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  • Springer  (7,106)
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  • 1995-1999  (7,151)
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  • 1999  (7,151)
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  • 1
    Electronic Resource
    Electronic Resource
    Cable analysis of a motor-nerve terminal branch in a volume conductor (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1-17 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0066
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  • 2
    Electronic Resource
    Electronic Resource
    A mathematical model for simulating virus transport through synthetic barriers (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 113-140 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0080
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  • 3
    Electronic Resource
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    Analysis of intra-uterine fluid motion induced by uterine contractions (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 221-238 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0069
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  • 4
    Electronic Resource
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    Replication potential of cells via the protein kinase C-MAPK pathway: Application of a mathematical model (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 379-398 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0077
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  • 5
    Electronic Resource
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    Velocity and stability of solitary planar travelling wave solutions of intracellular [Ca]2+ (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 273-301 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0081
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  • 6
    Electronic Resource
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    Numerical simulations of stochastic circulatory models (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 365-377 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0094
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  • 7
    Electronic Resource
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    About deterministic extinction in ratio-dependent predator-prey models (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 19-32 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0072
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  • 8
    Electronic Resource
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    Parkinsonian tremor and simplification in network dynamics (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 157-177 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0086
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  • 9
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    Computational experience with a parallel algorithm for tetrangle inequality bound smoothing (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 987-1008 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0123
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  • 10
    Electronic Resource
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    Membrane skeleton detachment in spherical and cylindrical microexovesicles (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1019-1030 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0128
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  • 11
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    Book review (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1209-1210 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0135
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  • 12
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    Controlling chaos in ecology: From deterministic to individual-based models (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1187-1207 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0141
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  • 13
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    Persistence in metabolic nets (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 573-595 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0103
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  • 14
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    Book reviews (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 597-600 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0092
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  • 15
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    RNA structures with pseudo-knots: Graph-theoretical, combinatorial, and statistical properties (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 437-467 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0085
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  • 16
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    A hydrostatic Michell framework supports frog lungs (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 683-700 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0104
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  • 17
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    Theory of fast neurotransmitter release control based on voltage-dependent interaction between autoreceptors and proteins of the exocytotic machinery (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 701-725 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0107
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  • 18
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    Book reviews (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 799-805 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1006/bulm.1999.0099
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  • 19
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    Cellular automaton models for competition in patchy environments: Facilitation, inhibition, and tolerance (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 625-649 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0090
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  • 20
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    Reaction and diffusion on growing domains: Scenarios for robust pattern formation (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1093-1120 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0131
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  • 21
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    On the evolution of pure winner and loser effects: A game-theoretic model (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1151-1186 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    URL: http://dx.doi.org/10.1006/bulm.1999.0137
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  • 22
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    Multiple attractors, saddles, and population dynamics in periodic habitats (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 1121-1149 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0136
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  • 23
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    Decreasing rearranged Fourier series (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 1-19 
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    ISSN: 1531-5851
    Keywords: Primary: 42A20 ; Secondary 42C20 ; divergence of Fourier series ; rearrangement of Fourier series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF01274186
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  • 24
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    Wavelets as unconditional bases inL p (ℝ) (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 73-85 
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    ISSN: 1531-5851
    Keywords: 42C10 ; 46B15 ; 46E30 ; Wavelet ; unimodular wavelet ; unconditional basis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1007/BF01274190
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    Compactly supported refinable distributions in Triebel-Lizorkin spaces and besov spaces (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 87-104 
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    ISSN: 1531-5851
    Keywords: 42C15 ; 46E35 ; 42B30 ; refinable distribution ; Triebel-Lizorkin space ; Besov space ; multiresolution ; wavelet ; joint spectral radius
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    Topics: Mathematics
    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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    Positive matrix functions on the bitorus with prescribed Fourier coefficients in a band (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 21-44 
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    ISSN: 1531-5851
    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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    A sharper stability bound of Fourier frames (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 67-71 
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    ISSN: 1531-5851
    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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    On the stability of wavelet and Gabor frames (Riesz bases) (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
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    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
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    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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    On lower bounds of exponential frames (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 185-192 
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    ISSN: 1531-5851
    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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    A necessary condition for Calderón-Zygmund singular integral operators (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 303-308 
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    ISSN: 1531-5851
    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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    Spectral pairs in cartesian coordinates (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 285-302 
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    ISSN: 1531-5851
    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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    Fourier asymptotics of statistically self-similar measures (1999)
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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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    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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    Editorial statement (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. v 
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    A necessary and sufficient condition for dual Weyl-Heisenberg frames to be compactly supported (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 409-419 
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    ISSN: 1531-5851
    Keywords: Weyl-Heisenberg frame ; Zak transform ; polynomial matrix ; 42C15
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    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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    Editorial statement (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 521-522 
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    Topics: Mathematics
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    Rational smoothness and fixed points of torus actions (1999)
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    Transformation groups 4 (1999), S. 127-156 
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    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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    Towards spetses I (1999)
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    Transformation groups 4 (1999), S. 157-218 
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    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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    Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure onG/B (1999)
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    Transformation groups 4 (1999), S. 355-374 
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    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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    Weighted norm inequalities for geometric fractional maximal operators (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 45-66 
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    Keywords: 42B25 ; Fractional maximal operator ; weighted norm inequalities
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    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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    On discrete and continuous norms in Paley-Wiener spaces and consequences for exponential frames (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 193-201 
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    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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    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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    Fractal differential equations on the Sierpinski gasket (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 203-284 
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    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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    Injectivity sets for spherical means on the Heisenberg group (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 363-372 
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    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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    Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 465-494 
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    Keywords: Fractional ARIMA ; midpoint displacement technique ; fractional Gaussian noise ; fractional derivative ; generalized functions ; self-similarity ; Primary 60G18 ; secondary 41A58 ; 60F15.
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    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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    Book review (1999)
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    Bulletin of mathematical biology 61 (1999), S. 207-208 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
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    Modelling the internalization of labelled cells in tumour spheroids (1999)
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    Bulletin of mathematical biology 61 (1999), S. 601-623 
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    Notes: Abstract In this paper a mathematical model is developed to describe the migration of labelled particles within a multicell spheroid. In the model, spatial variations in cell proliferation and death create an internal velocity field which leads to redistribution of the labelled and unlabelled cells. By applying a range of numerical and analytical techniques to the model equations, it is possible to show that, whilst the speed with which the labelled cells migrate through the tumour is independent of the type of cells that are labelled, their limiting distribution depends crucially on whether inert polystyrene microspheres or live tumour cells are labelled. These predictions are shown to be in good qualitative agreement with independent experimental results.
