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  • Springer  (61,770)
  • American Physical Society  (12,247)
  • 2005-2009
  • 1995-1999  (74,017)
  • 1997  (74,017)
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  • 2005-2009
  • 1995-1999  (74,017)
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  • 1
    Electronic Resource
    Electronic Resource
    Adaptive superparasitism and host-parasitoid dynamics (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 23-41 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider a host-solitary parasitoid system with three categories of individuals: parasitoids, healthy hosts and parasitized hosts. Parasitoids are assumed to discriminate perfectly between the two kinds of hosts and they can reject those which are already parasitized. If parasitoids systematically accept or reject superparasitism or behave randomly, the system is always unstable. Using an optimal foraging model, we determine the behavior of parasitoids which leads to maximization of the instantaneous reproductive rate. When following this adaptive decision rule, parasitoids accept or refuse superparasitism according to the densities of both healthy and parasitized hosts. We study the dynamics of the system when parasitoids follow the optimal rule and show that under certain conditions it possesses a locally stable equilibrium point. In addition, our model predicts that at equilibrium parasitoids show partial preferences for superparasitism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459469
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  • 2
    Electronic Resource
    Electronic Resource
    Chemotherapeutic treatments: A study of the interplay among drug resistance, toxicity and recuperation from side effects (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 205-232 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of differential equations for the control of tumor growth cells in a cycle nonspecific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account, and a criterion for the selection of chemotherapeutic treatment is used. This criterion purports to describe the possibility of improvement of the patient's health when treatment is discontinued. Contrary to our early results which also take drug resistance into account, in this context strategies of continuous chemotherapy in which rest periods take part may be better than maximum drug concentration throughout the treatment (which appears to be in accordance with clinical practice). This bears out our previous conjecture that when drug resistance is accounted for, the imperfections in the usual modelling of treatment criteria, which in general do not allow for patient recuperation, ruled out the possibility of rest periods in optimal continuous chemotherapy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462001
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  • 3
    Electronic Resource
    Electronic Resource
    Matrix population model with density-dependent recruitment for assessment of age-structured wildlife populations (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 255-262 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A logistic density-dependent matrix model is developed in which the matrices contain only parameters and recruitment is a function of adult population density. The model was applied to simulate introductions of white-tailed deer into an area; the fitted model predicted a carrying capacity of 215 deer, which was close to the observed carrying capacity of 220 deer. The rate of population increase depends on the dominant eigenvalue of the Leslie matrix, and the age structure of the simulated population approaches a stable age distribution at the carrying capacity, which was similar to that generated by the Leslie matrix. The logistic equation has been applied to study many phenomena, and the matrix model can be applied to these same processes. For example, random variation can be added to life history parameters, and population abundances generated with random effects on fecundity show both the affect of annual variation in fecundity and a longer-term pattern resulting from the age structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462003
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  • 4
    Electronic Resource
    Electronic Resource
    Book reviews (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 399-406 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462008
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  • 5
    Electronic Resource
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    Conflicting objectives in chemotherapy with drug resistance (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 707-724 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic treatment. For general cell growth, some results are given, whereas for the special case of Malthusian (exponential) growth of tumor cells and rather general growth rate for normal cells, the optimal strategy is worked out. The latter, from the clinical standpoint, corresponds to maximum drug concentration throughout the treatment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458426
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  • 6
    Electronic Resource
    Electronic Resource
    Book reviews (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 787-807 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458430
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  • 7
    Electronic Resource
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    Dynamical consequences of optimal host feeding on host-parasitoid population dynamics (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 809-831 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This study examines the influence of various host-feeding patterns on host-parasitoid population dynamics. The following types of host-feeding patterns are considered: concurrent and non-destructive, non-concurrent and non-destructive, and non-concurrent and destructive. The host-parasitoid population dynamics is described by the Lotka-Volterra continuous-time model. This study shows that when parasitoids behave optimally, i.e. they maximize their fitness measured by the instantaneous per capita growth rate, the non-destructive type of host feeding stabilizes host-parasitoid dynamics. Other types of host feeding, i.e. destructive, concurrent, or non-concurrent, do not qualitatively change the neutral stability of the Lotka-Volterra model. Moreover, it is shown that the pattern of host feeding which maximizes parasitoid fitness is either non-concurrent and destructive, or concurrent and non-destructive host feeding, depending on the host abundance and parameters of the model. The effects of the adaptive choice of host-feeding patterns on host-parasitoid population dynamics are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459994
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  • 8
    Electronic Resource
    Electronic Resource
    Multi-player matrix games (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 931-952 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Game theory has had remarkable success as a framework for the discussion of animal behaviour and evolution. It suggested new interpretations and prompted new observational studies. Most of this work has been done with 2-player games. That is the individuals of a population compete in pairwise interactions. While this is often the case in nature, it is not exclusively so. Here we introduce a class of models for situations in which more than two (possibly very many) individuals compete simultaneously. It is shown that the solutions (i.e. the behaviour which may be expected to be observable for long periods) are more complex than for 2-player games. The concluding section lists some of the new phenomena which can occur.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460000
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  • 9
    Electronic Resource
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    The “clustered structure” of the purines/pyrimidines distribution in DNA distinguishes systematically between coding and non-coding sequences (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 975-992 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method allowing to measure the inhomogeneous distribution of purines/pyrimidines in nucleotide sequences is developed. We show that this measure relates to the coding or non-coding character of the considered sequence. Coding sequences present a near to the random Pu or Py distribution. This property is shared by both protein-coding DNA and functional RNA-coding DNA. Non-coding sequences present a highly clustered inhomogeneity. We propose the hypothesis, corroborated with appropriate computer simulations, that this is due to the action of various transposition events accumulated for long time periods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460002
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  • 10
    Electronic Resource
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    Quantal currents and potential in the three-dimensional anisotropic bidomain model of smooth muscle (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1047-1075 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The potential generated in the smooth muscle of the vas deferens on release of a quantum of transmitter from a varicosity was analyzed using a three-dimensional bidomain continuum model. Current was injected at the origin of the bidomain; this current had the temporal characteristics of the junctional current. The membrane potential, intracellular potential, and extracellular potential, as well as the extracellular current, were then calculated throughout the bidomain at different times. Calculations were performed to show the effect of changing the anisotropy ratios of the intracellular and extracellular conductivities on the spread of current and potential in each of the three dimensions. These results provide a theoretical framework for ascertaining the time course of transmitter interaction at a varicosity following the secretion of a quantum of transmitter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460101
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  • 11
    Electronic Resource
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    An extremum principle for parabolic competition (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1145-1154 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Parabolic growth invariably results in the survival of all competing types. Under the constraint of constant total concentration, there is a unique equilibrium in the simplex interior, which is asymptotically stable inside the whole simplex. The appropriate Lyapunov function is obtained in terms of the excess productivity which is shown to be maximized for the competitive system with fractional order kinetics. Claims to the contrary are refuted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460105
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  • 12
    Electronic Resource
