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  • 1993  (64,934)
  • 1
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    Bulletin of mathematical biology 55 (1993), S. 1-13 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simple one-dimensional model of single-species populations is studied by means of computer simulations. Although the model has a rich spectrum of dynamics including chaotic behavior, the introduction of survival thresholds makes the chaotic region so small that it can be hardly observed. Stochastic fluctuations further reduce the chaotic region because they accidentally lead populations to extinction. The model thus naturally explains the observation that the majority of natural populations do not show chaotic behavior but a monotonic return to a stable equilibrium point following a disturbance.
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  • 2
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    Notes: Abstract Current understanding of the pattern of proliferation within intestinal crypts involves the notion of a cutoff region introduced by Cairnieet al. (Exp. Cell. Res. 39, 539–553, 1965b). (Cells produced above the cutoff are non-cycling, whereas cells produced below the cutoff are cycling.) They contrasted the predicted distribution of proliferation in the extreme cases of a cutoff of width 0 (a sharp cutoff) with one eight cells wide (a slow cutoff) and concluded that the data were better explained by the latter. We have shown that crypt size variation artificially broadens the apparent distribution of proliferating cells in the crypt (Totafurnoet al., Biophys. J. 54, 845–858, 1988). Here we show that the measurement and analysis of crypts of a specified height reduces this artifact. This work introduces the use of distance from the crypt base (in microns) to specify the location of cells within the crypt as an improvement over the cell position ordering traditionally used in the determination of the distribution of proliferating cells. We also show how to explicitly correct for several artifacts in the measurement of the labelling index. We conclude that cell proliferation within the crypt is more localized than previously realized; in fact, a cutoff as slow as eight cells wide is rejected.
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  • 3
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    Bulletin of mathematical biology 55 (1993), S. 141-154 
    ISSN: 1522-9602
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    Notes: Abstract Multiple string (sequence) alignment is a difficult and important problem in computational biology, where it is central in two related tasks: finding highly conserved subregions or embedded patterns of a set of biological sequences (strings of DNA, RNA or amino acids), and inferring the evolutionary history of a set of taxa from their associated biological sequences. Several precise measures have been proposed for evaluating the goodness of a multiple alignment, but no efficient methods are known which compute the optimal alignment for any of these measures in any but small cases. In this paper, we consider two previously proposed measures, and given two computationaly efficient multiple alignment methods (one for each measure) whose deviation from the optimal value isguaranteed to be less than a factor of two. This is the novel feature of these methods, but the methods have additional virtues as well. For both methods, the guaranteed bounds are much smaller than two when the number of strings is small (1.33 for three strings of any length); for one of the methods we give a related randomized method which is much faster and which gives, with high probability, multiple alignments with fairly small error bounds; and for the other measure, the method given yields a non-obviouslower bound on the value of the optimal alignment.
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    Bulletin of mathematical biology 55 (1993), S. 197-212 
    ISSN: 1522-9602
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    Notes: Abstract The kinematics of helical motion are descirbed for an organism treated as a rigid body with six degrees of freedom relative to the organism's frame of reference, i.e. the organism can translate in the direction of, or rotate around any of, three orthogonal axes fixed to its body. Equations are derived that express the unit vectors of the Frenet trihedron and the torsion and curvature of the trajectory in terms of the organism's translational and rotational velocities. These equations permit description of the radius, pitch, angular velocity and axis of a helical trajectory in terms of the translational and rotational velocities of the organism swimming along that trajectory. The results of this analysis are then used in two later papers that describe how organisms can orient to an external stimulus.
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    Bulletin of mathematical biology 55 (1993), S. 257-257 
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    Bulletin of mathematical biology 55 (1993), S. 231-255 
    ISSN: 1522-9602
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    Notes: Abstract Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.