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    Bulletin of mathematical biology 61 (1999), S. 1009-1013 
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    Modeling the T-cell dynamics and pathogenesis of HTLV-I infection (1999)
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    Bulletin of mathematical biology 61 (1999), S. 935-947 
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    Notes: Abstract Human T-cell lymphotropic virus type I (HTLV-I) infection in humans causes a chronic infection of CD4+ T cells, and is associated with various disease outcomes, among them with the development of adult T-cell leukemia (ATL). The T-cell dynamics after HTLV-I infection can be described in a mathematical model with coupled differential equations. The infection process is modeled assuming cell-to-cell infection of CD4+ T cells. The model allows for CD4+ T cell subsets of susceptible, latently infected and actively infected cells as well as for leukemia cells. Latently infected T cells may harbor the virus for several years until they become activated and able to infect susceptible T cells. Uncontrolled proliferation of CD4+ T cells with monoclonal DNA-integration of HTLV-I results in the development of ATL. The model describes basic features that characterize HTLV-I infection; the chronic infection of CD4+ T cells, the increasing number of abnormal cells and the possible progression to ATL.
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    Size hierarchy and stability in competitive plant populations (1999)
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    Bulletin of mathematical biology 61 (1999), S. 949-961 
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    Notes: Abstract A neighbourhood-based competition model for plant individuals is studied to evaluate how a hierarchical structure related to size may emerge in plant communities. It is shown by numerical simulations and linear stability analysis that many stable states exist in the hierarchical structure when both the total number of individuals and the degree of asymmetry of competition are high. When the hierarchical structures are self-organized by the dynamic instability of the homogeneous state due to non-linearity of competition, it is proved that these states are always locally stable. The relevance of the results to size structures in real plant communities (boreal forests vs tropical and temperate forests) is discussed. This is suggested to be the mechanism responsible for the coexistence of species in plant communities.
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    Comparative dynamics of three models for host-parasitoid interactions in a patchy environment (1999)
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    Bulletin of mathematical biology 61 (1999), S. 141-155 
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    Topics: Biology , Mathematics
    Notes: Abstract Phenomenological models represent a simplified approach to the study of complex systems such as host-parasitoid interactions. In this paper we compare the dynamics of three phenomenological models for host-parasitoid interactions developed by May (1978), May and Hassell (1981) and May et al. (1981). The essence of the paper by May and Hassell (1981) was to define a minimum number of parameters that would describe the interactions, avoiding the technical difficulties encountered when using models that involve many parameters, yet yielding a system of equations that could capture the essence of real world interactions in patchy environments. Those studies dealt primarily with equilibrium and coexistence phenomena. Here we study the dynamics through bifurcation analysis and phase portraits in a much wider range of parameter values, carrying the models beyond equilibrium states. We show that the dynamics can be either stable or chaotic depending on the location of a damping term in the equations. In the case of the stable system, when host density dependence acts first, a stable point is reached, followed by a closed invariant curve in phase space that first increases then decreases, finally returning to an asymptotically stable point. Chaos is not seen. On the other hand, when parasitoid attack occurs before host density dependence, chaos is inevitably apparent. We show, as did May et al. (1981) and stated earlier byWang and Gutierrez (1980), that the sequence of events in host-parasitoid interactions is crucial in determining their stability. In a chaotic state the size of the host (e.g., insect pests) population becomes unpredictable, frequently becoming quite large, a biologically undesirable outcome. From a mathematical point of view the system is of interest because it reveals how a strategically placed damping term can dramatically alter the outcome. Our study, reaching beyond equilibrium states, suggests a strategy for biological control different from that of May et al. (1981).
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    Effects of parasitism over two competing host populations leading to persistence (1999)
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    Bulletin of mathematical biology 61 (1999), S. 179-205 
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    Topics: Biology , Mathematics
    Notes: Abstract In this paper we study the uniform persistence (UP) of an association of two competing host species sharing a directly transmitted macroparasite. Like predators, parasites can regulate UP while the hosts are either coexisting or in a dominance relationship without any infections, but cannot regulate UP in case the hosts are in bistability. The regulatory mechanism depends on the relationships between the parameters, such as host intrinsic growth rate, host carrying capacity, susceptibility, parasite pathogenicity and the magnitude of parasite aggregation. In the case of coexistence the parametric space for UP is more than that for global stability of the host-parasite equilibrium, but is less than that for UP in the case of dominance. In the case of dominance, the parasites can alter the competitive outcome locally or can enhance the local exclusion of the inferior competitor and thus, unlike the predation, parasitism has an beneficial effect over competition. We derive explicitly the range of the values of ratios of the rates of reproduction and survivorship of the hosts, and also of the values of the degree of aggregations, with which macroparasites are not effective in maintaining its beneficial effect over competition. Finally our results support the body-size hypothesis of Price et al. (1988), with possible explanations of certain exceptional examples of the hypothesis.
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    Parametric-equation representation of biconcave erythrocytes (1999)
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    Bulletin of mathematical biology 61 (1999), S. 209-220 
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    Topics: Biology , Mathematics
    Notes: Abstract The representation of the shape of a biconcave erythrocyte by a set of three parametric equations was achieved by using the expressions that transform the curvilinear coordinates from the disc-cyclide coordinate system [denoted J2R; Moon and Spencer (1988), Field Theory Handbook, Springer-Verlag, Berlin] to Cartesian coordinates. The equations are products of elliptic functions, so the challenge was to relate the three major ’shape-defining’ measurements of the human erythrocyte in Cartesian coordinates to three parameters in the new curvilinear coordinates, to give a realistic representation of the shape of the membrane-surface. The relationships between the coefficients of the Cartesian degree-4 surface that describes the discocyte and the coordinate transformation equations were derived with the aid of Mathematica; and the membrane-surface of the cell was drawn using the ParametricPlot3D function in this ‘package’. By having the erythrocyte shape expressed in its new form it is readily amenable to further transformations that might be used to model those changes in shape that are seen when the cells are immersed in media of various osmolalities, or when they change metabolic ’states’. On the other hand, the relationship between the coefficients of the Cartesian expression for the disc-cyclide surface is relevant to image analysis of erythrocytes, as determined by physical methods that rely on Cartesian imaging ’slices’. These methods include confocal microscopy and various nuclear magnetic resonance microimaging procedures.