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    Book reviews (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1191-1201 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460108
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  • 13
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    Understanding drug resistance for monotherapy treatment of HIV infection (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 763-785 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The purpose of this study was to investigate strategies in the monotherapy treatment of HIV infection in the presence of drug-resistant (mutant) strains. A mathematical system is developed to model resistance in HIV chemotherapy. It includes the key players in the immune response to HIV infection: virus and both uninfected CD4+ and infected CD4+ T-cell populations. We model the latent and progressive stages of the disease, and then introduce monotherapy treatment. The model is a system of differential equations describing the interaction of two distinct classes of HIV—drug-sensitive (wild type) and drug-resistant (mutant)—with lymphocytes in the peripheral blood. We then introduce chemotherapy effects. In the absence of treatment, the model produces the three types of qualitative clinical behavior—anuninfected steady state, andinfected steady state (latency), andprogression to AIDS. Simulation of treatment is provided for monotherapy, during theprogression to AIDS state, in the consideration of resistance effects. Treatment benefit is based on an increase or retention in CD4+ T-cell counts together with a low viral titer. We explore the following treatment approaches: an antiviral drug which reduces viral infectivity that is administered early—when the CD4+ T-cell count is ≥300/mm3, and late—when the CD4+ T-cell count is less than 300/mm3. We compare all results with data. When treatment is initiated during the progression to AIDS state, treatment prevents T-cell collapse, but gradually loses effectiveness due to drug resistance. We hypothesize that it is the careful balance of mutant and wild-type HIV strains which provides the greatest prolonged benefit from treatment. This is best achieved when treatment is initiated when the CD4+ T-cell counts are greater than 250/mm3, but less than 400/mm3 in this model (i.e. not too early, not too late). These results are supported by clinical data. The work is novel in that it is the first model to accurately simultate data before, during and after monotherapy treatment. Our model also provides insight into recent clinical results, as well as suggests plausible guidelines for clinical testing in the monotherapy of HIV infection.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458429
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  • 14
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    Mathematical modeling of adhesion of bacteria to host cell lines (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 833-856 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model which describes adhesion of bacteria to host cell lines is presented. The model is flexible enough to account for the following situations: extracellular bacteria are either in exponential or in stationary phase. Adhesion is described as a reversible binding process in which the bacteria attach to or detach from specific receptors uniformly distributed on the cell surface. In turn, attached bacteria can either replicate or, conversely, they are restrained to remain in stationary phase. In the first case, however, we must consider the problem of whether the decrease of unoccupied receptors as adhesion progresses imposes a limit to the replicating capacity of the attached bacteria. The effect exerted by the multiplicity of infection (MOI), i.e. the ratio of the number of bacteria to the number of host cells, on the process of adhesion is also contemplated by the model. This has revealed that experiments performed at the same values of MOI can show completely different levels of adhered bacteria, depending on the number of host cells in the assays. This finding demonstrates that the report of the MOI values is insufficient to characterize comparative studies of bacterial adhesion since it could lead to a misunderstanding of the corresponding data. Simplified models based on the steady-state approximation and in equilibrium analysis by means of a Lagmuir adsorption isotherm for the attached bacteria are also discussed. This allows us to define the adhesion coefficient (β) in a given bacterium-cell system so that, with the exception of those systems where these coefficients cannot be defined, larger values of β are related to a greater adhesion capacity. An overview of the procedures to perform quantitative adhesion data analysis is outlined. Finally, theoretical predictions are compared with experimental results from the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459995
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  • 15
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    A new measure of xenobiotic toxicity to the first-line human defence system from the time-resolved phagocyte luminescence (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 897-910 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new measure of toxicity based on stochastic modelling of single photon-counting processes, representing time-resolved phagocyte luminescence of xenobiotic-perturbed human neutrophils, has been constructed. The stochastic measure of toxicity has been verified by the QSAR method, and then compared and contrasted with the traditional toxicity measure used in bio- and chemiluminescent research. Phenol and benzene homologues were chosen as perturbers due to their importance from the viewpoint of ecotoxicology and occupational medicine.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459998
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  • 16
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    Dynamics of human milk extraction: A comparative study of breast feeding and breast pumping (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 953-973 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suction only. Our model is based on quasi-linear poroelasticity whereby the teat is modelled as a cylindrical porous elastic material saturated with fluid. We impose a cyclic axial suction pressure difference across the teat and impose a radial compressive force moving along the teat which mimics infant suckling. This is compared to the case of cyclic and steady pumping only which models the action of breast pumps. The results illustrate that there is an optimal time to apply the compressive force during the suction cycle that will increase the flow rate in our theoretical teat. The model and results may be of use in the future design of effective breast pumps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460001
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  • 17
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    The effect of shear stress on solitary waves in arteries (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 993-1012 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materals are depicted in graphical forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissues.
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    URL: http://dx.doi.org/10.1007/BF02460003
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  • 18
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    Role of fibroblast migration in collagen fiber formation during fetal and adult dermal wound healing (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1077-1100 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Adult dermal wounds, in contrast to fetal wounds, heal with the formation of scar tissue. A crucial factor in determining the degree of scarring is the ratio of types I and III collagen, which regulates the diameter of the combined fibers. We developed a reaction-diffusion model which focuses on the control of collagen synthesis by different isoforms of the polypeptide transforming growth factor-β (TGFβ). We used the model to investigate the current controversy as to whether the fibroblasts migrate into the wound from the surrounding unwounded dermis or from the underlying subcutaneous tissue. Numerical simulations of a spatially independent, temporal model led to a value of the collagen ratio consistent with that of healthy tissue for the fetus, but corresponding to scarring in the adult. We investigated the effect of topical application of TGFβ and show that addition of isoform 3 reduces scar tissue formation, in agreement with the experiment. However, numerical solutions of the reaction-diffusion system do not exhibit this sensitivity to growth factor application. Mathematically, this corresponds to the observation that behind healing wavefront solutions, a particular healed state is always selected independent of transients, even though there is a continuum of possible positive steady states. We explain this phenomenon using a caricature system of equations, which reflects the key qualitative features of the full model but has a much simpler mathematical form. Biologically, our results suggest that the migration into a wound of fibroblasts and TGFβ from the surrounding dermis alone cannot account for the essential features of the healing process, and that fibroblasts entering from the underlying subcutaneous tissue are crucial to the healing process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460102
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  • 19
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    Agonist-induced calcium waves in oscillatory cells: A biological example of Burgers' equation (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1125-1144 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1, 4, 5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.
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    URL: http://dx.doi.org/10.1007/BF02460104
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  • 20
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    Cell communities and robustness in development (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1183-1189 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The robustness of patterning events in development is a key feature that must be accounted for in proposed models of these events. When considering explicitly cellular systems, robustness can be exhibited at different levels of organization. Consideration of two widespread patterning mechanisms suggests that robustness at the level of cell communities can result from variable development at the level of individual cells; models of these mechanisms show how interactions between participating cells guarantee community-level robustness. Cooperative interactions enhance homogeneity within communities of like cells and the sharpness of boundaries between communities of distinct cells, while competitive interactions amplify small inhomogeneities within communities of initially equivalent cells, resulting in fine-grained patterns of cell specialization.
