    Notes: Abstract Normal cardiac muscle contraction occurs in response to a rapid rise followed by a slower decay in intracellular calcium concentration. When cardiac muscle cells are loaded with calcium, an intracellular store releases calcium into the cytosol by the process of calcium-induced calcium release (CICR). This release contributes to the rise in intracellular calcium which in turn triggers contraction. We use two qualitative piecewise linear reaction-diffusion models of this behaviour to investigate the speed, stability and waveform of plane waves using singular perturbation techniques.
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    Bulletin of mathematical biology 61 (1999), S. 365-377 
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    Notes: Abstract Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.
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    Bulletin of mathematical biology 61 (1999), S. 19-32 
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    Notes: Abstract Ratio-dependent predator-prey models set up a challenging issue regarding their dynamics near the origin. This is due to the fact that such models are undefined at (0, 0). We study the analytical behavior at (0, 0) for a common ratio-dependent model and demonstrate that this equilibrium can be either a saddle point or an attractor for certain trajectories. This fact has important implications concerning the global behavior of the model, for example regarding the existence of stable limit cycles. Then, we prove formally, for a general class of ratio-dependent models, that (0, 0) has its own basin of attraction in phase space, even when there exists a non-trivial stable or unstable equilibrium. Therefore, these models have no pathological dynamics on the axes and at the origin, contrary to what has been stated by some authors. Finally, we relate these findings to some published empirical results.
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    Bulletin of mathematical biology 61 (1999), S. 157-177 
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    Notes: Abstract We explore the behavior of richly connected inhibitory neural networks under parameter changes that correspond to weakening of synaptic efficacies between network units, and show that transitions from irregular to periodic dynamics are common in such systems. The weakening of these connections leads to a reduction in the number of units that effectively drive the dynamics and thus to simpler behavior. We hypothesize that the multiple interconnecting loops of the brain’s motor circuitry, which involve many inhibitory connections, exhibit such transitions. Normal physiological tremor is irregular while other forms of tremor show more regular oscillations. Tremor in Parkinson’s disease, for example, stems from weakened synaptic efficacies of dopaminergic neurons in the nigro-striatal pathway, as in our general model. The multiplicity of structures involved in the production of symptoms in Parkinson’s disease and the reversibility of symptoms by pharmacological and surgical manipulation of connection parameters suggest that such a neural network model is appropriate. Furthermore, fixed points that can occur in the network models are suggestive of akinesia in Parkinson’s disease. This model is consistent with the view that normal physiological systems can be regulated by robust and richly connected feedback networks with complex dynamics, and that loss of complexity in the feedback structure due to disease leads to more orderly behavior.
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    Bulletin of mathematical biology 61 (1999), S. 987-1008 
    ISSN: 1522-9602
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    Notes: Abstract Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the $$\frac{{n(n - 1)}}{2}$$ atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the $$\frac{{n(n - 1)}}{2}$$ pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and ∞. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality—the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley—Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the ( 4 n ) quadruples requires O(n 4) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n 3 log n) time on a CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with $$O\left( {\frac{n}{{\log n}}} \right)$$ processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.
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    Notes: Abstract We observed that amphiphile-induced microexovesicles may be spherical or cylindrical, depending on the species of the added amphiphile. The spherical microexovesicle corresponds to an extreme local difference between the two monolayer areas of the membrane segment with a fixed area, while the cylindrical microexovesicle corresponds to an extreme local area difference if the area of the budding segment is increased due to lateral influx of anisotropic membrane constituents. Protein analysis showed that both types of vesicles are highly depleted in the membrane skeleton. It is suggested that a partial detachment of the skeleton in the budding region is favoured due to accumulated skeleton shear deformations in this region.
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    Bulletin of mathematical biology 61 (1999), S. 1209-1210 
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    Bulletin of mathematical biology 61 (1999), S. 1187-1207 
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    Notes: Abstract The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.
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    Bulletin of mathematical biology 61 (1999), S. 573-595 
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    Notes: Abstract In an attempt to improve the understanding of complex metabolic dynamic phenomena, we have analysed several ‘metabolic networks’, dynamical systems which, under a single formulation, take into account the activity of several catalytic dissipative structures, interconnected by substrate fluxes and regulatory signals. These metabolic networks exhibit a rich variety of self-organized dynamic patterns, with e.g., phase transitions emerging in the whole activity of each network. We apply Hurst’s R/S analysis to several time series generated by these metabolic networks, and measure Hurst exponents H 〈 0.5 in most cases. This value of H, indicative of antipersistent processes, is detected at very high significance levels, estimated with detailed Monte Carlo simulations. These results show clearly the considered type of metabolic networks exhibit long-term memory phenomena.