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    A physical-biological coupled model for algal dynamics in lakes (1999)
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    Bulletin of mathematical biology 61 (1999), S. 239-272 
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    Topics: Biology , Mathematics
    Notes: Abstract A coupled model is presented for simulating physical and biological dynamics in fresh water lakes. The physical model rests upon the assumption that the turbulent kinetic energy in a water column of the lake is fully contained in a mixed layer of variable depth. Below this layer the mechanical energy content is assumed to vanish. Additionally, the horizontal currents are ignored. This one-dimensional two-layered model describes the internal conversion of the mechanical and thermal energy input from the atmosphere into an evolution of the mixed layer depth by entrainment and detrainment mechanisms. It is supposed to form the physical domain in which the simulation of the biological processes takes place. The biological model describes mathematically the typical properties of phyto-and zooplankton, their interactions and their response to the physical environment. This description then allows the study of the behaviour of Lagrangian clusters of virtual plankton that are subjected to such environments. The essence of the model is the dynamical simulation of an arbitrary number of nutrient limited phytoplankton species and one species of zooplankton. The members of the food web above and below affect the model only statically. The model is able to reproduce the typical progression of a predator-prey interaction between phyto-and zooplankton as well as the exploitative competition for nutrients between two phytoplankton species under grazing pressure of Daphnia. It suggests that the influence of the biological system on the physical system results in a weak increase of the surface temperature for coupled simulations, but a considerably higher seasonal thermocline in spring and a lower one in autumn.
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    Zooplankton mortality and the dynamical behaviour of plankton population models (1999)
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    Bulletin of mathematical biology 61 (1999), S. 303-339 
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    Notes: Abstract We investigate the dynamical behaviour of a simple plankton population model, which explicitly simulates the concentrations of nutrient, phytoplankton and zooplankton in the oceanic mixed layer. The model consists of three coupled ordinary differential equations. We use analytical and numerical techniques, focusing on the existence and nature of steady states and unforced oscillations (limit cycles) of the system. The oscillations arise from Hopf bifurcations, which are traced as each parameter in the model is varied across a realistic range. The resulting bifurcation diagrams are compared with those from our previouswork, where zooplankton mortality was simulated by a quadratic function—here we use a linear function, to represent alternative ecological assumptions. Oscillations occur across broader ranges of parameters for the linear mortality function than for the quadratic one, although the two sets of bifurcation diagrams show similar qualitative characteristics. The choice of zooplankton mortality function, or closure term, is an area of current interest in the modelling community, and we relate our results to simulations of other models.
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    Use of Bayes theorem to correct size-specific sampling bias in growth data (1999)
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    Bulletin of mathematical biology 61 (1999), S. 355-363 
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    Notes: Abstract The bayesian decomposition of posterior distribution was used to develop a likelihood function to correct bias in the estimates of population parameters from data collected randomly with size-specific selectivity. Positive distributions with time as a parameter were used for parametrization of growth data. Numerical illustrations are provided. The alternative applications of the likelihood to estimate selectivity parameters are discussed.
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    Probability density functions useful for parametrization of heterogeneity in growth and allometry data (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1015-1016 
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    Pattern formation of scale cells in lepidoptera by differential origin-dependent cell adhesion (1999)
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    Bulletin of mathematical biology 61 (1999), S. 807-828 
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    Notes: Abstract We present a model for the formation of parallel rows of scale cells in the developing adult wing of moths and butterflies. Precursors of scale cells differentiate throughout each epithelial monolayer and migrate into rows that are roughly parallel to the body axis. Grafting experiments have revealed what appears to be a gradient of adhesivity along the wing. What is more, cell adhesivity character is maintained after grafting. Thus we suggest that it is a cell’s location prior to migration that determines its interactions during migration. We use nonlinear bifurcation analysis to show that differential origin-dependent cell adhesion can result in the stabilization of rows over spots.
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    Modeling epithelial cell homeostasis: Steady-state analysis (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1065-1091 
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    Notes: Abstract Critical to epithelial cell viability is the homeostasis of cell volume and composition during changes in transcellular transport. In this study, two previously developed mathematical models (principal cell of the collecting duct and proximal tubule cell) are approximated by their linearizations about a reference condition. This yields matrices which estimate cell volume, cell composition, and transcellular fluxes in response to perturbations of bath conditions and membrane transporter activity. These approximations are themselves extended with the inclusion of linear dependence of membrane transport coefficients on cell variables (e.g., volume, solute concentrations, or electrical potential). This provides cell models with variable permeabilities, which may be homeostatic, and which can be examined systematically: sequentially testing each membrane permeability and its controlling cell variable. In the proximal tubule approximation, volume-mediated increases in peritubular K—Cl or Na—3HCO3 cotransport, and volume-mediated decreases in Na,K-ATPase activity are homeostatic; modulation of peritubular K permeability has little impact. In the principal cell model, volume homeostasis is afforded by volume-sensitive peritubular Na/H exchange or Cl− conductance. Predictions from the linear analysis are confirmed in the full models. This approach yields a systematic examination of homeostasis in an epithelial model, and identifies candidate control parameters.
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    A fast transform for spherical harmonics (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 159-184 
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    Keywords: Primary 65T20 ; secondary 42C10 ; 33C55 ; spherical harmonics ; fast transforms ; associated Legendre functions
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    Notes: Abstract Spherical harmonics arise on the sphere S2 in the same way that the (Fourier) exponential functions {eikθ}k∈ℤ arise on the circle. Spherical harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform (FFT). Without a fast transform, evaluating (or expanding in) spherical harmonic series on the computer is slow—for large computations probibitively slow. This paper provides a fast transform. For a grid ofO(N2) points on the sphere, a direct calculation has computational complexityO(N4), but a simple separation of variables and FFT reduce it toO(N3) time. Here we present algorithms with timesO(N5/2 log N) andO(N2(log N)2). The problem quickly reduces to the fast application of matrices of associated Legendre functions of certain orders. The essential insight is that although these matrices are dense and oscillatory, locally they can be represented efficiently in trigonometric series.