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    URL: http://dx.doi.org/10.1007/BF02460107
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  • 21
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    Equivariant Chow groups for torus actions (1997)
    Springer
    Transformation groups 2 (1997), S. 225-267 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study Edidin and Graham's equivariant Chow groups in the case of torus actions. Our main results are: (i) a presentation of equivariant Chow groups in terms of invariant cycles, which shows how to recover usual Chow groups from equivariant ones; (ii) a precise form of the localization theorem for torus actions on projective, nonsingular varieties; (iii) a construction of equivariant multiplicities, as functionals on equivariant Chow groups; (iv) a construction of the action of operators of divided differences on theT-equivariant Chow group of any scheme with an action of a reductive group with maximal torusT. We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations. In particular, we obtain a presentation of the Chow ring of any smooth, projective spherical variety.
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    URL: http://dx.doi.org/10.1007/BF01234659
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  • 22
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    A family of affine Weyl group representations (1997)
    Springer
    Transformation groups 2 (1997), S. 375-390 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we explicitly determine the virtual representations of the finite Weyl subgroups of the affine Weyl group on the cohomology of the space of affine flags containing a family of elementsn t in an affine Lie algebra. We also compute the Euler characteristic of the space of partial flags containingn t and give a connection with hyperplane arrangements.
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    URL: http://dx.doi.org/10.1007/BF01234541
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  • 23
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    Weakly symmetric spaces and bounded symmetric domains (1997)
    Springer
    Transformation groups 2 (1997), S. 351-374 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetG be a connected, simply-connected, real semisimple Lie group andK a maximal compactly embedded subgroup ofG such thatD=G/K is a hermitian symmetric space. Consider the principal fiber bundleM=G/K s →G/K, whereK s is the semisimple part ofK=K s ·Z K 0 andZ K 0 is the connected center ofK. The natural action ofG onM extends to an action ofG 1=G×Z K 0 . We prove as the main result thatM is weakly symmetric with respect toG 1 and complex conjugation. In the case whereD is an irreducible classical bounded symmetric domain andG is a classical matrix Lie group under a suitable quotient, we provide an explicit construction ofM=D×S 1 and determine a one-parameter family of Riemannian metrics Ω onM invariant underG 1. Furthermore,M is irreducible with respect to Ω. As a result, this provides new examples of weakly symmetric spaces that are nonsymmetric, including those already discovered by Selberg (cf. [M]) for the symplectic case and Berndt and Vanhecke [BV1] for the rank-one case.
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    URL: http://dx.doi.org/10.1007/BF01234540
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  • 24
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    Modified Wigner bispectrum and its generalizations (1997)
    Springer
    Circuits, systems and signal processing 16 (1997), S. 27-40 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The Wigner bispectrum of multicomponent signals is studied, and its modified and reduced forms are introduced. A generalization of the presented forms to the Wigner higher-order spectra (WHOS), in the case of multicomponent signals, is provided. From our previous work it is known that cross terms removal (reduction) is possible for odd-order spectra with equal numbers of conjugated and nonconjugated terms. Here, we extend the analysis to even-order spectra. The theory is illustrated by examples.
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    URL: http://dx.doi.org/10.1007/BF01183173
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    On identifiability and information-regularity in parametrized normal distributions (1997)
    Springer
    Circuits, systems and signal processing 16 (1997), S. 83-89 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We describe methods to establish identifiability and information-regularity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability distribution and they are information-regular when their Fisher information matrix is full rank. In normal distributions, information-regularity implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without having to explicitly compute the information matrix. Some examples are given.
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    Two-dimensional model-based power spectrum estimation for nonextendible correlation bisequences (1997)
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    Circuits, systems and signal processing 16 (1997), S. 141-163 
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    Notes: Abstract The extendibility of estimated correlation bisequences from an available sampled data array is described in terms of the generating functions of associated block Toeplitz with Toeplitz block (BTTB) matrices. The periodogram-based correlation bisequences are shown to be extendible. It is shown that the method of resultants and subresultants is convenient for generating the nonlinear constraints in the optimization problem which is solved iteratively for power spectrum estimation. A nontrivial example illustrates the concepts developed.
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    A multiresolutional approach to 3D object recognition (1997)
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    Circuits, systems and signal processing 16 (1997), S. 217-239 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A multiresolutional approach is presented for effectively recognizing three-dimensional (3D) objects. The approach is both pose and scale invariant. A multiresolutional model base is constructed, and multiscale edges of the object are detected using the wavelet transform. The minimum alignment between model base and object is realized by the linear mapping scheme.
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    Fractal interpolation functions and data compression for tracking (1997)
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    Circuits, systems and signal processing 16 (1997), S. 59-67 
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    Notes: Abstract The potential for data compression in using fractal interpolation functions (FIFs) is realized by the construction of a set of multirate filters. The filter tap weights are determined by optimizing the energy contents of a preselected set of frequency bands. This filter bank implementation of the FIF is successfully used to compress data simulated in a tracking environment.
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    On cyclically time-varying autoregressive digital filters (1997)
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    Circuits, systems and signal processing 16 (1997), S. 91-106 
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    Notes: Abstract A first-order autoregressive filter is altered by changing the constant gain to two or more gains that cyclically alternate in time. The advantages of this system are shown, and the relation to linear autoregressive moving average difference equations of higher order is derived.
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    Fast implementation of the forward positional acceleration of robots via the distributed arithmetic technique (1997)
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    Circuits, systems and signal processing 16 (1997), S. 165-195 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper refers to the fast implementation of the positional forward acceleration of the end effector of revolute robotic arms with spherical wrists, using the distributed arithmetic technique. The acceleration of the end effector is calculated by a cascade configuration of two pipelined arrays that calculate the Jacobian matrix and its time derivative, as well as the centrifugal-Coriolis and linear accelerations. These partial accelerations are then added in the adder tree. The building blocks of the arrays are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculations. The digit-serial configuration of the proposed implementation of the positional forward acceleration of the end effector is described. The serial and the parallel configurations may result as special cases of the digit-serial configuration. The proposed distributed arithmetic (DA) implementation of the positional forward acceleration may be applied, after appropriate modifications, to the general case of robots having either revolute or prismatic joints, with any type of wrist.
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    Locations and amplitudes of the extrema of the sinx/x function (1997)
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    Circuits, systems and signal processing 16 (1997), S. 241-245 
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    Notes: Abstract This paper addresses the calculation of the extrema of the sin x/x function. First the Newton-Raphson method is used, which allows us to obtain the extrema locations very fast through the use of a recursion formula. Then a second approach is proposed, which gives the extrema locations and the extrema amplitudes in the form of series expansions. Simple, accurate algebraic expressions are derived.
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    Unicursal resistive networks (1997)
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    Circuits, systems and signal processing 16 (1997), S. 307-324 
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    Notes: Abstract We give some existence results for a resistive network in which the components are neither voltage nor current controlled; that is, they are merely unicursal. In fact we allow coupling. Degree arguments give existence and bounds. We study several ways of avoiding the requirement of eventual passivity. No-gain and passive multiterminal elements are included. The results are extended to infinite networks.