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    Bulletin of mathematical biology 61 (1999), S. 597-600 
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    Bulletin of mathematical biology 61 (1999), S. 437-467 
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    Notes: Abstract The secondary structures of nucleic acids form a particularly important class of contact structures. Many important RNA molecules, however, contain pseudo-knots, a structural feature that is excluded explicitly from the conventional definition of secondary structures. We propose here a generalization of secondary structures incorporating ‘non-nested’ pseudo-knots, which we call bi-secondary structures, and discuss measures for the complexity of more general contact structures based on their graph-theoretical properties. Bi-secondary structures are planar trivalent graphs that are characterized by special embedding properties. We derive exact upper bounds on their number (as a function of the chain length n) implying that there are fewer different structures than sequences. Computational results show that the number of bi-secondary structures grows approximately like 2.35n. Numerical studies based on kinetic folding and a simple extension of the standard energy model show that the global features of the sequence-structure map of RNA do not change when pseudo-knots are introduced into the secondary structure picture. We find a large fraction of neutral mutations and, in particular, networks of sequences that fold into the same shape. These neutral networks percolate through the entire sequence space.
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    Bulletin of mathematical biology 61 (1999), S. 683-700 
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    Notes: Abstract A braced framework of tubular struts, in the walls and air spaces of frog lungs, suspends the respiratory surface and holds the lung open at zero transmural pressure withstanding imploding forces created by abdominal viscera, much as would the supports of a bell tent. The struts are tubes, having a larger second moment of area than do solid struts of the same cross-sectional area, and so are stronger, and contain pulmonary vessels within a flexible wall. The orthogonal arrangement of the struts in the framework, explained in part by Maxwell’s Lemma and Michell’s Theorem, strengthens the framework and minimizes its weight; orthogonality is maintained as the lungs change size. A model is presented, in which a frog might control pre-and post-pulmonary vascular resistances and, hence, blood volume in the struts, without compromising pulmonary perfusion. Such adjustments could vary the area of lung and the extent of perfused capillaries exposed to pulmonary gas, helping match the lung’s surface area, weight and metabolic load to activity.
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    Notes: Abstract A molecular-level theory is constructed for the control of fast neurotransmitter release, based on recent experimental findings that depolarization shifts presynaptic autoreceptors to a low affinity state and that an autoreceptor must be bound to a transmitter before it can become associated with the exocytotic apparatus. It is assumed that such an association blocks release; experimental support for this assumption is cited. The theory provides mechanisms for key experimental results concerning the essence of the matter, what controls the time course of evoked release? The same general model can account for both evoked and spontaneous release. The new theory can be regarded as a molecular implementation of the (phenomenological) calcium-voltage hypothesis that was suggested earlier.
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    Bulletin of mathematical biology 61 (1999), S. 799-805 
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    Bulletin of mathematical biology 61 (1999), S. 625-649 
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    Notes: Abstract We have developed cellular automaton models for two species competing in a patchy environment. We have modeled three common types of competition: facilitation (in which the winning species can colonize only after the losing species has arrived) inhibition (in which either species is able to prevent the other from colonizing) and tolerance (in which the species most tolerant of reduced resource levels wins). The state of a patch is defined by the presence or absence of each species. State transition probabilities are determined by rates of disturbance, competitive exclusion, and colonization. Colonization is restricted to neighboring patches. In all three models, disturbance permits regional persistence of species that are excluded by competition locally. Persistence, and hence diversity, is maximized at intermediate disturbance frequencies. If disturbance and dispersal rates are sufficiently high, the inferior competitor need not have a dispersal advantage to persist. Using a new method for measuring the spatial patterns of nominal data, we show that none of these competition models generates patchiness at equilibrium. In the inhibition model, however, transient patchiness decays very slowly. We compare the cellular automaton models to the corresponding mean-field patch-occupancy models, in which colonization is not restricted to neighboring patches and depends on spatially averaged species frequencies. The patch-occupancy model does an excellent job of predicting the equilibrium frequencies of the species and the conditions required for coexistence, but not of predicting transient behavior.