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    Editorial statement (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. v 
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    Claude Chevalley (1999)
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    Transformation groups 4 (1999), S. i 
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    Editorial statement (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. v 
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    Weakly symmetric spaces and spherical varieties (1999)
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    Transformation groups 4 (1999), S. 3-24 
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    Notes: Abstract Weakly symmetric homogeneous spaces were introduced by A. Selberg in 1956. We prove that, for a real reductive algebraic group, they can be characterized as the spaces of real points of affine spherical homogeneous varieties of the complexified group. As an application, under the same assumption on the transitive group, we show that weakly symmetric spaces are precisely the homogeneous Riemannian manifolds with commutative algebra of invariant differential operators.
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    Affine modifications and affine hypersurfaces with a very transitive automorphism group (1999)
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    Transformation groups 4 (1999), S. 53-95 
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    Notes: Abstract We study the modificationA→A′ of an affine domainA which produces another affine domainA′=A[I/f] whereI is a nontrivial ideal ofA andf is a nonzero element ofI. First appeared in passing in the basic paper of O. Zariski [Zar], it was further considered by E. D. Davis [Da]. In [Ka1] its geometric counterpart was applied to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions (more general than those in [Ka1]) which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurfaceX⊂C k+2, given by the equationuv=(p(x 1,...,xk) wherep∈C[x 1,...,x k ],k≥2, actsm-transitively on the smooth part regX ofX for anym∈N. We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.
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    Compactification of symmetric varieties (1999)
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    Transformation groups 4 (1999), S. 273-300 
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    Notes: Abstract The symmetric varieties considered in this paper are the quotientsG/H, whereG is an adjoint semi-simple group over a fieldk of characteristic ≠ 2, andH is the fixed point group of an involutorial automorphism ofG which is defined overk. In the casek=C, De Concini and Procesi (1983) constructed a “wonderful” compactification ofG/H. We prove the existence of such a compactification for arbitraryk. We also prove cohomology vanishing results for line bundles on the compactification.
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    Quasi-Hopf twistors for elliptic quantum groups (1999)
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    Transformation groups 4 (1999), S. 303-327 
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    Notes: Abstract The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al. [FIJKMY1], Felder [Fe]). Frønsdal [Fr1, Fr2] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebraU q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universalR matrix ofU q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Frønsdal's findings. This construction entails that, for generic values of the deformation parameters, the representation theory forU q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebraA q,p ( $$\widehat{\mathfrak{s}\mathfrak{l}}_2 $$ ).
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    A convexity theorem for noncommutative gradient flows (1999)
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    Transformation groups 4 (1999), S. 375-404 
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    Notes: Abstract In this survey we shall prove a convexity theorem for gradient actions of reductive Lie groups on Riemannian symmetric spaces. After studying general properties of gradient maps, this proof is established by (1) an explicit calculation on the hyperbolic plane followed by a transfer of the results to general reductive Lie groups, (2) a reduction to a problem on abelian spaces using Kostant's Convexity Theorem, (3) an application of Fenchel's Convexity Theorem. In the final section the theorem is applied to gradient actions on other homogeneous spaces and we show, that Hilgert's Convexity Theorem for moment maps can be derived from the results.
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    Estimates, decay properties, and computation of the dual function for Gabor frames (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 545-562 
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    Keywords: 42C15 ; Weyl-Heisenberg frame ; dual window ; spline
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    Notes: Abstract We present a simple proof of Ron and Shen's frame bounds estimates for Gabor frames. The proof is based on the Heil and Walnut's representation of the frame operator and shows that it can be decomposed into a continuous family of infinite matrices. The estimates then follow from a simple application of Gershgorin's theorem to each matrix. Next, we show that, if the window function has exponential decay, also the dual function has some exponential decay. Then, we describe a numerical method to compute the dual function and give an estimate of the error. Finally, we consider the spline of order 2; we investigate numerically the region of the time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.
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    Gibbs phenomenon on sampling series based on Shannon's and Meyer's wavelet analysis (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 575-588 
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    Keywords: 42C15 ; 94A12 ; sampling ; multiresolution analysis ; Gibbs phenomenon
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    Notes: Abstract We deal with the maximum Gibbs ripple of the sampling wavelet series of a discontinuous function f at a point t ∈R, for all possible values of a satisfyingf(t)=αf(t−0)+(1−a)f(t+0). For the Shannon wavelet series, we make a complete description of all ripples, for any a in [0,1]. We show that Meyer sampling series exhibit Gibbs Phenomenon for α〈0.12495 and α〉0.306853. We also give Meyer sampling formulas with maximum overshoots shorter than Shannon's for several α in [0,1].
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    The journal of Fourier analysis and applications 5 (1999), S. v 
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    Convergence and summability of Gabor expansions at the Nyquist density (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 127-157 
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    Keywords: Primary 30D10 ; 42C30 ; Secondary 40G99 ; 41A58 ; 94A12
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    Notes: Abstract It is well known that Gabor expansions generated by a lattice of Nyquist density are numerically unstable, in the sense that they do not constitute frame decompositions. In this paper, we clarify exactly how “bad” such Gabor expansions are, we make it clear precisely where the edge is between “enough” and “too little,” and we find a remedy for their shortcomings in terms of a certain summability method. This is done through an investigation of somewhat more general sequences of points in the time-frequency plane than lattices (all of Nyquist density), which in a sense yields information about the uncertainty principle on a finer scale than allowed by traditional density considerations. An important role is played by certain Hilbert scales of function spaces, most notably by what we call the Schwartz scale and the Bargmann scale, and the intrinsically interesting fact that the Bargmann transform provides a bounded invertible mapping between these two scales. This permits us to turn the problems into interpolation problems in spaces of entire functions, which we are able to treat.