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    Bulletin of mathematical biology 55 (1993), S. 277-294 
    ISSN: 1522-9602
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    Notes: Abstract A basic but neglected property of neuronal trees is their finite length. This finite length restricts the length of a segment to a certain maximum. The implications of the finite length of the tree with respect to the segment length distributions of terminal and intermediate segments are shown by means of a stochastic model. In the model it is assumed that branching is governed by a Poisson process. The model shows that terminal segments are expected to be longer than intermediate segments. Terminal and intermediate segments are expected to decrease in length with incrasing centrifugal order. The results are compared with data fromin vivo pyramidal cells from rat brain and tissue cultured ganglion cells from chicken. A good agreement between data and model was found.
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    Bulletin of mathematical biology 55 (1993), S. 345-364 
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    Notes: Abstract Shape and size of elongating cells were examined in three plant tissues: the adaxial epidermis of the petiole ofZebrina pendula L., the abaxial epidermis ofAnacharis densa L. leaves and the abaxial epidermis of the scale leaf ofAllium cepa L. Based on a few simple assumptions, the expected probability distribution frequencies (pdf) for cell length and number of adjacent walls were calculated. Actual data of cell lengths closely approximated those expected with the pdfs being asymmetrical since there are more younger, shorter cells than older, longer cells. Data for number of lateral walls of real cells were similar to that expected and these walls increase in compensating mechanism exists to maintain a constant range of cell lengths through many cell generations. It is expressed by longer than average new daughter cells dividing relatively soon while shorter than average new daughter cells divide after a relatively long cycle.
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    Bulletin of mathematical biology 55 (1993), S. 365-384 
    ISSN: 1522-9602
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    Notes: Abstract Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.
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  • 10
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    Notes: Abstract The particular dynamics of the previously proposed model of a catalytic network formed byn error-prone self-replicative species without and with superimposed competition is analysed. In the first case, two situations are studied in detail: a uniform network in which all the species are inter-coordinated in the same way, and a network with a species differentiated in its catalytic relation with the remaining elements. In the second case, the superimposed competition is introduced at two levels: first, as an asymmetry in one of the network species amplification factor considering a null self-catalytic vector, and secondly, as a non-null self-catalytic vector with no asymmetry in the other propertics of the species. This kind of system does not present complex behaviour and can be adequately deseribed by performing a standard linear analysis, which gives direct information on the asymptotic behaviour of the sytem. Finally, the biological implications of this analysis within the framework of biological evolution are discussed.
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    Bulletin of mathematical biology 55 (1993), S. 451-464 
    ISSN: 1522-9602
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    Notes: Abstract A theoretical model is proposed for the formation of cell distribution patterns in the slug stage of the cellular slime moldDictyostelium discoideum. The equilibrium distribution of two types of cells, prestalk and prespore, is obtained by minimizing the free energy, which is defined in terms of differential chemotaxis, differential cell adhesion and randomness of cell movement. Resulting distributions show various segregation patterns of cell types. The condition for cell sorting is obtained from stability analysis of the set of diffusion equations governing the evolution of cell type distribution and the concentration of chemoattractant. The intensities of differential chemotaxis and random cell movement are quantitatively evaluated from experimental data to show that two cell types can sort themselves completely by these forces.
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    Bulletin of mathematical biology 55 (1993), S. 655-674 
    ISSN: 1522-9602
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    Notes: Abstract Multicell spheroids, small spherical clusters of cancer cells, have become an importantin vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.
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    Bulletin of mathematical biology 55 (1993), S. 675-691 
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    Bulletin of mathematical biology 55 (1993), S. 693-693 
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    Bulletin of mathematical biology 55 (1993), S. 695-713 
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    Notes: Abstract In recent years, methods of consensus, developed for the solution of problems in the social sciences, have become widely used in molecular biology. Westudy a method of consensus originally due to Watermanet al. (Waterman, Galas and Arratia. 1984. Pattern recognition in several sequences: consensus and alignment.Bull. math. Biol. 46, 515–527) which is used to identify patterns or features in a molecular sequence where a pattern can vary in position within a given window. We show that some well-known consensus methods of the social sciences, the median and the mean, are special cases of this method for certain choices of the parameters used in it and give a precise account of the parameters for which these special cases arise. We also show that the specific parameters used in the method of Watermanet al. make their method equivalent to the median procedure which is widely used in the social sciences.