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    Bulletin of mathematical biology 61 (1999), S. 1093-1120 
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    Notes: Abstract We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation.
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    Bulletin of mathematical biology 61 (1999), S. 1151-1186 
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    Notes: Abstract The persistence of linear dominance hierarchies is often attributed to higher probabilities of a win after a win or a loss after a loss in agonistic interactions, yet there has been no theory on the evolution of such prior-experience effects. Here an analytic model, based on the idea that contests are determined by subjective perceptions of resource-holding potential (RHP) which animals may revise in the light of experience, demonstrates that winner and loser effects can evolve through round-robin competition among triads of animals drawn randomly from their population, and that the probability of a hierarchy increases with the strength of the combined effect. The effects are pure, in the sense that a contestant observes neither its own RHP nor its opponent’s RHP or RHP perception or win—loss record; and so the strength of an effect is unmodified by the RHPs of particular individuals, but depends on the distribution of RHP among the population at large. The greater the difference between an individual’s and its opponent’s RHP perception, the more likely it is to win a contest; however, if it overestimates its RHP, then the cost of fighting increases with the overestimate. A winner or loser effect exists only if the fitness gain of the beta individual in a hierarchy, relative to that of the alpha, is less than 0.5. Then a loser effect can exist alone, or it can coexist with a winner effect; however, there cannot exist a winner effect without a loser effect.
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    Bulletin of mathematical biology 61 (1999), S. 1121-1149 
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    Notes: Abstract Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. A periodically-forced, stage-structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic habitats of fluctuating flour volume. Predictions included multiple (2-cycle) attractors, resonance and attenuation phenomena, and saddle influences. Stochasticity, combined with the deterministic effects of an unstable ’saddle cycle’ separating the two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing multiple attractors, the presence of unstable invariant sets, as well as stochasticity and the nature, location, and size of basins of attraction, are all central to the interpretation of data.
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    Circuits, systems and signal processing 15 (1996), S. 555-572 
    ISSN: 1531-5878
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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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    The journal of Fourier analysis and applications 5 (1999), S. 1-19 
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    Keywords: Primary: 42A20 ; Secondary 42C20 ; divergence of Fourier series ; rearrangement of Fourier series
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    Notes: Abstract There exists a continuous function whose Fourier sum, when taken in decreasing order of magnitude of the coefficients, diverges unboundedly almost everywhere.
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    The journal of Fourier analysis and applications 5 (1999), S. 73-85 
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    Keywords: 42C10 ; 46B15 ; 46E30 ; Wavelet ; unimodular wavelet ; unconditional basis
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    Notes: Abstract We present weak sufficient conditions for decay of a wavelet so that the wavelet basis is an unconditional basis in Lp(ℝ), 1 〈p 〈 ∞. We also prove that some unimodular wavelets yield unconditional bases in Lp(ℝ).
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    The journal of Fourier analysis and applications 5 (1999), S. 87-104 
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    Keywords: 42C15 ; 46E35 ; 42B30 ; refinable distribution ; Triebel-Lizorkin space ; Besov space ; multiresolution ; wavelet ; joint spectral radius
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    Notes: Abstract The aim of this article is to characterize compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a finitely dimensional space.
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    The journal of Fourier analysis and applications 5 (1999), S. 21-44 
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    Keywords: 42B99 ; 47B35 ; 15A54 ; 60G35 ; Positive extensions ; Toeplitz operators ; matrix functions on bitorus ; Wiener algebra ; band method ; entropy ; almost periodic functions ; ARMA processes
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    Notes: Abstract Let S be a band in Z2 bordered by two parallel lines that are of equal distance to the origin. Given a positive definite ℓ1 sequence of matrices {cj}j∈S we prove that there is a positive definite matrix function f in the Wiener algebra on the bitorus such that the Fourier coefficients $$\widehat{f(k)}$$ equal ck for k ∈ S. A parameterization is obtained for the set of all positive extensions f of {cj}j∈S. We also prove that among all matrix functions with these properties, there exists a distinguished one that maximizes the entropy. A formula is given for this distinguished matrix function. The results are interpreted in the context of spectral estimation of ARMA processes.