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    A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical (1999)
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    Transformation groups 4 (1999), S. 35-52 
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    Notes: Abstract LetG be a classical algebraic group defined over an algebraically closed field. We classify all instances when a parabolic subgroupP ofG acts on its unipotent radicalP u , or onp u , the Lie algebra ofP u , with only a finite number of orbits. The proof proceeds in two parts. First we obtain a reduction to the case of general linear groups. In a second step, a solution for these is achieved by studying the representation theory of a particular quiver with certain relations. Furthermore, for general linear groups we obtain a combinatorial formula for the number of orbits in the finite cases.
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    Traces of oscillating functions (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 331-345 
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    Keywords: 26B35 ; 42B05 ; 42B99 ; chirp ; oscillating function
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    Notes: Abstract We show that the trace of an indefinitely oscillating function on a subspace of ℝd is not always indefinitely oscillating. In the periodic case, the number of oscillations of the trace depends on the regularity of the function. In the general case, we exhibit a definitive counter-example.
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    Spectral radius properties for layer potentials associated with the elastostatics and hydrostatics equations in nonsmooth domains (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 385-408 
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    Keywords: Primary: 45E05, 47A10 ; Secondary: 35J25, 42B20 ; layer potentials ; spectral radius ; polyhedra ; Lipschitz domains
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    Notes: Abstract By producing a L2 convergent Neumann series, we prove the invertibility of the elastostatics and hydrostatics boundary layer potentials on arbitrary Lipschitz domains with small Lipschitz character and 3D polyhedra with large dihedral angles.
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    Localization and convergence of eigenfunction expansions (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 431-447 
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    Keywords: Eigenfunction expansions ; localization ; Primary: 42C14 ; Secondary: 42B08
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    Notes: Abstract We state a localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator and we prove an equiconvergence result between eigenfunction expansions and trigonometric expansions. We then study the Gibbs phenomenon for eigenfunction expansions of piecewise smooth functions on two-dimensional manifolds.
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    Analytic and asymptotic properties of non-symmetric Linnik's probability densities (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 523-544 
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    Keywords: primary 62H05 ; 60E10 ; secondary 32E25 ; Cauchy type integral ; characteristic function ; completely monotonicity ; Liouville numbers ; Plemelj-Sokhotskii formula ; unimodality
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    Notes: Abstract The function $$\varphi _\alpha ^\theta (t) = \frac{1}{{1 + e^{ - i\theta \operatorname{s} gnt} \left| t \right|^\alpha }},\alpha \in (0,2),\theta \in ( - \pi ,\pi ]$$ , is a characteristic function of a probability distribution iff $$\left| \theta \right| \leqslant \min (\tfrac{{\pi \alpha }}{2},\pi - \tfrac{{\pi \alpha }}{2})$$ . This distribution is absolutely continuous; for θ=0 it is symmetric. The latter case was introduced by Linnik in 1953 [13] and several applications were found later. The case θ≠0 was introduced by Klebanov, Maniya, and Melamed in 1984 [9], while some special cases were considered previously by Laha [12] and Pillai [18]. In 1994, Kotz, Ostrovskii and Hayfavi [10] carried out a detailed investigation of analytic and asymptotic properties of the density of the distribution for the symmetric case θ=0. We generalize their results to the non-symmetric case θ≠0. As in the symmetric case, the arithmetical nature of the parameter α plays an important role, but several new phenomena appear.
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    Multivariate nonhomogeneous refinement equations (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 589-597 
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    Keywords: 42C15 ; 39B99 ; multivariate ; nonhomogeneous ; refinement
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract We give necessary and sufficient conditions for the existence and uniqueness of compactly supported distribution solutionsf=(f 1,...,f r)T of nonhomogeneous refinement equations of the form $$f(x) = h(x) + \sum\limits_{\alpha \in A} {c_\alpha f(2x - \alpha )(x \in R^s )} $$ , where h=(h1,...,hr)Tis a compactly supported vector-valued multivariate distribution, A⊂Z+ s has compact support, and the coefficientsc α are real-valued r×r matrices. In particular, we find a finite dimensional matrix B, constructed from the coefficientsc α of the equation (I−B)q=p, where the vectorp depends on h. Our proofs proceed in the time domain and allow us to represent each solution regardless of the spectral radius of P(0):=2−s∑c α , which has been a difficulty in previous investigations of this nature.
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    Rates of convergence for the approximation of dual shift-invariant systems in ℓ2(ℤ) (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 599-615 
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    ISSN: 1531-5851
    Keywords: 41A25 ; 42C15 ; 47B35 ; 15A99 ; shift-invariant systems ; finite section method ; block Toeplitz matrices ; Laurent operator ; Gabor frame ; filter banks ; band matrices
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract A shift-invariant system is a collection of functions {gm,n} of the form gm,n(k)=gm(k−an). Such systems play an important role in time-frequency analysis and digital signal processing. A principal problem is to find a dual system γm,n(k)=γm(k−an) such that each functionf can be written asf= ∑〈f, γm,n〉gm,n. The mathematical theory usually addresses this problem in infinite dimensions (typically in L2 (ℝ) or ℓ2(ℤ)), whereas numerical methods have to operate with a finite-dimensional model. Exploiting the link between the frame operator and Laurent operators with matrix-valued symbol, we apply the finite section method to show that the dual functions obtained by solving a finite-dimensional problem converge to the dual functions of the original infinite-dimensional problem in ℓ2(ℤ). For compactly supported gm, n (FIR filter banks) we prove an exponential rate of convergence and derive explicit expressions for the involved constants. Further we investigate under which conditions one can replace the discrete model of the finite section method by the periodic discrete model, which is used in many numerical procedures. Again we provide explicit estimates for the speed of convergence. Some remarks on tight frames complete the paper.
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    Actions of compact groups on coherent sheaves (1999)
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    Transformation groups 4 (1999), S. 25-34 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider actions of compact real Lie GroupsK on complex spacesX such that the associated reducedK-space admits a semistable quotient, e.g.X is a Stein space. We show that there is a complex spaceX c endowed with a holomorphic action of the universal complexificationG ofK that containsX as an openK-stable subset. As our main result, we prove that every coherentK-sheaf onX extends uniquely to a holomorphicG-sheaf onX c .