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    A new approach for estimating spectra from randomly sampled sequences (1997)
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    Circuits, systems and signal processing 16 (1997), S. 375-386 
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    Notes: Abstract Random sampling is one of the methods that can overcome the Nyquist limit when evaluating a frequency spectrum of a signal. However, the computational complexity becomesN 2 as the FFT cannot be used. A new approach, called hybrid additive random sampling, is proposed. This new scheme is devised by concatenating random sampling sequences in such a way that symmetry is created in the transform kernel for reducing the computational effort while the anti-alias property is maintained. A savings of the least 75% in computation is achieved. The sampling scheme is also found to be suitable for parallel implementation. In this paper, the algorithms for generating the sampling sequence and evaluating the spectrum are described in detail. The performances of the scheme in terms of noise, accuracy, etc., are compared with genuine random sampling and another approach proposed previously. The advantages and limitations are included.
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    A quick neural network for computer vision of gray images (1997)
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    Circuits, systems and signal processing 16 (1997), S. 41-58 
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    Notes: Abstract This paper presents a comparison between the traditional image processing method and the area vector concept as well as the new technique of artificial neural networks. Freeman chain coding is considered in the study, and the principle of segmentation may be based and implemented for further investigations resulting from the proposed work. The pattern recognition concept is analyzed and defined through the sigmoid function and the determination of the threshold of a gray image for an object. The block schemes for the given protocols are summarized in a single scheme for illustration and comparison purposes. The synthetic pictures are generated and investigated regarding the dependence of computer vision on the contents of the artificial neural network. The normalization technique is included to eliminate noise and zooming problems. The minimum computational time for image processing with the generated pictures is also determined. The rate of deflection in the computational time is recommended for sensing the minimum computational time according to the variation of the number of hidden units in the hidden layer. A three-layer neural network has been used. The study of gray binary imaging for color pictures is illustrated to save computational time and effort.
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    Time-limited and band-limited environment: Signals and systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 247-270 
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    Notes: Abstract Of concern is an environment made up of signals and systems tightly confined both in time and frequency. Such an environment is often encountered in transmission line circuits, radar, sonar, and optical circuits, and when the principal signals are well-defined sharp pulses. It will be seen that once this environment is achieved, the signals and systems possess some attractive properties. A conventional system may preserve the symmetry of a propagating signal or change its symmetry from even to odd or from odd to even. Another system may be used to predict the arrival of an incoming pulse with a high degree of accuracy. Electrical networks may also be associated with these properties. Approximation problems, existence theorems, and realization schemes will be addressed and developed.
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    Digitally redesigned PAM controller and ideal state reconstructor for input time-delay/nondelay systems with nonsynchronous sampling (1997)
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    Circuits, systems and signal processing 16 (1997), S. 325-347 
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    Notes: Abstract This paper develops a new digitally redesigned pulse-amplitude modulated (PAM) controller for a continuous-time input time-delay/nondelay system with nonsynchronous sampling. The concept of the law of the mean from the input integral calculus is utilized for the development of the equivalent digital predictor controllers from the available analog predictor controllers. As a result, the digitally controlled states closely match the original continuous-time states. To implement the developed discrete-time state-feedback PAM controller, this paper also develops an ideal discrete-time state using nonsynchronously sampled input-output data of the continuous-time input delay/nondelay system without establishing a dynamic observer.
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    Model matching under external and input-output equivalence (1997)
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    Circuits, systems and signal processing 16 (1997), S. 429-438 
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    Notes: Abstract The model-matching problem for systems described by external models is considered in frameworks of both external and input-output equivalence. Necessary conditions for the solvability of the problem are produced, and it is shown that in certain cases these conditions are also sufficient. In the case where necessary and sufficient conditions exist, the solutions of the problem are obtained in a constructive way and a parametrization of solutions is given.
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    Invariance property of Gaussian signals: A new interpretation, extension and applications (1997)
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    Circuits, systems and signal processing 16 (1997), S. 523-536 
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    Notes: Abstract This paper addresses the invariance property of Gaussian signals, originally derived by Bussgang, which characterizes the input/output moment relation of a hybrid nonlinear moment (HNM) estimator based on a zero-memory nonlinearity (ZMN) g(y). Some re-derivations of this property are reviewed, and an original, direct, and simple proof is presented (Appendix 1). The paper then derives a new interpretation of this property (Theorem 1) that shows a moment-sense equivalence between g(y) and a linear mappingh 1(y) whose coefficients a0 and a1 are completely characterized in terms ofg(y) and are shown to be optimal in a mean square error (MSE) sense. A direct and very interesting byproduct of this interpretation is a simple linear relationship between the input and output of the HNM estimator involved. The property is then generalized (Theorem 2) to signals other than Gaussian, resulting in an infinite cumulant series expansion of the HNM estimator output, whose coefficients are all characterized in terms ofg(y). Applications of Theorem 1 to some ZMNs commonly used in signal processing and control theory are presented that clearly illustrate the power and elegance of the invariance property. Finally, some conclusions are given.
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    The discrete Einstein relation (1997)
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    Circuits, systems and signal processing 16 (1997), S. 547-557 
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    Notes: Abstract In this paper the connection between ‘mass’M, ‘resistance’ϱ and ‘commute time’θ for random walks on graphs is further explored, and the relationθ=2M ·ϱ is proved. An extension of the result is made to multigraphs, which are an extension of the graph concept where a black box is treated like an edge.
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    Input-output systems whose transmission operators furnish nearly best approximations to a given map (1997)
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    Circuits, systems and signal processing 16 (1997), S. 625-647 
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    Notes: Abstract Let {S(A):A ∈A}, whereA is a subset of an infinite-dimensional normed linear spaceL, be a class of general nonlinear input-output systems that are governed by operator equations relating the input, state, and output, all of which are in extended spaces. IfQ is a given operator from a specified set ¯D i, of inputs into the space of outputs ¯H 0, the problem we consider is to find, for a given ɛ〉0, a “parameter”A ε∈A such that the transmission operatorR(A ε) ofS(A ε) furnishes a nearly best (or ɛ-best) approximation toQ from allR(A),A ∈A. Here the “distance” betweenQ andR(A) is defined as the supremum of distances betweenQz andR(A)z taken over allz ∈ ¯D i. In Theorems 2 through 5 we show that ifS(A) is “normal” (Definition 2),A satisfies some mild requirement andL contains a fundamental sequence, then establishingA ε∈A reduces to minimizing a certain continuous functional on a compact subset ofR n, and thus can be carried out by conventional methods. The applications of results are illustrated by the example of a model-matching problem for a nonlinear system, and of optimal tracking.
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    Notes on uniform approximation of shift-varying systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 649-654 
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    Notes: Abstract It is shown that the elementsG of a large class of input-output maps can be uniformly approximated arbitrarily well using a certain structure if and only ifG is continuous. For the case considered the system inputs and outputs are defined on a discrete set {0, 1,...,a 1}×...{0, 1,...,a m }, in which a1,...,a m are positive integers. Our approximating structure involves certain functions that can be chosen in different ways. For the special case in which these functions are taken to be certain polynomial functions, the input-output map of our structure is a generalized discrete Volterra series. Our results provide an analytical basis for the use of such series.