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    Bulletin of mathematical biology 55 (1993), S. 745-780 
    ISSN: 1522-9602
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    Notes: Abstract We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.
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    Bulletin of mathematical biology 55 (1993), S. 781-816 
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    Notes: Abstract Two types of behavior have been previously reported in models of immune networks. The typical behavior of simple models, which involve B cells only, is stationary behavior involving several steady states. Finite amplitude perturbations may cause the model to switch between different equilibria. The typical behavior of more realistic models, which involve both B cells and antibody, consists of autonomous oscillations and/or chaos. While stationary behavior leads to easy interpretations in terms of idiotypic memory, oscillatory behavior seems to be in better agreement with experimental data obtained in unimmunized animals. Here we study a series of models of the idiotypic interaction between two B cell clones. The models differ with respect to the incorporation of antibodies, B cell maturation and compartmentalization. The most complicated model in the series has two realistic parameter regimes in which the behavior is respectively stationary and chaotic. The stability of the equilibrium states and the structure and interactions of the stable and unstable manifolds of the saddle-type equilibria turn out to be factors influencing the model's behavior. Whether or not the model is able to attain any form of sustained oscillatory behavior, i.e. limit cycles or chaos, seems to be determined by (global) bifurcations involving the stable and unstable manifolds of the equilibrium states. We attempt to determine whether such behavior should be expected to be attained from reasonable initial conditions by incorporating an immune response to an antigen in the model. A comparison of the behavior of the model with experimental data from the literature provides suggestions for the parameter regime in which the immune system is operating.
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    Bulletin of mathematical biology 55 (1993), S. 865-867 
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    Bulletin of mathematical biology 55 (1993), S. 869-889 
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    Notes: Abstract We show that the existence of diffusional resistance due to the presence of a solid phase can have a positive effect on the metabolic reactions of plant cells. In this case the efficiency of metabolic reactions, defined as the ratio of rate of production of biomass of aggregated cells/rate of production of biomass of dispersed cells, can be greater than unity for a certain range of aggregate sizes for both solid spheres (common plant cell aggregates) and hollow spheres (e.g.Volvox aggregates). This means that, under appropriate conditions, plant cells tend to stay in the aggregated form to improve the efficiency of their metabolic reactions. The result of the present analysis provides an explanation as to why aggregates of plant cells are observed under typical culture conditions.
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    Bulletin of mathematical biology 55 (1993), S. 937-952 
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    Notes: Abstract The Hodgkin and Huxley equations model action potentials in squid giant axons. Variants of these equations are used in most models for electrial activity of excitable membranes. Computational tools based upon the theory of nonlinear dynamical systems are used here to illustrate how the dynamical behavior of the Hodgkin Huxley model changes as functions of two of the system parameters.
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    Bulletin of mathematical biology 55 (1993), S. 919-936 
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    Notes: Abstract The description of the “microbial loop” has led to some major changes in our understanding of nutrient cycling within aquatic ecosystems. It now appears that in many settings it is not uncommon for some 50% of phytoplankton production to be diverted into microbial pathways rather than passing up to higher trophic levels. As a result the microbial loop is responsible for enhanced and rapid nutrient cycling at the very base of the food web. Since tight recycling is often associated with unstable positive feedback, we use a model to examine the possible repercussions in more detail. The model simulates the dynamics of the microbial loop and finds it to greatly affect the way in which aquatic primary production responds to nutrient pulses.
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    Bulletin of mathematical biology 55 (1993), S. 953-971 
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    Notes: Abstract The maintenance activity of plants is investigated in terms of a simple model. Maximization of a certain biomass fraction we refer to asnonactive biomass is postulated. Optimal behaviour of plants according to this principle is explicitly derived and expressed depending on environmental conditions. Several interesting hypotheses result, e.g. a quadratic law relating specific growth rate and gross rate of photosynthesis. A qualitative comparison with data from the literature is performed, with a special emphasis on the question whether plants stressed by air pollutants repair optimally. Regarding long-term constant environmental conditions, no data were found that contradict optimal behaviour. Exact quantitative testing of the theory is desirable, appropriate experiments are suggested.