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    An infinitesimal characterization of the complexity of homogeneous spaces (1999)
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    Transformation groups 4 (1999), S. 97-101 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A characterization of the complexity of a homogeneous space $$\mathcal{O}$$ of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of $$\mathcal{O}$$ and the (−1)-eigenspace of a Weyl involution of $$\mathcal{O}$$ .
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    Chevalley: Some reminiscences (1999)
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    Transformation groups 4 (1999), S. 119-125 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
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    Structure of some ℤ-graded lie superalgebras of vector fields (1999)
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    Transformation groups 4 (1999), S. 219-272 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we classifyℤ-graded transitive Lie superalgebras with prescribed nonpositive parts listed in [K2]. The classification of infinite-dimensional simple linearly compact Lie superalgebras given in [K2] is based on this result. We also study the structure of the exceptionalℤ-graded transitive Lie superalgebras and give their geometric realization.
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    The size of a hyperbolic Coxeter simplex (1999)
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    Transformation groups 4 (1999), S. 329-353 
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    ISSN: 1531-586X
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    Notes: Abstract We determine the covolumes of all hyperbolic Coxeter simplex reflection groups. These groups exist up to dimension 9. the volume computations involve several different methods according to the parity of dimension, subgroup relations and arithmeticity properties.
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    Th1/Th2 differentiation and cross-regulation (1999)
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    Bulletin of mathematical biology 61 (1999), S. 403-436 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The T helper (Th) phenotypes, Th1/Th2, are acquired upon interaction of a naive T helper cell and an antigen presenting cell (APC). Naive T helper cells may differentiate into either phenotype, and the actual outcome is determined by the density and avidity of the antigenic determinants presented by the APC, and the APCs inherent costimulatory properties. Until recently it was thought that differentiation is further affected by cytokines. However, Murphy et al. (1996, J. Exp. Med. 183, 901) have demonstrated that the experimental results, formerly interpreted as Th1/Th2 differentiation, in effect comprise an observation of two consecutive processes. (i) An interaction between naive T cells and APC creates a mixture of mature cells irreversibly committed to Th1 or Th2 phenotype. (ii) Subsequent addition of regulatory cytokines, promotes expansion of one phenotype while suppressing the other. The consequent shift in the per culture production of marker cytokines mimics the appearance of a cellular phenotype switch. We present and analyse a mathematical model that extrapolates these experimental facts into systemic behavior during an immune response. Despite the fact that differentiation produces cells of Th1 and Th2 phenotypes with the same receptor specificity, our results indicate that competition for antigenic stimulation, mediated by the APCs, combines with cytokine mediated cross-suppression between phenotypes to yield a response that is eventually dominated by T helper cells that are uniform in both receptor specificity (clonotype) and in cytokine secretion phenotype.
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    URL: http://dx.doi.org/10.1006/bulm.1998.0074
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    A two-dimensional numerical study of spatial pattern formation in interacting Turing systems (1999)
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    Bulletin of mathematical biology 61 (1999), S. 483-505 
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    ISSN: 1522-9602
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    Notes: Abstract For many years Turing systems have been proposed to account for spatial and spatiotemporal pattern formation in chemistry and biology. We extend the study of Turing systems to investigate the rôle of boundary conditions, domain shape, non-linearities, and coupling of such systems. We show that such modifications lead to a wide variety of patterns that bear a striking resemblance to pigmentation patterns in fish, particularly those involving stripes, spots and transitions between them. Using the Turing system as a metaphor for activator—inhibitor models we conclude that such a mechanism, with the aforementioned modifications, may play a rôle in fish patterning.
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    URL: http://dx.doi.org/10.1006/bulm.1998.0093
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    The effect of heterogeneously-distributed RyR channels on calcium dynamics in cardiac myocytes (1999)
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    Bulletin of mathematical biology 61 (1999), S. 651-681 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Calcium plays an essential role in excitation-contraction coupling in muscle, and derangements in calcium handling can produce a variety of potentially harmful conditions, especially in cardiac muscle. In cardiac tissue specialized invaginations of the sarcolemma, called T-tubules, penetrate deep into each sarcomere, and depolarization of the SL leads to an influx of calcium through voltage-sensitive channels in the T-tubules that in turn triggers further calcium release from the sarcoplasmic reticulum via ryanodine-sensitive calcium channels. Under certain conditions, such as elevated external Ca2+, cardiac cells can release calcium from the sarcoplasmic reticulum spontaneously, producing a calcium ’spark’ and propagating traveling waves of elevated Ca2+ concentration, without depolarization of the SL (Wier and Blatter, 1991a, Cell Calcium 12, 241–254; Williams, 1993, Cell Calcium 14, 724–735; Cheng et al., 1993a, Science 262, 740–744). However, under normal resting conditions these potentially harmful waves seldom occur. In this paper we investigate the role of the periodic distribution of ryanodine-sensitive channels in determining whether a spark can trigger a wave, using a modification of the kinetic model proposed by Tang and Othmer, 1994b, Biophys. J. 67, 2223–2235, for calcium-induced calcium release. We show that the spatial localization of these channels near the T-tubules has a significant effect on both wave propagation and the onset of oscillations in this system. Spatial localization provides a possible explanation for the differing effects of various experimental protocols on the system’s ability to propagate a traveling wave.
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    Bayesian predictive identification and cumulative classification of bacteria (1999)
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    Bulletin of mathematical biology 61 (1999), S. 85-111 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract In this paper we give a mathematically precise formulation of an old idea in bacterial taxonomy, namely cumulative classification, where the taxonomy is continuously updated and possibly augmented as new strains are identified. Our formulation is based on Bayesian predictive probability distributions. The criterion for founding a new taxon is given a firm theoretical foundation based on prediction and it is given a clear-cut interpretation. We formulate an algorithm for cumulative classification and apply it to a large database of bacteria belonging to the family Enterobacteriaceae. The resulting taxonomy makes microbiological sense.
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    URL: http://dx.doi.org/10.1006/bulm.1998.0076
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    Models of classical conditioning (1999)
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    Bulletin of mathematical biology 61 (1999), S. 33-83 
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    ISSN: 1522-9602
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    Notes: Abstract Classical conditioning is a basic form of associative learning in the animal kingdom. Many paradigmatic features of classical conditioning appear to be conserved throughout species and phyla and are independent of stimulus nature. This paper presents an analysis of trial-based and real-time models of classical conditioning which are mathematical abstractions of the underlying processing principles. Various models are reviewed and in a formal analysis, their capability of simulating and explaining classical conditioning is investigated. Since every existing model fails to simulate some particular conditioning phenomena and since some modelling approaches are not appropriate for detailed mathematical analysis, new model components will be introduced that overcome most of the weaknesses observed in the other models.