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    The journal of Fourier analysis and applications 5 (1999), S. 67-71 
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    Keywords: 42C15 ; Frame ; Frame sequence ; Fourier frame
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    Notes: Abstract Given a real sequence {λn}n∈ℤ. Suppose that $$\left\{ {e^{i\lambda _n x} } \right\}_{n \in \mathbb{Z}}$$ is a frame for L2[−π, π] with bounds A, B. The problem is to find a positive constant L such that for any real sequence {μn}n∈ℤ with ¦μn −λn¦ ≤δ 〈L, $$\left\{ {e^{i\mu _n x} } \right\}_{n \in \mathbb{Z}}$$ is also a frame for L2[−π, π]. Balan [1] obtained $$L_R = \tfrac{1}{4} - \tfrac{1}{\pi }$$ arcsin $$\left( {\tfrac{1}{{\sqrt 2 }}\left( {1 - \sqrt {\tfrac{A}{B}} } \right)} \right)$$ . This value is a good stability bound of Fourier frames because it covers Kadec's 1/4-theorem $$\left( {L_R = \tfrac{1}{4}ifA = B} \right)$$ and is better than $$L_{DS} = \tfrac{1}{\pi }\ln \left( {1 + \sqrt {\tfrac{A}{B}} } \right)$$ (see Duffin and Schaefer [3]). In this paper, a sharper estimate is given.
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
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    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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    The journal of Fourier analysis and applications 5 (1999), S. 185-192 
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    Keywords: 42C15 ; 30A10 ; 94A12 ; lower bound ; exponential frame ; sine-type-function ; irregular sampling
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    Topics: Mathematics
    Notes: Abstract Lower frame bounds for sequences of exponentials are obtained in a special version of Avdonin's theorem on “1/4 in the mean” [1] and in a theorem of Duffin and Schaeffer [4].
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    The journal of Fourier analysis and applications 5 (1999), S. 303-308 
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    Keywords: 42B20 ; 42B30 ; Hardy spaces ; Calderon-Zygmund singular integral operator ; multipliers
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    Notes: Abstract Calderón-Zygmund singular integral operators have been extensively studied for almost half a century. This paper provides a context for and proof of the following result: If a Calderón-Zygmund convolution singular integral operator is bounded on the Hardy space H1 (Rn), then the homogeneous of degree zero kernel is in the Hardy space H1(Sn−1) on the sphere.
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    The journal of Fourier analysis and applications 5 (1999), S. 285-302 
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    Keywords: 42C05 ; 22D25 ; 46L55 ; 47C05 ; spectral pair ; translations ; tilings ; Fourier basis ; operator extensions ; induced representations ; spectral resolution ; Hilbert space
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    Notes: Abstract Let Ω ⊂ℝd have finite positive Lebesgue measure, and let $$\mathcal{L}^2$$ (Ω) be the corresponding Hilbert space of $$\mathcal{L}^2$$ -functions on Ω. We shall consider the exponential functionse λ on Ω given bye λ(x)=e i2πλ·x . If these functions form an orthogonal basis for $$\mathcal{L}^2$$ (Ω), when λ ranges over some subset Λ in ℝ d , then we say that (Ω, Λ) is a spectral pair, and that Λ is a spectrum. We conjecture that (Ω, Λ) is a spectral pair if and only if the translates of some set Ω′ by the vectors of Λ tile ℝd. In the special case of Ω=Id, the d-dimensional unit cube, we prove this conjecture, with Ω′=Id, for d≤3, describing all the tilings by Id, and for all d when Λ is a discrete periodic set. In an appendix we generalize the notion of spectral pair to measures on a locally compact abelian group and its dual.
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    The journal of Fourier analysis and applications 5 (1999), S. 355-362 
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    Keywords: 28A80 ; 42B10 ; 60G57 ; random self-similar measures ; Fourier dimension ; Salem sets
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    Topics: Mathematics
    Notes: Abstract In this paper we investigate the pointwise Fourier decay of some selfsimilar random measures. As an application we construct statistically selfsimilar Salem sets. For example, our result shows that a “slight” random perturbation of the classical Cantor set becomes a “nice” set in the sense that its Fourier dimension equals its Hausdorff dimension.