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    Bulletin of mathematical biology 55 (1993), S. 993-1011 
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    Notes: Abstract In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.
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    Bulletin of mathematical biology 55 (1993), S. 1039-1061 
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    Notes: Abstract A transient multispecies model for quantifying microbial space competition in biofilm is derived from existing models, introducing a new approach to biomass detachment modelling. This model includes inert biomass, substrate diffusion and utilization rate within the biofilm and diffusional layers. It predicts the evolution of biofilm thickness, bulk substrate concentration, species distribution and substrate concentration within the biofilm. A zero-dimensional transient model is described. Its steady-state solution is used to set up initial conditions of the one-dimensional model and case computation towards steady-state solution. Some numerical tools have been developed, enabling fast computation on microcomputers. Simulations show the validity of a zero-dimensional model and perturbated systems are also simulated. Simulations with experimental data give acceptable results.
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    Bulletin of mathematical biology 55 (1993), S. 1025-1038 
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    Notes: Abstract Recently, we proposed a new model of DNA sequence evolution (Arquès and Michel. 1990b.Bull. math. Biol. 52, 741–772) according to which actual genes on the purine/pyrimidine (R/Y) alphabet (R=purine=adenine or guanine, Y=pyrimidine=cytosine or thymine) are the result of two successive evolutionary genetic processes: (i) a mixing (independent) process of non-random oligonucleotides (words of base length less than 10: YRY(N)6, YRYRYR and YRYYRY are so far identified; N=R or Y) leading to primitive genes (words of several hundreds of base length) and followed by (ii) a random mutation process, i.e. transformations of a base R (respectively Y) into the base Y (respectively R) at random sites in these primitive genes. Following this model the problem investigated here is the study of the variation of the 8 R/Y codon probabilities RRR,..., YYY under random mutations. Two analytical expressions solved here allow analysis of this variation in the classical evolutionary sense (from the past to the present, i.e. after random mutations), but also in the inverted evolutionary sense (from the present to the past, i.e. before random mutations). Different properties are also derived from these formulae. Finally, a few applications of these formulae are presented. They prove the proposition in Arquès and Michel (1990b.Bull. math. Biol. 52, 741–772), Section 3.3.2, with the existence of a miximal mean number of random mutations per base of the order 0.3 in the protein coding genes. They also confirm the mixing process of oligonucleotides by excluding the purine/pyrimidine contiguous and alternating tracts from the formation process of primitive genes.
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    Bulletin of mathematical biology 55 (1993), S. 1199-1210 
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    Notes: Abstract It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two-and three-dimensional mathematical model describing the folding process as a free energy minimization problems is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard (“conditionally intractable”). Some of the possible ramifications of this results are speculated upon.
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    Bulletin of mathematical biology 55 (1993), S. 1133-1182 
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    Notes: Abstract A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation preceeds differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a “mexican-hat” effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively chanbed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.
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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 
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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 12 (1993), S. 153-154 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    Notes: Abstract Once designed, implementation of an optimal mean-square binary morphological filter is extremely fast, especially when the erosions are implemented on a suitable parallel processor. On the other hand, optimal filter design involes a computationally burdensome search procedure that can, in practice, be intractable. The present paper provides an algorithm for filter design that is based on the relationship between the optimal morphological filter and the conditional expectation. The algorithm proceeds by changing the conditional expectation into a morphological filter while at the same time increasing the mean-square error by a minimal amount. It does so by switching observations between the 1-set and the 0-set of the conditional expectation. The switching algorithm is extremely efficient in many noise environments, and therefore provides a filter design that can be useful for online structuring-element updating. Owing to the relationship between stack and morphological filters, the algorithm is at once useful for finding optimal binary stack filters.
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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 
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    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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    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 
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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 
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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
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    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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    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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    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 12 (1993), S. 263-278 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract New characteristics of feedback neural networks are studied. We discuss in detail the question of updating of neurons given incomplete information about the state of the neural network. We show how the mechanism of self-indexing for such updating provides better results than assigning ‘don't know’ values to the missing parts of the state vector. Issues related to the choice of the neural model for a feedback network are also considered. Properties of a new complex valued neuron model that generalizes McCulloch-Pitts neurons are examined.