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    URL: http://dx.doi.org/10.1006/bulm.1998.9998
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    Book reviews (1999)
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    Bulletin of mathematical biology 61 (1999), S. 399-401 
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    URL: http://dx.doi.org/10.1006/bulm.1998.0079
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    Threshold parameters and metapopulation persistence (1999)
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    Bulletin of mathematical biology 61 (1999), S. 341-353 
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    Notes: Abstract A method is presented to estimate the minimum viable metapopulation size based on the basic reproductive number R 0 and the expected time to extinction τ E for epidemiological models. We exemplify our approach with two simple deterministic metapopulation models of the patch occupancy type and then proceed to stochastic versions that permit the estimation of the minimum viable metapopulation size.
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    Evolution of migration in a metapopulation (1999)
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    Bulletin of mathematical biology 61 (1999), S. 531-550 
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    ISSN: 1522-9602
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    Notes: Abstract In this paper a general deterministic discrete-time metapopulation model with a finite number of habitat patches is analysed within the framework of adaptive dynamics. We study a general model and prove analytically that (i) if the resident populations state is a fixed point, then the resident strategy with no migration is an evolutionarily stable strategy, (ii) a mutant population with no migration can invade any resident population in a fixed point state, (iii) in the uniform migration case the strategy not to migrate is attractive under small mutational steps so that selection favours low migration. Some of these results have been previously observed in simulations, but here they are proved analytically in a general case. If the resident population is in a two-cyclic orbit, then the situation is different. In the uniform migration case the invasion behaviour depends both on the type of the residents attractor and the survival probability during migration. If the survival probability during migration is low, then the system evolves towards low migration. If the survival probability is high enough, then evolutionary branching can happen and the system evolves to a situation with several coexisting types. In the case of out-of-phase attractor, evolutionary branching can happen with significantly lower survival probabilities than in the in-phase attractor case. Most results in the two-cyclic case are obtained by numerical simulations. Also, when migration is not uniform we observe in numerical simulations in the two-cyclic orbit case selection for low migration or evolutionary branching depending on the survival probability during migration.
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    Determination of the true intraocular pressure and modulus of elasticity of the human cornea in vivo (1999)
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    Bulletin of mathematical biology 61 (1999), S. 551-572 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The purpose of this study was to determine the true intraocular pressure and modulus of elasticity of the human cornea in vivo. The cornea was modeled as a shell, and the equations for the deformations of a shell due to applanating and intraocular pressures were combined to model the behavior of the cornea during applanation tonometry. At certain corneal dimensions called the calibration dimensions, the applanating and intraocular pressures are considered to be equal. This relationship was used to determine the modulus of elasticity of the cornea and the relationship between the applanating and intraocular pressures. The true intraocular pressure (IOPT) was found to be related to Goldmann’s applanating pressure (IOPG) as (IOPT = IOPG/K, where K is a correction factor. For the calibration corneal thickness of 0.52 mm, the modulus of elasticity E in MPa of the human cornea was found to be related to the true intraocular pressure IOPT in mmHg as E = 0.0229IOPT. The generalization of the Imbert—Fick law that takes into account the effect of corneal dimensions and stiffness was found to be given by IOPT = 73.5W/(K A), where W is the applanating weight in gf (gram force) and A is the applanated area in mm2. The calculated true intraocular pressure and modulus of elasticity were found to agree with published experimental results. The mathematical model developed may therefore be used to improve results from applanation tonometry and to estimate the mechanical property of the cornea in vivo.
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    URL: http://dx.doi.org/10.1006/bulm.1999.0102
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    A model of survival times for predator populations: The case of the army ants (1999)
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    Bulletin of mathematical biology 61 (1999), S. 469-482 
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    Notes: Abstract We develop a method to estimate the expected time of survival of a predator population as a function of the size of the habitat island on which it lives and the dynamic parameters of the population and its prey. The model may be thought of either as a patch occupancy model for a structured population or as a model of metapopulation type. The method is applied to a keystone predator species, the neotropical army ant Eciton burchelli. Predictions are made as to how many of the islands and habitat islands in and around Gatun Lake in the Panama Canal, most of which were formed when the canal was dug, can be expected to support such a population today, and these are compared with data.
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    URL: http://dx.doi.org/10.1006/bulm.1998.0091
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    Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5-trisphosphate signal in a model for intracellular Ca2+ oscillations (1999)
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    Bulletin of mathematical biology 61 (1999), S. 507-530 
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    Notes: Abstract We investigate the various types of complex Ca2+ oscillations which can arise in a model based on the mechanism of Ca2+-induced Ca2+ release (CICR), that takes into account the Ca2+-stimulated degradation of inositol 1,4,5-trisphosphate (InsP3) by a 3-kinase. This model was previously proposed in the course of an investigation of plausible mechanisms capable of generating complex Ca2+ oscillations (Borghans et al., 1997). Besides simple periodic behavior, this model for cytosolic Ca2+ oscillations in nonexcitable cells shows complex oscillatory phenomena like bursting or chaos. We show that the model also admits a coexistence between two stable regimes of sustained oscillations (birhythmicity). The occurrence of these various modes of oscillatory behavior is analysed by means of bifurcation diagrams. Complex oscillations are characterized by means of Poincaré sections, power spectra and Lyapounov exponents. The results point to the role of self-modulation of the InsP3 signal by 3-kinase as a possible source for complex temporal patterns in Ca2+ signaling.