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    The journal of Fourier analysis and applications 5 (1999), S. v 
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    The journal of Fourier analysis and applications 5 (1999), S. 409-419 
    ISSN: 1531-5851
    Keywords: Weyl-Heisenberg frame ; Zak transform ; polynomial matrix ; 42C15
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    Topics: Mathematics
    Notes: Abstract In this note we consider continuous-time Weyl-Heisenberg (Gabor) frame expansions with rational oversampling. We present a necessary and sufficient condition on a compactly supported function g(t) generating a Weyl-Heisenberg frame for L2 (ℝ) for its minimal dual (Wexler-Razdual) γ0 (t) to be compactly supported. We furthermore provide a necessary and sufficient condition for a band-limited function g(t) generating a Weyl-Heisenberg frame for L2 (ℝ) to have a band-limited minimal dual γ0 (t). As a consequence of these conditions, we show that in the cases of integer oversampling and critical sampling a compactly supported (band-limited) g(t) has a compactly supported (band-limited) minimal dual γ0(t) if and only if the Weyl-Heisenberg frame operator is a multiplication operator in the time (frequency) domain. Our proofs rely on the Zak transform, on the Zibulski-Zeevi representation of the Weyl-Heisenberg frame operator, and on the theory of polynomial matrices.
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    The journal of Fourier analysis and applications 5 (1999), S. 521-522 
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    The journal of Fourier analysis and applications 3 (1996), S. 131-192 
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    Topics: Mathematics
    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 journal of Fourier analysis and applications 3 (1996), S. 103-129 
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    Topics: Mathematics
    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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    The journal of Fourier analysis and applications 3 (1996), S. 193-205 
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    Topics: Mathematics
    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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    Transformation groups 4 (1999), S. 127-156 
    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract We obtain a criterion for rational smoothness of an algebraic variety with a torus action, with applications to orbit closures in flag varieties, and to closures of double classes in regular group completions.
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    Transformation groups 4 (1999), S. 157-218 
    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract We present a formalization, using data uniquely defined at the level of the Weyl group, of the construction and combinatorial properties of unipotent character sheaves and unipotent characters for reductive algebraic groups over an algebraic closure of a finite field. This formalization extends to the case where the Weyl group is replaced by a complex reflection group, and in many cases we get families of unipotent characters for a mysterious object, a kind of reductive algebraic group with a nonreal Weyl group, the “spets”. In this first part, we present the general results about complex reflection groups, their associated braid groups and Hecke algebras, which will be needed later on for properties of “spetses”. Not all irreducible complex reflection groups will give rise to a spets (the ones which do so are called “spetsial”), but all of them afford properties which already allow us to generalize many of the notions attached to the Weyl groups through the approach of “generic groups” (see [BMM1]).
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    Transformation groups 4 (1999), S. 355-374 
    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract For the flag manifoldX=G/B of a complex semi-simple Lie groupG, we make connections between the Kostant harmonic forms onG/B and the geometry of the Bruhat Poisson structure. We show that on each Schubert cell, the corresponding Kostant harmonic form can be described using only data coming from the Bruhat Poisson structure. We do this by using an explicit set of coordinates on the Schubert cell.
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    The journal of Fourier analysis and applications 5 (1999), S. 45-66 
    ISSN: 1531-5851
    Keywords: 42B25 ; Fractional maximal operator ; weighted norm inequalities
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    Topics: Mathematics
    Notes: Abstract For 0 ≤α 〈 ∞ let Tαf denote one of the operators $$M_{\alpha ,0} f(x) = \mathop {\sup }\limits_{I \mathrel\backepsilon x} \left| I \right|^\alpha \exp \left( {\frac{1}{{\left| I \right|}}\int_I {\log \left| f \right|} } \right),M_{\alpha ,0}^* f(x) = \mathop {\lim }\limits_{r \searrow 0} \mathop {\sup }\limits_{I \mathrel\backepsilon x} \left| I \right|^\alpha \left( {\frac{1}{{\left| I \right|}}\int_I {\left| f \right|^r } } \right)^{{1 \mathord{\left/ {\vphantom {1 r}} \right. \kern-\nulldelimiterspace} r}} .$$ We characterize the pairs of weights (u, v) for which Tα is a bounded operator from Lp(v) to Lq(u), 0 〈p ≤q 〈 ∞. This extends to α 〉 0 the norm inequalities for α=0 in [4, 16]. As an application we give lower bounds for convolutions ϕ ⋆ f, where ϕ is a radially decreasing function.