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    Circuits, systems and signal processing 12 (1993), S. 391-407 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper deals with chained eigenstructure assignment for strongly controllable singular systems of the form Êx (t)=Â x(t)+B u(t) with state feedback control of the formu(t)=Kx(t)+w(t). The development of our method depends crucially on the properties of standard form singular systems. The closed-loop system will satisfy the following requirements: regularity, impulse-free response and rankÊ arbitrary eigenvalues assignment. This parametric characterization conveniently organizes the nonunique gain matrixK to modify the dynamic response of the systems. The result can be used for discrete-time descriptor systems, in which a zero-value eigenvalue may well be a desired closed-loop eigenvalue. One illustrative example is included.
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    Circuits, systems and signal processing 12 (1993), S. 453-464 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An efficient bi-state stochastic gradient is proposed for spontaneous constrained time delay estimation. The quantized stochastic gradient is an approximation of the polarity of the instantaneous delay estimation error. It is adjusted in such a way that it has a much higher probability to move in the correct direction at each iteration so as to enable a speed-up in the delay estimate to converge to global minimum in steady state. The performance of the delay estimator is evaluated statistically and an analytical solution for its convergence behavior is established. It is demonstrated that the proposed algorithm has at least a two-fold improvement in convergence speed when compared with the conventional approach, and this is verified by extensive simulation results.
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    Circuits, systems and signal processing 12 (1993), S. 503-531 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this work, we extend the coding theory approach to error control in redundant residue number systems (RRNS). The concept of erasure correction capability in RRNS is introduced. We derive the relationship between the minimum distance and the error detection and error/erasure correction capability. New computationally efficient algorithms are derived for simultaneously correcting single errors and multiple erasures and detecting multiple errors. These algorithms reduce the computational complexity of the previously known algorithms by at least an order of magnitude. Another attractive feature of the algorithms is that all the arithmetic operations are modulo operations. Consequently, the need to process large valued integers is avoided.
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    Circuits, systems and signal processing 12 (1993), S. 579-587 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a general expression relating the complex-normalized scattering matrix of ann-port network to that of its augmentedn-port network normalizing to then 1 −Ω resistances, where the Darlington equivalent network may be either reciprocal or nonreciprocal.
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    Circuits, systems and signal processing 12 (1993), S. 211-221 
    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper • Rigorously establishes the robustness of feedforward network realizations. • Uses a theorem of Wiener and ideas of translation invariant subspaces to provide conditions for universal approximations toL 1 andL 2 functions by networks, for quite general activation functions. The second result extends and simplifies some of the recent results of Stinchcombe and White, at least for the special cases ofL 1 andL 2 functions.
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    Circuits, systems and signal processing 18 (1999), S. 27-42 
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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Risk analysis 19 (1999), S. 283-294 
    ISSN: 1539-6924
    Keywords: Risk perception ; pesticides ; pest management ; health effects ; agricultural pollution
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    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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    ISSN: 1539-6924
    Keywords: Ethnicity ; fish consumption ; advisories ; Savannah River ; methylmercury ; risk perception
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    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.
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    Risk analysis 19 (1999), S. 453-459 
    ISSN: 1539-6924
    Keywords: Efficiency ; nonquantal ; probit ; quantal
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Methods of quantitative risk assessment for toxic responses that are measured on a continuous scale are not well established. Although risk-assessment procedures that attempt to utilize the quantitative information in such data have been proposed, there is no general agreement that these procedures are appreciably more efficient than common quantal dose–response procedures that operate on dichotomized continuous data. This paper points out an equivalence between the dose–response models of the nonquantal approach of Kodell and West(1) and a quantal probit procedure, and provides results from a Monte Carlo simulation study to compare coverage probabilities of statistical lower confidence limits on dose corresponding to specified additional risk based on applying the two procedures to continuous data from a dose–response experiment. The nonquantal approach is shown to be superior, in terms of both statistical validity and statistical efficiency.