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    Dominance orders in animal societies: The self-organization hypothesis revisited (1999)
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    Bulletin of mathematical biology 61 (1999), S. 727-757 
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    ISSN: 1522-9602
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    Notes: Abstract In previous papers (Theraulaz et al., 1995; Bonabeau et al., 1996) we suggested, following Hogeweg and Hesper (1983, 1985), that the formation of dominance orders in animal societies could result from a self-organizing process involving a double reinforcement mechanism: winners reinforce their probability of winning and losers reinforce their probability of losing. This assumption, and subsequent models relying on it, were based on empirical data on primitively eusocial wasps (Polistes dominulus). By reanalysing some of the experimental data that was previously thought to be irrelevant, we show that it is impossible to distinguish this assumption from a competing assumption based on preexisting differences among individuals. We propose experiments to help discriminate between the two assumptions and their corresponding models—the self-organization model and the correlational model. We urge other researchers to be cautious when interpreting their dominance data with the ’self-organization mindset’; in particular, ‘winner and loser effects’, which are often considered to give support to the self-organization assumption, are equally consistent with the correlational assumption.
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    Hypoxia and reoxygenation: A pressure for mutant p53 cell selection and tumour progression (1999)
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    Bulletin of mathematical biology 61 (1999), S. 759-778 
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    Notes: Abstract Recent findings indicate that in a hypoxic environment, oncogenically transformed cells with a mutant form of the tumour suppressor gene p53 may have a survival advantage over similar cells with wild-type p53. This is because the extent of hypoxia-induced apoptosis has been observed to diminish with the loss of wild-type p53 function in certain cell lines. Hypoxic conditions, common in most solid tumours, may thus provide a physiological pressure to select for cells with mutations in the p53 gene. A new model incorporating cell-specific parameters is proposed here to quantify the survival advantage of mutant or null p53 cells over their wild-type counterparts at any level of oxygen deprivation. Predictions are in good agreement with previous monolayer culture experiments comparing hypoxic survival of null and wild-type p53 cells. By extending the model we are able to investigate the effects of repeated rounds of hypoxia and reoxygenation on a mixture of wild-type and mutant or null p53 cells and determine how many rounds are required before a subpopulation of mutant or null p53 cells overtakes a given population of wild-type p53 cells.
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    Non-standard numerical methods applied to subsurface biobarrier formation models in porous media (1999)
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    Bulletin of mathematical biology 61 (1999), S. 779-798 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Biofilm forming microbes have complex effects on the flow properties of natural porous media. Subsurface biofilms have the potential for the formation of biobarriers to inhibit contaminant migration in groundwater. Another example of beneficial microbial effects is the biotransformation of organic contaminants to less harmful forms, thereby providing an in situ method for treatment of contaminated groundwater supplies. Mathematical models that describe contaminant transport with biodegradation involve a set of coupled convection-dispersion equations with non-linear reactions. The reactive solute transport equation is one for which numerical solution procedures continue to exhibit significant limitations for certain problems of groundwater hydrology interest. Accurate numerical simulations are crucial to the development of contaminant remediation strategies. A new numerical method is developed for simulation of reactive bacterial transport in porous media. The non-standard numerical approach is based on the ideas of the ‘exact’ time-stepping scheme. It leads to solutions free from the numerical instabilities that arise from incorrect modeling of derivatives and reaction terms. Applications to different biofilm models are examined and numerical results are presented to demonstrate the performance of the proposed new method.
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    URL: http://dx.doi.org/10.1006/bulm.1999.0113
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    Analytic models for the patchy spread of plant disease (1999)
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    Bulletin of mathematical biology 61 (1999), S. 849-874 
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    Notes: Abstract Plant epidemiologists have long been concerned with the patchy nature of plant disease epidemics. This paper presents a new analytical model for patchy plant epidemics (and patchy dynamics in general), using a second-order approximation to capture the spatial dynamics in terms of the densities and spatial covariances of healthy and infected hosts. Using these spatial moment equations helps us to explain the dynamic growth of patchiness during the early phase of the epidemic, and how the patchiness feeds back on the growth rate of the epidemic. Both underlying heterogeneity in the host spatial arrangement and dynamically generated heterogeneity in the spatial arrangement of infected plants initially accelerate but later decelerate the epidemic.
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    The pathogenesis of normal pressure hydrocephalus: A theoretical analysis (1999)
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    Bulletin of mathematical biology 61 (1999), S. 875-916 
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    Notes: Abstract Hydrocephalus is an abnormal accumulation of cerebrospinal fluid (CSF) in the cerebral ventricles, usually caused by impaired absorption of the fluid into the bloodstream. Despite obstructed absorption and continued secretion of CSF into the ventricles at a near normal rate, the ventricular CSF pressure (VCSFP) is often normal. We attempt to understand how hydrocephalus can exist with normal VCSFP by exploring the role of the brain parenchyma in absorbing CSF in hydrocephalus. We test three theories: (1) the ventricular wall is impermeable to CSF; (2) ventricular CSF seeps into the parenchyma, from which it is efficiently absorbed; and (3) ventricular CSF seeps into the parenchyma but is absorbed inefficiently. We model the brain as a thick spherical shell consisting of a porous, elastic, solid matrix, containing interstitial fluid and blood. We modify the equations of poroelasticity, which describe flow of fluid through porous solids, to allow for parenchymal absorption. For each of the three theories we calculate the steady state changes in VCSFP and in parenchymal fluid pressure caused by an incremental defect in CSF absorption. We also calculate the steady state changes in fluid content, tissue volume, tissue displacement, and stresses caused by a small increment of VCSFP. We conclude that only the second theory—seepage of CSF with efficient parenchymal absorption—accounts for the clinical features of normal pressure hydrocephalus. These features include sustained ventricular dilatation despite normal VCSFP, increased periventricular fluid content, and localized periventricular white matter damage.
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    A theoretical experimental method to determine the locus of desensitization (1999)
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    Bulletin of mathematical biology 61 (1999), S. 963-986 
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    Notes: Abstract Consider a ligand-gated channel with n agonist binding sites which can undergo desensitization. We present a theoretical experimental procedure for pinpointing the principal receptor state from which there is a transition to the desensitized state. The method is based on the observation that the dependence of the slope of the time constant of desensitization vs agonist concentration, at low concentrations, represents the state from which desensitization occurs. In those receptors where desensitization occurs from the open state (or the one immediately preceding it), the method also enables us to determine the number of binding sites.
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    Diffusively coupled bursters: Effects of cell heterogeneity (1999)
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    Bulletin of mathematical biology 61 (1999), S. 1017-1017 
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    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1006/bulm.1999.0125
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