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    Guaranteed stability margins for discrete-time LQ optimal regulators for the performance index with cross-product terms (1997)
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    Circuits, systems and signal processing 16 (1997), S. 663-701 
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    Notes: Abstract In this paper, the stability robustness of deterministic state feedback discretetime linear quadratic (LQ) optimal regulators for the performance index with cross-product terms is analyzed. Guaranteed stability margins for such a type of LQ optimal regulator are suggested for the first time. These stability margins are obtained on the basis of a modified return difference equality and are expressed directly in terms of the elementary cost and system matrices. Sufficient conditions to guarantee the required stability margins are presented. Finally, the connection between the suggested stability margins and the selection of weighting state, input, and cross-product matrices is investigated, and useful guidelines for choosing proper weighting matrices are presented.
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    Stability and instability properties of aggregation of single chain amphiphiles into binary mixtures (1997)
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    Bulletin of mathematical biology 59 (1997), S. 43-61 
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    Notes: Abstract In a lysophospholipid binary mixture, there are three ways of association between the mixture components of single-chain amphiphiles: (a) between two identical molecules each of the first and second component (self-association process) and (b) between two different molecules (cross-association process). Association probabilities for three binary mixtures were analysed as functions depending on the electric dipole moments of the polar head groups. A 3-D view representation is most suitable for this analysis. The most important finding is that for certain values of the electric dipole moments there are molecular couples which have a maximum stability to the changes in the external electrolytic medium. This fact confirms the formation of clusters and their stability, which is equivalent to the existence of micro-heterogeneities within the lipid bilayers. On the other hand, there are unstable molecular associations, and this fact influences the appearance of some phase transitions. Generally, the increase of the electric dipole moment or the increase of the acyl-chain length of one component from a binary lipid mixture decreases the self-association probability between its own molecules, but it increases the self-association probability of the other mixture components. Furthermore, the cross-association probability has high values for any binary lipid mixture of single-chain amphiphiles.
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    A mathematical model for intracellular effects of toxins on DNA adduction and repair (1997)
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    Bulletin of mathematical biology 59 (1997), S. 89-106 
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    Notes: Abstract The processes by which certain classes of toxic compounds or their metabolites may react with DNA to alter the genetic information contained in subsequent generations of cells or organisms are a major component of hazard associated with exposure to chemicals in the environment. Many classes of chemicals may form DNA adducts and there may or may not be a defined mechanism to remove a particular adduct from DNA independent of replication. Many compounds and metabolites that bind DNA also readily bind existing proteins; some classes of toxins and DNA adducts have the capacity to inactivate a repair enzyme and divert the repair process competitively. This paper formulates anintracellular dynamic model for one aspect of the action of toxins that form DNA adducts, recognizing a capacity for removal of those adducts by a repair enzyme combined with reaction of the toxin and/or the DNA adduct to inactivate the repair enzyme. This particular model illustrates the possible saturation of repair enzyme capacity by the toxin dosage and shows that bistable behavior can occur, with the potential to induce abrupt shifts away from steady-state equilibria. The model suggests that bistable behavior, dose and variation between individuals or tissues may combine under certain conditions to amplify the biological effect of dose observed as DNA aduction and its consequences as mutation. A model recognizing stochastic phenomena also indicates that variation in within-cell toxin concentration may promote jumps between stable equilibria.
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    Integrodifference models for persistence in fragmented habitats (1997)
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    Bulletin of mathematical biology 59 (1997), S. 107-137 
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    Notes: Abstract Integrodifference models of growth and dispersal are analyzed on finite domains to investigate the effects of emigration, local growth dynamics and habitat heterogeneity on population persistence. We derive the bifurcation structure for a range of population dynamics and present an approximation that allows straighforward calculation of the equilibrium populations in terms of local growth dynamics and dispersal success rates. We show how population persistence in a heterogeneous environment depends on the scale of the heterogeneity relative to the organism's characteristic dispersal distance. When organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence.
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    Positive feedback and angiogenesis in tumor growth control (1997)
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    Bulletin of mathematical biology 59 (1997), S. 233-254 
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    Notes: Abstract In vivo tumor growth data from experiments performed in our laboratory suggest that basic fibroblast growth factor (bFGF) and vascular endothelial growth factor (VEGF) are angiogenic signals emerging from an up-regulated genetic message in the proliferating rim of a solid tumor in response to tumor-wide hypoxia. If these signals are generated in response to unfavorable environmental conditions, i.e. a decrease in oxygen tension, then the tumor may play an active role in manipulating its own environment. We have idealized this type of adaptive behavior in our mathematical model via a parameter which represents the carrying capacity of the host for the tumor. If that model parameter is held constant, then environmental control is limited to tumor shape and mitogenic signal processing. However, if we assume that the response of the local stroma to these signals is an increase in the host's ability to support an ever larger tumor, then our models describe a positive feedback control system. In this paper, we generalize our previous results to a model including a carrying capacity which depends on the size of the proliferating compartment in the tumor. Specific functional forms for the carrying capacity are discussed. Stability criteria of the system and steady state conditions for these candidate functions are analyzed. The dynamics needed to generate stable tumor growth, including countervailing negative feedback signals, are discussed in detail with respect to both their mathematical and biological properties.
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    Erratum (1997)
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    Bulletin of mathematical biology 59 (1997), S. 407-407 
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    The community effect and ectoderm-mesoderm interaction inXenopus muscle differentiation (1997)
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    Bulletin of mathematical biology 59 (1997), S. 409-425 
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    Notes: Abstract Community effects are believed to play an important role in the patterning of many tissues during development. They involve an interaction between neighbouring equivalent cells that is necessary for them to proceed to their fully differentiated state. However, the mechanisms underlying these effects remain unclear. In this paper, diffusion-based mathematical models are constructed and analysed in order to study possible mechanisms for the community effect inXenopus muscle differentiation. These models differ from each other in the assumptions that are made about the nature of an inhibitory effect that ectodermal tissue has been observed to have on muscle differentiation. It is possible to construct consistent models based on all the forms of inhibition considered. However, each model requires the diffusible factors on which it is based to have different properties. The current data from tissues reaggregate experiments are insufficient to determine the mechanisms underlying the community effect; the work presented here suggests that quantitative analysis of a further series of reaggregate experiments will make it possible to distinguish between the proposed mechanisms.
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    Controlling spatial chaos in metapopulations with long-range dispersal (1997)
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    Bulletin of mathematical biology 59 (1997), S. 497-515 
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    Notes: Abstract We propose two methods to control spatial chaos in an ecological metapopulation model with long-range dispersal. The metapopulation model consists of local populations living in a patchily distributed habitat. The habitat patches are arranged in a one-dimensional array. In each generation, density-dependent reproduction occurs first in each patch. Then individuals disperse according to a Gaussian distribution. The model corresponds to a chain of coupled oscillators with long-range interactions. It exhibits chaos for a broad range of parameters. The proposed control methods are based on the method described by Güémez and Matías for single difference equations. The methods work by adjusting the local population sizes in a selected subset of all patches. In the first method (pulse control), the adjustments are made periodically at regular time intervals, and consist of always removing (or adding) a fixed proportion of the local populations. In the second method (wave control), the adjustments are made in every generation, but the proportion of the local population that is affected by the control changes sinusoidally. As long as dispersal distances are not too low, these perturbations can drive chaotic metapopulations to cyclic orbits whose period is a multiple of the control period. we discuss the influence of the magnitude of the pulses and wave amplitudes, and of the number and the distribution of controlled patches on the effectiveness of control. When the controls start to break down, interesting dynamic phenomena such as intermittent chaos can be observed.