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    ISSN: 1539-6924
    Keywords: Threshold ; measurement error ; mortality ; air pollution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The association between daily fluctuations in ambient particulate matter and daily variations in nonaccidental mortality have been extensively investigated. Although it is now widely recognized that such an association exists, the form of the concentration–response model is still in question. Linear, no threshold and linear threshold models have been most commonly examined. In this paper we considered methods to detect and estimate threshold concentrations using time series data of daily mortality rates and air pollution concentrations. Because exposure is measured with error, we also considered the influence of measurement error in distinguishing between these two completing model specifications. The methods were illustrated on a 15-year daily time series of nonaccidental mortality and particulate air pollution data in Toronto, Canada. Nonparametric smoothed representations of the association between mortality and air pollution were adequate to graphically distinguish between these two forms. Weighted nonlinear regression methods for relative risk models were adequate to give nearly unbiased estimates of threshold concentrations even under conditions of extreme exposure measurement error. The uncertainty in the threshold estimates increased with the degree of exposure error. Regression models incorporating threshold concentrations could be clearly distinguished from linear relative risk models in the presence of exposure measurement error. The assumption of a linear model given that a threshold model was the correct form usually resulted in overestimates in the number of averted premature deaths, except for low threshold concentrations and large measurement error.
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    Risk analysis 19 (1999), S. 527-545 
    ISSN: 1539-6924
    Keywords: breast-feeding ; chlorinated compounds ; risk assessment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Exposure to persistent organochlorines in breast milk was estimated probabilistically for Canadian infants. Noncancer health effects were evaluated by comparing the predicted exposure distributions to published guidance values. For chemicals identified as potential human carcinogens, cancer risks were evaluated using standard methodology typically applied in Canada, as well as an alternative method developed under the Canadian Environmental Protection Act. Potential health risks associated with exposure to persistent organochlorines were quantitatively and qualitatively weighed against the benefits of breast-feeding. Current levels of the majority of contaminants identified in Canadian breast milk do not pose unacceptable risks to infants. Benefits of breast-feeding are well documented and qualitatively appear to outweigh potential health concerns associated with organochlorine exposure. Furthermore, the risks of mortality from not breast-feeding estimated by Rogan and colleagues exceed the theoretical cancer risks estimated for infant exposure to potential carcinogens in Canadian breast milk. Although levels of persistent compounds have been declining in Canadian breast milk, potentially significant risks were estimated for exposure to polychlorinated biphenyls, dibenzo-p-dioxins, and dibenzofurans. Follow-up work is suggested that would involve the use of a physiologically based toxicokinetic model with probabilistic inputs to predict dioxin exposure to the infant. A more detailed risk analysis could be carried out by coupling the exposure estimates with a dose–response analysis that accounts for uncertainty.
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  • 93
    ISSN: 1539-6924
    Keywords: air dispersion ; models ; validation ; Rocky Flats
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Five atmospheric transport models were evaluated for use in Phase II of the Historical Public Exposures Studies at the Rocky Flats Plant. Models included a simple straight-line Gaussian plume model (ISCST2), several integrated puff models (RATCHET, TRIAD, and INPUFF2), and a complex terrain model (TRAC). Evaluations were based on how well model predictions compared with sulfur hexafluoride tracer measurements taken in the vicinity of Rocky Flats in February 1991. Twelve separate tracer experiments were conducted, each lasting 9 hr and measured at 140 samplers in arcs 8 and 16 km from the release point at Rocky Flats. Four modeling objectives were defined based on the endpoints of the overall study: (1) the unpaired maximum hourly average concentration, (2) paired time-averaged concentration, (3) unpaired time-averaged concentration, and (4) arc-integrated concentration. Performance measures were used to evaluate models and focused on the geometric mean and standard deviation of the predicted-to-observed ratio and the correlation coefficient between predicted and observed concentrations. No one model consistently outperformed the others in all modeling objectives and performance measures. About 75% of the maximum hourly concentration predictions were within a factor of 5 of the observations. About 64% of the paired and 80% of the unpaired time-averaged model predictions were within a factor of 5 of the observations. The overall performance of the RATCHET model was somewhat better than the other models. All models appeared to experience difficulty defining plume trajectories, which was attributed to the influence of multilayered flow initiated by terrain complexities and the diurnal flow patterns characteristic of the Colorado Front Range.