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    The journal of Fourier analysis and applications 5 (1999), S. 193-201 
    ISSN: 1531-5851
    Keywords: Primary 30D15 ; 42C15 ; Secondary 30D10 ; 42C30 ; Paley-Wiener space ; entire functions of exponential type ; exponential frames ; discrete norms ; sampling theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well known that for certain sequences {tn}n∈ℤ the usual Lp norm ∥·∥p in the Paley-Wiener space PW τ p is equivalent to the discrete norm ‖f‖p,{tn}:=(∑ n=−∞ ∞ |f(tn)|p)1/p for 1 ≤ p = 〈 ∞ and ‖f‖∞,{tn}:=sup n∈ℤ|f(tn| for p=∞). We estimate ∥f∥p from above by C∥f∥p, n and give an explicit value for C depending only on p, τ, and characteristic parameters of the sequence {tn}n∈ℤ. This includes an explicit lower frame bound in a famous theorem of Duffin and Schaeffer.
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    The journal of Fourier analysis and applications 5 (1999), S. 203-284 
    ISSN: 1531-5851
    Keywords: Primary 31C45 ; 42C99 ; Fractal differential equations ; analysis on fractals ; Sierpinski gasket ; eigenfunctions of the Laplacian ; wave propagation on fractals
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    Topics: Mathematics
    Notes: Abstract Let Δ denote the symmetric Laplacian on the Sierpinski gasket SG defined by Kigami [11] as a renormalized limit of graph Laplacians on the sequence of pregaskets Gm whose limit is SG. We study the analogs of some of the classical partial differential equations with Δ playing the role of the usual Laplacian. For harmonic functions, biharmonic functions, and Dirichlet eigenfunctions of Δ, we give efficient algorithms to compute the solutions exactly, we display the results of implementing these algorithms, and we prove various properties of the solutions that are suggested by the data. Completing the work of Fukushima and Shima [8] who computed the Dirichlet eigenvalues and their multiplicities, we show how to construct a basis (but not orthonormal) for the eigenspaces, so that we have the analog of Fourier sine series on the unit interval. We also show that certain eigenfunctions have the property that they are a nonzero constant along certain lines contained in SG. For the analogs of the heat and wave equation, we give algorithms for approximating the solution, and display the results of implementing these algorithms. We give strong evidence that the analog of finite propagation for the wave equation does not hold because of inconsistent scaling behavior in space and time.
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    The journal of Fourier analysis and applications 5 (1999), S. 363-372 
    ISSN: 1531-5851
    Keywords: Primary 43A80 ; Secondary 44A12 ; spherical means ; Heisenberg group ; twisted spherical means ; Laguerre functions ; hypergeometric functions
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    Topics: Mathematics
    Notes: Abstract We prove that the boundary of a bounded domain is a set of injectivity for the twisted spherical means on ℂ n for a certain class of functions on ℂ n . As a consequence we obtain results about injectivity of the spherical mean operator in the Heisenberg group and the complex Radon transform.
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    The journal of Fourier analysis and applications 5 (1999), S. 465-494 
    ISSN: 1531-5851
    Keywords: Fractional ARIMA ; midpoint displacement technique ; fractional Gaussian noise ; fractional derivative ; generalized functions ; self-similarity ; Primary 60G18 ; secondary 41A58 ; 60F15.
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    Topics: Mathematics
    Notes: Abstract We provide an almost sure convergent expansion of fractional Brownian motion in wavelets which decorrelates the high frequencies. Our approach generalizes Lévy's midpoint displacement technique which is used to generate Brownian motion. The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series. The wavelets fill in the gaps and provide the necessary high frequency corrections. We also obtain a way of constructing an arbitrary number of non-Gaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.
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    Circuits, systems and signal processing 15 (1996), S. 505-514 
    ISSN: 1531-5878
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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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    Circuits, systems and signal processing 15 (1996), S. 543-554 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    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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    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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    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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    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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    Circuits, systems and signal processing 15 (1996), S. 145-164 
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    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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    Circuits, systems and signal processing 15 (1996), S. 335-342 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    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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    Circuits, systems and signal processing 15 (1996), S. 515-518 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Circuits, systems and signal processing 15 (1996), S. 573-580 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    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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    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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    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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    Circuits, systems and signal processing 18 (1999), S. 27-42 
    ISSN: 1531-5878
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    Notes: Abstract Of concern is the propagation of distortionless surface waves in a medium that may be nonuniform relative to depth. Distortionless wave propagation in inhomogeneous media was discussed by V. Burke, R. J. Duffin and D. Hazony, inQuart. Appl. Math., 183–194 (1976). Accordingly, the media could be modeled by a distributed electrical ladder network, nonuniform along the axis. We give a two-dimensional development based on Hooke's law and Newton's law which leads to the well-known case of Rayleigh waves in homogeneous media. It will be seen that the available pool of propagation modes greatly increases when high-pass propagation is included. The emphasis is on media where the elastic coefficients track one another as a function of depth. Special cases are studied in detail showing that as a disturbance travels along the surface, it may assume a broadband phase change, which translates into a shape distortion in the time domain, which is periodic with distance. Applications may be found in acousto-optics, in situ monitoring of elongated bodies, high-frequency SAW filters, microstrips, and any situations where surface waves are used in an environment of high precision or relatively large distances.