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    Hierarchically coupled ultradian oscillators generating robust circadian rhythms (1997)
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    Bulletin of mathematical biology 59 (1997), S. 517-532 
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    Notes: Abstract Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many coupled oscillators predict that the output period should vary as the square root of the number of participating units, thus being inconsistent with the well-established experimental result that ablation of substantial parts of the suprachiasmatic nuclei (SCN), the main circadian pacemaker in mammals, does not eliminate the overt circadian functions, which show no changes in the phases or periods of the rhythms. From these observations, we have developed a theoretical model that exhibits the robustness of the circadian clock to changes in the number of cells in the SCN, and that is readily adaptable to include the successful features of other known models of circadian regulation, such as the phase response curves and light resetting of the phase.
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    An indirect method for absorption rate estimation: Flurothyl-induced seizures (1997)
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    Bulletin of mathematical biology 59 (1997), S. 569-579 
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    Notes: Abstract This paper develops a method to estimate a minimal amount of flurothyl necessary to induce the seizures (the seizure threshold). A simple mathematical model is proposed which permits one to determine the drug absorption rate from the amount which has been administered and from the measured latency to onset of seizure. Experimental animal (rats) were exposed to a continuous intake of flurothyl in two different situations: either being alone in the airtight chamber or sharing it in a pair. In the latter case, we assume that the two rats uniformly share the infused drug. Our calculations estimate that approximately 20 μl of flurothyl is necessary to induced twitches, whereas 25 μl of flurothyl is the dose required for the induction of clonic seizures. The model can be used to estimate the threshold amounts of any drug producing obvious behavioral changes irrespective of the route of administration.
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    A search for maximum species abundances in ecological communities under conditional diversity optimization (1997)
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    Bulletin of mathematical biology 59 (1997), S. 649-677 
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    Notes: Abstract We study a multispecies community of autotrophic microorganisms which grow in a batch culture regime with several perfectly complementary resources. A basic hypothesis is that a stationary phase of the polyculture corresponds to a maximum diversity under the constraints having the meaning of matter conservation laws. The corresponding conditional extremum problem is studied in detail. It is shown that a unique solution to this problem—a “species structure formula”—adequately describes the experimental data. We prove a number of strict statements concerning the domain of definition and maxima of the obtained solutions. These statements find an adequate interpretation as limitation principles in ecology and in the problems of community structure control.
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    Gene therapy of T helper cells in HIV infection: Mathematical model of the criteria for clinical effect (1997)
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    Bulletin of mathematical biology 59 (1997), S. 725-745 
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    Notes: Abstract The paper presents a mathematical analysis of the criteria for gene therapy of T helper cells to have a clinical effect on HIV infection. The analysis indicates that for such a therapy to be successful, it must protect the transduced cells against HIV-induced death. The transduced cells will not survive as a population if the gene therapy only blocks the spread of virus from transduced cells that become infected. The analysis also suggests that the degree of protection against disease-related cell death provided by the gene therapy is more important than the fraction of cells that is initially transduced. If only a small fraction of the cells can be transduced, transduction of T helper cells and transduction of haematopoietic progenitor cells will result in the same steady-state level of transduced T helper cells. For gene therapy to be efficient against HIV infection, our analysis suggests that a 100% protection against viral escape must be obtained. The study also suggests that a gene therapy against HIV infection should be designed to give the transduced cells a partial but not necessarily total protection against HIV-induced cell death, and to avoid the production of viral mutants insensitive to the gene therapy.
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    Frobenius splitting and invariant theory (1997)
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    Transformation groups 2 (1997), S. 183-195 
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    Notes: Abstract We consider varieties over an algebraically closed field k of characteristicp〉0. Given a linear representation of a reductive group, we prove that the ring of invariants is F-regular provided the associated projective quotient is Frobenius-split, the twisting sheaves are Cohen-Macaulay (C-M), and a mild technical condition is met. As an example of how this can be used, we show that the ring of invariants (under the adjoint action of SL (3)) ofg copies ofM 3 is C-M. (HereM 3 denotes the vector space of 3×3 matrices over k andp〉3.) The method of proof involves an induction, and is potentially of wide applicability. As a corollary we obtain that the moduli space of rank 3 and degree 0 bundles on a smooth projective curve of genusg is C-M.
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    A note on homogeneous locally symmetric spaces (1997)
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    Transformation groups 2 (1997), S. 269-277 
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    Notes: Abstract Let $$(g,\theta )$$ denote an orthogonal symmetric Lie algbra and let (G, K) be an associated pair, i.e., Lie(G = $$g$$ and Lie(K°) = $$g^\theta $$ . In this paper we prove that the homogeneous spaceG/K has a structure of a globally symmetric space for every choice ofG andK, especially forG being compact.
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    Superrigidity for homomorphisms into isometry groups of CAT(−1) spaces (1997)
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    Transformation groups 2 (1997), S. 289-323 
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    Notes: Abstract CAT(−1) spaces are generalizations of manifolds with negative curvature. In this paper, we prove three types of rigidity results related to CAT(−1) spaces, namely the rigidity of the isometric actions on CAT(−1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles. The main idea for our approach relies on a study of the boundary theory we established for the general CAT(−1) spaces.
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    Multivalued groups, their representations and Hopf algebras (1997)
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    Transformation groups 2 (1997), S. 325-349 
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    Notes: Abstract This paper introduces the concept ofn-valued groups and studies their algebraic and topological properties. We explore a number of examples. An important class consists of those that we calln-coset groups; they arise as orbit spaces of groupsG modulo a group of automorphisms withn elements. However, there are many examples that do not arise from this construction. We see that the theory ofn-valued groups is distinct from that of groups with a given automorphism group. There are natural concepts of the action of ann-valued group on a space and of a representation in an algebra of operators. We introduce the (purely algebraic) notion of ann-Hopf algebra and show that the ring of functions on ann-valued group and, in the topological case, the cohomology has ann-Hopf algebra structure. The cohomology algebra of the classifying space of a compact Lie group admits the structure of ann-Hopf algebra, wheren is the order of the Weyl group; the homology with dual structure is also ann-Hopf algebra. In general the group ring of ann-valued group is not ann-Hopf algebra but it is for ann-coset group constructed from an abelian group. Using the properties ofn-Hopf algebras we show that certain spaces do not admit the structure of ann-valued group and that certain commutativen-valued groups do not arise by applying then-coset construction to any commutative group.