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  • 94
    ISSN: 1539-6924
    Keywords: initiation ; Monte Carlo methods ; promotion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract We present the results of a quantitative assessment of the lung cancer risk associated with occupational exposure to refractory ceramic fibers (RCF). The primary sources of data for our risk assessment were two long-term oncogenicity studies in male Fischer rats conducted to assess the potential pathogenic effects associated with prolonged inhalation of RCF. An interesting feature of the data was the availability of the temporal profile of fiber burden in the lungs of experimental animals. Because of this information, we were able to conduct both exposure–response and dose–response analyses. Our risk assessment was conducted within the framework of a biologically based model for carcinogenesis, the two-stage clonal expansion model, which allows for the explicit incorporation of the concepts of initiation and promotion in the analyses. We found that a model positing that RCF was an initiator had the highest likelihood. We proposed an approach based on biological considerations for the extrapolation of risk to humans. This approach requires estimation of human lung burdens for specific exposure scenarios, which we did by using an extension of a model due to Yu. Our approach acknowledges that the risk associated with exposure to RCF depends on exposure to other lung carcinogens. We present estimates of risk in two populations: (1) a population of nonsmokers and (2) an occupational cohort of steelworkers not exposed to coke oven emissions, a mixed population that includes both smokers and nonsmokers.
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  • 95
    ISSN: 1539-6924
    Keywords: accident risk ; population distribution ; RADTRAN ; transportation ; radioactive materials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Calculation of accident dose-risk estimates with the RADTRAN code requires input data describing the population likely to be affected by the plume of radioactive material (RAM) released in a hypothetical transportation accident. In the existing model, population densities within 1/2 mile (0.8 km) of the route centerline are tabulated in three ranges (Rural, Suburban, and Urban). These population densities may be of questionable validity since the plume in the RADTRAN analysis is assumed to extend out to 120 km from the hypothetical accident site. We present a GIS-based population model which accounts for the actual distribution of population under a potential plume, and compare accident-risk estimates based on the resulting population densities with those based on the existing model. Results for individual points along a route differ greatly, but the cumulative accident risks for a sample route of a few hundred kilometers are found to be comparable, if not identical. We conclude, therefore, that for estimation of aggregate accident risks over typical routes of several hundred kilometers, the existing, simpler RADTRAN model is sufficiently detailed and accurate.
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  • 96
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    Risk analysis 19 (1999), S. 685-687 
    ISSN: 1539-6924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 97
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    Risk analysis 19 (1999), S. 703-710 
    ISSN: 1539-6924
    Keywords: probabilistic risk analysis ; subjective judgment ; risk-informed regulation ; robust Bayesian analysis ; human performance ; human error ; management and organizational factors ; corporate culture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper discusses a number of the key challenges to the acceptance and application of probabilistic risk analysis (PRA). Those challenges include: (a) the extensive reliance on subjective judgment in PRA, requiring the development of guidance for the use of PRA in risk-informed regulation, and possibly the development of “robust” or “reference” prior distributions to minimize the reliance on judgment; and (b) the treatment of human performance in PRA, including not only human error per se but also management and organizational factors more broadly. All of these areas are seen as presenting interesting research challenges at the interface between engineering and other disciplines.