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    Circuits, systems and signal processing 18 (1999), S. 131-147 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This study presents a linear output-based controller for stabilizing a rigid-link flexible-joint electrically driven (RLFJED) robot manipulator. The proposed controller ensures local exponential stability under some uncertainty conditions. It is assumed that the velocity signals from the link side are not measurable. The controller is analyzed by using tools for pole placement by an output-feedback in the framework of the linear system theory. Some useful structural properties of the systems under consideration have been studied. Applications of the results to the set-point regulation control problem are considered.
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    Circuits, systems and signal processing 18 (1999), S. 205-223 
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    Notes: Abstract In this paper we consider an adaptive controller with vanishing gain and excitation of the reference signal. We use the burst recovery concept to show that all signals in the adaptive loop remain uniformly bounded. We also show that the mean-square performance converges so that the adaptive system is optimal in the sense that the parameter estimation error and the one-step ahead prediction error are uncorrelated in the mean despite the presence of the unmodeled dynamics.
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    Circuits, systems and signal processing 18 (1999), S. 191-204 
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    Notes: Abstract Finite homogeneous Markov chains ξ, which admit invariant probability distributions, can be defined by the cycloids { $$\bar C_k $$ } (closed polygonal lines whose consecutive edges have various orientations that do not necessarily determine a common direction for $$\bar C_k $$ ) occurring in their graphs. These Markov chains are called cycloid chains, and the corresponding finite-dimensional distributions are linear expressions on the cycloids { $$\bar C_k $$ } with the real coefficients αk. Then the collection {{ $$\bar C_k $$ }, {αk}}, called the cycloid decomposition of ξ, gives a minimal description of the finite-dimensional distributions that, except for a choice of the maximal tree, uniquely determines the chain ξ. Furthermore, the cycloid decompositions have an interpretation in terms of the transition probability functions expressing the same essence as the known Chapman-Kolmogorov equations.
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    Circuits, systems and signal processing 18 (1999), S. 241-267 
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    Notes: Abstract We study solutions of the “linear system in a saturated mode” $$\begin{array}{*{20}c} {(M)} & {x' \in Tx + c - \partial I_{D^n } x.} \\ \end{array} $$ We show that a trajectory is in a constant face of the cubeD n on some interval (0,d]. We answer a question about comparing the two systems: (M) and $$\begin{array}{*{20}c} {(H)} & {\begin{array}{*{20}c} {Cu' = T\upsilon + c - R^{ - 1} u,} & {\upsilon = G(\lambda } \\ \end{array} u)} \\ \end{array} $$ . As λ→∞, limits ofv corresponding to asymptotically stable equilibrium points of (H) are asymptotically stable equilibrium points of (M), and the converse is also true. We study the assumptions to see which are required and which may be weakened.
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    Circuits, systems and signal processing 18 (1999), S. 291-314 
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    Notes: Abstract In this paper we introduce a new computational method for solving the diffusion equation. In particular, we construct a “generalized” state-space system and compute the impulse response of an equivalent truncated state-space system. In this effort, we use a 3D finite element method (FEM) to obtain the state-space system. We then use the Arnoldi iteration to approximate the state impulse response by projecting on the dominant controllable subspace. The idea exploited here is the approximation of the impulse response of the linear system. We study the homogeneous and heterogeneous cases and discuss the approximation error. Finally, we compare our computational results to our experimental setup.
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    Circuits, systems and signal processing 18 (1999), S. 351-364 
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    Notes: Abstract A simple state-space approach for the four-block singular nonlinearH ∞ control problem is proposed in this paper. This approach combines a (J, J′)-lossless and a class of conjugate (J, J′)-expansive systems to yield a family of nonlinearH ∞ output feedback controllers. The singular nonlinearH ∞ control problem is thus transformed into a simple lossless network problem that is easy to deal with in a network-theory context.