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    Feedback design and precompensation for generalized systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 611-624 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Feedback control designs are useful for removing the impulses that disturb the behavior of generalized state space systems. The aim of this paper is to detail the design of dynamic precompensators for the implementation of such feedback control designs. Necessary and sufficient conditions are given so that the resulting regulators are biproper. It is pointed out that these conditions are restrictive and that feedback control designs can lead to nonproper precompensators. To overcome this difficulty, a class of proper precompensators is proposed. These regulators, which result from an adaptation of the Silverman structure algorithm, remove the impulse behaviors that occur after the initial time by smoothing out the input vector.
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    Analysis of the Chinese remainder theorem and cyclotomic polynomials-based algorithms for cyclic convolution—Part II: Complex rational number system (1997)
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    Circuits, systems and signal processing 16 (1997), S. 595-610 
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    Notes: Abstract This paper investigates the factorization properties of cyclotomic polynomials over the field of complex rational numbers. Based on this factorization and the Chinese remainder theorem, we analyze the mathematical structure of the associated algorithms for computing the cyclic convolution of data sequences. The relevant results pertaining to finite integer and complex integer rings are also summarized.Note: This work is being reported in two parts. In Part I, we analyze the structure of the cyclic convolution algorithms over the rational number system. In Part II, we describe complex cyclotomic polynomials and the structure of the resulting cyclic convolution algorithms over the complex rational number system.
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    Analysis of the Chinese remainder theorem and cyclotomic polynomials-based algorithms for cyclic convolution—Part I: Rational number system (1997)
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    Circuits, systems and signal processing 16 (1997), S. 569-594 
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    Notes: Abstract The Chinese remainder theorem plays a central role in the design of fast algorithms for computing cyclic and acyclic convolution of data sequences. A mathematical analysis of the theorem and related aspects form the topic of this investigation. The focus is almost exclusively on cyclic convolution algorithms. The number system that is studied is the field of rational numbers. Several properties related to the mathematical structure of the algorithms are derived.Note: This work is being reported in two parts. In Part I, we analyze the structure of the cyclic convolution algorithms over the rational number system. In Part II, we describe complex cyclotomic polynomials and the structure of the resulting cyclic convolution algorithms over the complex rational number system.
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    On a “central inequality” in the theory of input-output systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 655-661 
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    Notes: Abstract In the stability and sensitivity theory of general, nonlinear input-output systems we encounter a certain inequality concerning solely the nominal system that plays a central role in the whole theory. In particular, this “central inequality,” combined with other assumptions, implies (a) stability of the nominal system, (b) robustness, and (c) insensitivity of the input-output system. This paper presents conditions equivalent to this central inequality, and a further result on the stability-robustness problem.
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    On the zeros of discrete-time linear periodic systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 703-718 
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    Notes: Abstract Discrete-time linear periodic single-input/single-output (SISO) systems having uniform relative degree are considered. A closed-form expression of the blocking input is derived and exploited to obtain a computationally advantageous characterization of the structural zeros. Indeed, it suffices to compute the eigenvalues of a suitably defined (n × n) matrix, wheren is the system order. It is shown that, in contrast to the general case studied in previous papers, the number of zeros of linear periodic SISO systems with uniform relative degree is always time invariant and equal to the difference between the system order and the relative degree. The new characterization is also used to provide a simple expression for the zeros of linear periodic systems described by input-output difference equations.
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    Observability of nonlinear differential algebraic systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 271-285 
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    Notes: Abstract We define the smooth observability of nonlinear DAE systems and give sufficient conditions for this property to hold locally in a neighborhood of a solution. The matrix rank conditions for observability are verifiable by a combination of symbolic and numerical linear algebra computations. These conditions generalize conditions that have appeared in the literature for observability of linear time-varying DAE systems. We indicate how the main result is potentially useful in studying a system's zero dynamics. Some relevant rank properties of Hessenberg DAE systems are established.
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    A new family of Routh approximants (1997)
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    Circuits, systems and signal processing 16 (1997), S. 1-25 
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    Notes: Abstract Based on the combinatorial Routhα-β andγ-δ expansions of a stable transfer function, a new energy decomposition tree for linear systems is developed. The pertinent properties to the energy decomposition tree are investigated, and an algorithm is derived for synthesizing transfer functions from the tree. The synthesis process naturally leads to a new family of Routh approximants to the system. It is indicated that the selection of Routh approximants based on the values of impulse-response energy is often inadequate because there may be a number of different Routh approximants with the same order and the same impulse-response energy. In such cases, an additional performance criterion, such as the integral of squared error of impulse response or unit-step response, has to be used to select a suitable Routh approximant.
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    A genetic algorithm for the maximum likelihood estimation of the parameters of sinusoids in a noisy environment (1997)
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    Circuits, systems and signal processing 16 (1997), S. 69-81 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An adaptive generic algorithm was developed to solve the optimization problem of the maximum likelihood estimation of the sum of sinusoids in a noisy environment. The algorithm is based on genetic concepts and is extended, with modifications, to this problem. Simulation results were performed to see the effect of different parameters such as permutation and crossover probabilities. The effects of the signal-to-noise ratio (SNR) were also studied. It was found that the key factor for accuracy is the probabilities of permutation and crossover. Thus, we developed an adaptive method to estimate these probabilities, on line, to reduce the error. This was accomplished by considering them as unknown parameters to be estimated with the signal parameters. The mean square error of the frequency estimates was compared favorably to the Cramér-Rao lower bound. Several simulations are shown for SNR values ranging between −7 dB and 20 dB.
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    Fast algorithms for computing one- and two-dimensional convolution in integer polynomial rings (1997)
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    Circuits, systems and signal processing 16 (1997), S. 121-139 
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    Notes: Abstract In a recent work, the factorization properties of polynomials defined over finite integer polynomial rings were analyzed. These properties, along with other results pertaining to polymomial theory, led to the direct sum property and the American-Indian-Chinese extension of the Chinese remainder theorem over such integer rings. The objective of this paper is to describe algorithms for computing the one-and two-dimensional convolution of data sequences defined over finite integer rings. For one-dimensional convolution, algorithms for computing acyclic and cyclic convolution are described. For two-dimensional convolution, only the cyclic case is analyzed. Computational and other relevant aspects associated with the structure of these algorithms are also studied.
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    Robust adaptive beamforming for broadband arrays (1997)
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    Circuits, systems and signal processing 16 (1997), S. 207-216 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract It is very important in many applications to preserve a desired signal without distortion. This paper presents a robust adaptive beamforming method to extract a desired signal from the signals received by broadband arrays. The proposed method relaxes the requirement of approximate knowledge of the desired direction and the sensor gains and delays (phases). Also the method enhances the desired signal based on a focusing transform for that signal, requires less computation than the taped-delay-line beamforming method, and provides good results even in a multipath environment. Computer simulations are given to support the proposed method.