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  • 98
    Electronic Resource
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    Risk analysis 19 (1999), S. 689-701 
    ISSN: 1539-6924
    Keywords: risk ; risk perception ; risk assessment ; risk communication ; risk management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Risk management has become increasingly politicized and contentious. Polarized views, controversy, and conflict have become pervasive. Research has begun to provide a new perspective on this problem by demonstrating the complexity of the concept “risk” and the inadequacies of the traditional view of risk assessment as a purely scientific enterprise. This paper argues that danger is real, but risk is socially constructed. Risk assessment is inherently subjective and represents a blending of science and judgment with important psychological, social, cultural, and political factors. In addition, our social and democratic institutions, remarkable as they are in many respects, breed distrust in the risk arena. Whoever controls the definition of risk controls the rational solution to the problem at hand. If risk is defined one way, then one option will rise to the top as the most cost-effective or the safest or the best. If it is defined another way, perhaps incorporating qualitative characteristics and other contextual factors, one will likely get a different ordering of action solutions. Defining risk is thus an exercise in power. Scientific literacy and public education are important, but they are not central to risk controversies. The public is not irrational. Their judgments about risk are influenced by emotion and affect in a way that is both simple and sophisticated. The same holds true for scientists. Public views are also influenced by worldviews, ideologies, and values; so are scientists' views, particularly when they are working at the limits of their expertise. The limitations of risk science, the importance and difficulty of maintaining trust, and the complex, sociopolitical nature of risk point to the need for a new approach—one that focuses upon introducing more public participation into both risk assessment and risk decision making in order to make the decision process more democratic, improve the relevance and quality of technical analysis, and increase the legitimacy and public acceptance of the resulting decisions.
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  • 99
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    Risk analysis 19 (1999), S. 727-738 
    ISSN: 1539-6924
    Keywords: mitigation ; insurance ; catastrophic risk ; building codes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper examines the impact that insurance coupled with specific risk mitigation measures (RMMs) could have on reducing losses from hurricanes and earthquakes as well as improving the solvency position of insurers who provide coverage against these hazards. We first explore why relatively few individuals adopt cost-effective RMMs by reporting on the results of empirical studies and controlled laboratory studies. We then investigate the impact that an RMM has on both the expected losses and those from a worst case scenario in two model cities—Oakland (an earthquake-prone area) and Miami/Dade County (a hurricane-prone area) which were constructed respectively with the assistance of two modeling firms. The paper then explores three programs for forging a meaningful public-private sector partnership: well-enforced building codes, insurance premium reductions linked with long-term loans, and lower deductibles on insurance policies tied to mitigation. We conclude by briefly examining four issues for future research on linking mitigation with insurance.
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  • 100
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    Risk analysis 19 (1999), S. 711-726 
    ISSN: 1539-6924
    Keywords: variability ; exposure ; susceptibility ; risk assessment ; pharmacokinetics ; pharmacodynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper reviews existing data on the variability in parameters relevant for health risk analyses. We cover both exposure-related parameters and parameters related to individual susceptibility to toxicity. The toxicity/susceptibility data base under construction is part of a longer term research effort to lay the groundwork for quantitative distributional analyses of non-cancer toxic risks. These data are broken down into a variety of parameter types that encompass different portions of the pathway from external exposure to the production of biological responses. The discrete steps in this pathway, as we now conceive them, are: •Contact Rate (Breathing rates per body weight; fish consumption per body weight) •Uptake or Absorption as a Fraction of Intake or Contact Rate •General Systemic Availability Net of First Pass Elimination and Dilution via Distribution Volume (e.g., initial blood concentration per mg/kg of uptake) •Systemic Elimination (half life or clearance) •Active Site Concentration per Systemic Blood or Plasma Concentration •Physiological Parameter Change per Active Site Concentration (expressed as the dose required to make a given percentage change in different people, or the dose required to achieve some proportion of an individual's maximum response to the drug or toxicant) •Functional Reserve Capacity–Change in Baseline Physiological Parameter Needed to Produce a Biological Response or Pass a Criterion of Abnormal Function Comparison of the amounts of variability observed for the different parameter types suggests that appreciable variability is associated with the final step in the process–differences among people in “functional reserve capacity.” This has the implication that relevant information for estimating effective toxic susceptibility distributions may be gleaned by direct studies of the population distributions of key physiological parameters in people that are not exposed to the environmental and occupational toxicants that are thought to perturb those parameters. This is illustrated with some recent observations of the population distributions of Low Density Lipoprotein Cholesterol from the second and third National Health and Nutrition Examination Surveys.
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