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    Circuits, systems and signal processing 18 (1999), S. 395-406 
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    Notes: Abstract The stability of time-varying autoregressive (TVAR) models is an important issue in many applications such as time-varying spectral estimation, EEG simulation and analysis, and time-varying linear prediction coding (TVLPC). For stationary AR models there are methods that guarantee stability, but the for nonadaptive time-varying approaches there are no such methods. On the other hand, in some situations, such as in EEG analysis, the models that temporarily exhibit roots with almost unit moduli are difficult to use. Thus we may need a tighter stability condition such as stability with margin 1−ϱ. In this paper we propose a method for the estimation of TVAR models that guarantees stability with margin 1−ϱ, that is, the moduli of the roots of the time-varying characteristic polynomial are less than or equal to some arbitrary positive number ϱ for every time instant. The model class is the Subba Rao-Liporace class, in which the time-varying coefficients are constrained to a subspace of the coefficient time evolutions. The method is based on sequential linearization of the associated nonlinear constraints and the subsequent use of a Gauss-Newton-type algorithm. The method is also applied to a simulated autoregressive process.
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    Circuits, systems and signal processing 18 (1999), S. 443-443 
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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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    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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    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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    Circuits, systems and signal processing 15 (1996), S. 735-748 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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  • 98
    Electronic Resource
    Electronic Resource
    Springer
    Circuits, systems and signal processing 15 (1996), S. 771-805 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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  • 99
    Electronic Resource
    Electronic Resource
    Springer
    Risk analysis 19 (1999), S. 283-294 
    ISSN: 1539-6924
    Keywords: Risk perception ; pesticides ; pest management ; health effects ; agricultural pollution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Water pollution from agricultural pesticides continues to be a public concern. Given that the use of such pesticides on the farm is largely governed by voluntary behavior, it is important to understand what drives farmer behavior. Health belief models in public health and social psychology argue that persons who have adverse health experiences are likely to undertake preventive behavior. An analogous hypothesis set was tested here: farmers who believe they have had adverse health experiences from pesticides are likely to have heightened concerns about pesticides and are more likely to take greater precautions in dealing with pesticides. This work is based on an original survey of a population of 2700 corn and soybean growers in Maryland, New York, and Pennsylvania using the U.S. Department of Agriculture data base. It was designed as a mail survey with telephone follow-up, and resulted in a 60 percent response rate. Farm operators report experiencing adverse health problems they believe are associated with pesticides that is equivalent to an incidence rate that is higher than the reported incidence of occupational pesticide poisonings, but similar to the reported incidence of all pesticide poisonings. Farmers who report experiencing such problems have more heightened concerns about water pollution from fertilizers and pesticides, and illness and injury from mixing, loading, and applying pesticides than farmers who have not experienced such problems. Farmers who report experiencing such problems also are more likely to report using alternative pest management practices than farmers who do not report having such problems. This implies that farmers who have had such experiences do care about the effects of application and do engage in alternative means of pest management, which at least involve the reduction in pesticide use.
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  • 100
    ISSN: 1539-6924
    Keywords: Ethnicity ; fish consumption ; advisories ; Savannah River ; methylmercury ; risk perception
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract South Carolina has issued fish consumption advisories for the Savannah River based on mercury and radionuclide levels. We examine differences in fishing rates and fish consumption of 258 people interviewed while fishing along the Savannah River, as a function of age, education, ethnicity, employment history, and income, and test the assumption that the average consumption of fish is less than the recreational value of 19 kg/year assumed by risk assessors. Ethnicity and education contributed significantly to explaining variations in number of fish meals per month, serving size, and total quantity of fish consumed per year. Blacks fished more often, ate more fish meals of slightly larger serving sizes, and consumed more fish per year than did Whites. Although education and income were correlated, education contributed most significantly to behavior; people who did not graduate from high school ate fish more often, ate more fish per year, and ate more whole fish than people who graduated from high school. Computing consumption of fish for each person individually indicates that (1) people who eat fish more often also eat larger portions, (2) a substantial number of people consume more than the amount of fish used to compute risk to recreational fishermen, (3) some people consume more than the subsistence level default assumption (50 kg/year) and (4) Blacks consume more fish per year than Whites, putting them at greater risk from contaminants in fish. Overall, ethnicity, age, and education contributed to variations in fishing behavior and consumption.
    Type of Medium: Electronic Resource
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