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    On locally trivial G a -actions (1997)
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    Transformation groups 2 (1997), S. 137-145 
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    Notes: Abstract If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1). We investigate such normal affine algebras in the case of a locally trivial action on a factorial variety. If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3). Equivalently, ifC n , is the total space for a principalG a -bundle over some open subset ofC n−1 then the bundle is trivial. On the other hand, there is a locally trivialG a -action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
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    Some curious Kleinian groups and hyperbolic 5-manifolds (1997)
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    Transformation groups 2 (1997), S. 3-29 
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    Notes: Abstract We present a new family of discrete subgroups ofSO (5, 1) isomorphic to lattices inSO (3, 1). In some of the examples the limit sets are wildly knotted 2-spheres. As an application we produce complete hyperbolic 5-manifolds that are nontrivial plane bundles over closed hyperbolic 3-manifolds and conformally flat 4-manifolds that are nontrivial circle bundles over closed hyperbolic 3-manifolds.
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    Quantum integrable systems and differential Galois theory (1997)
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    Transformation groups 2 (1997), S. 31-56 
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    Notes: Abstract This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry. We investigate the eigenvalue problem for such systems and the correspondingD-module when the eigenvalues are in generic position. In particular, we show that the differential Galois group of this eigenvalue problem is reductive at generic eigenvalues. This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues. We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system. In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
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    Cones of highest weight vectors, weight polytopes, and Lusztig's q-analog (1997)
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    Transformation groups 2 (1997), S. 91-115 
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    Notes: Abstract We relate the invariant theory of cones of highest weight vectors to weight multiplicities and theirq-analogs. Whenever the action of a maximal torus on the coneCλ* has some nice properties, we obtain simple closed formulas for all weight multiplicities and theirq-analogs in the representationsV nλ ,n∈ℕ. We find a connection between the character ofV nλ and the respective weight polytopes.
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    Generalised Fibonacci manifolds (1997)
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    Transformation groups 2 (1997), S. 165-182 
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    Notes: Abstract Fibonacci manifolds have a hyperbolic structure which may be defined via Fibonacci numbers. Using related sequences of Lucas numbers, other 3-manifolds are constructed, their geometric structures determined, and a curious relationship between the homology and the invariant trace-field examined.
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    Generalized symmetrization in enveloping algebras (1997)
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    Transformation groups 2 (1997), S. 197-213 
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    Notes: Abstract Let g be a Lie algebra,S(g) the symmetric algebra,U(g) the universal enveloping algebra, andZ(g) the center ofU(g). The aim of this paper is to discuss a construction of a class of linear isomorphisms σ:S(g)→U(g) which commute with the adjoint representation. Applications to constructing a basis inZ(g) for classical g are also sketched.
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    The finite irreducible linear groups with polynomial ring of invariants (1997)
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    Transformation groups 2 (1997), S. 57-89 
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    Notes: Abstract We prove the following result: LetG be a finite irreducible linear group. Then the ring of invariants ofG is a polynomial ring if and only ifG is generated by pseudoreflections and the pointwise stabilizer inG of any nontrivial subspace has a polynomial ring of invariants. This is well-known in characteristic zero. For the case of positive characteristic we use the classification of finite irreducible groups generated by pseudoreflections due to Kantor, Wagner, Zalesskiî and Serežkin. This allows us to obtain a complete list of all irreducible linear groups with a polynomial ring of invariants.
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    Classical invariant theory for finite reflection groups (1997)
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    Transformation groups 2 (1997), S. 147-163 
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    Notes: Abstract We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups). As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras. In the interesting case when the group is of Coxeter typeD n (n≥4) we use higher polarization operators introduced by Wallach. The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables. We conjecture that this is also true for the exceptional reflection groups and then sketch a proof for the group of typeF 4.
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    A local-global principle for finiteness properties ofS-arithmetic groups over number fields (1997)
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    Transformation groups 2 (1997), S. 215-223 
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    Notes: Abstract In the preceding paper [AT] compactness propertiesC n andCP n for locally compact groups were introduced. They generalize the finiteness propertiesF n andFP n for discrete groups. In this paper a local-global principle forS-arithmetic groups over number fields is proved. TheS-arithmetic group г is of typeF n , resp.FP n , if and only if for allp inS thep-adic completionG p of the corresponding algebraic groupG is of typeC n resp.CP n . As a corollary we obtain an easy proof of a theorem of Borel and Serre: AnS-arithmetic subgroup of a semisimple group has all the finiteness propertiesF n .
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    Tensor ideals in the category of tilting modules (1997)
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    Transformation groups 2 (1997), S. 279-287 
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    Topics: Mathematics
    Notes: Abstract We study the tensor category $$Q$$ of tilting modules over a quantum groupU q with divided powers. The setX + of dominant weights is a union of closed alcoves $$\overline C _w $$ numbered by the elementsw∈W f of a certain subset of affine Weyl groupW. G. Lusztig and N. Xi defined a partition ofW f into canonical right cells and the right order ≤ R on the set of cells. For a cellA⊂W f we consider a full subcategory $$Q_{〈 A} $$ formed by direct sums of tilting modulesQ(λ) with highest weights $$\lambda \in \cup _{w \in B〈 _R A} \overline C _w $$ . We prove that $$Q_{〈 A} $$ is a tensor ideal in $$Q$$ , generalizing H. Andersen's theorem about the ideal of negligible modules which in our notations is nothing else then $$Q_{〈 \{ e\} } $$ . The proof is an application of a recent result by W. Soergel who has computed the characters of tilting modules.
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    URL: http://dx.doi.org/10.1007/BF01234661
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    Cayley transforms and orbit structure in complex flag manifolds (1997)
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    Transformation groups 2 (1997), S. 391-405 
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    ISSN: 1531-586X
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    Topics: Mathematics
    Notes: Abstract LetZ=G/Q be a complex flag manifold andG 0 a real form ofG. Suppose thatG 0 is the analytic automorphism group of an irreducible bounded symmetric domain and that some openG 0-orbit onZ is a semisimple symmetric space. Then theG 0-orbit structure ofZ is described explicitly by the partial Cayley transforms of a certain hermitian symmetric sub-flagF⊃Z. This extends the results and simplifies the proof for the classical orbit structure description of [10] and [11], which applies whenF=Z.
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    MODE-type algorithm for estimating damped, undamped, or explosive modes (1997)
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    Circuits, systems and signal processing 16 (1997), S. 349-362 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We propose a new algorithm for estimating the parameters of damped, undamped, or explosive sinusoidal signals. The algorithm resembles the MODE algorithm, which is commonly used for direction of arrival estimation in the array signal processing field. It is derived as a natural approximation to an asymptotically (high-SNR) optimal parameter estimator and has excellent statistical accuracy. Nevertheless, it is computationally simple and easy to implement. Numerical examples are included to illustrate the performance of the proposed method.
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    Uniform Approximation of Discrete-Space Multidimensional Myopic Maps (1997)
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    Circuits, systems and signal processing 16 (1997), S. 387-403 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Our main result is a theorem that gives, in a certain setting, a necessary and sufficient condition under which discrete-space multidimensional shift-invariant input-output maps with vector-valued inputs drawn from a certain large set can be uniformly approximated arbitrarily well using a structure consisting of a linear preprocessing stage followed by a memoryless nonlinear network. Noncausal as well as causal maps are considered. Approximations for noncausal maps for which inputs and outputs are functions of more than one variable are of current interest in connection with, for example, image processing.
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    Computation of simple and group factors of multivariate polynomials (1997)
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    Circuits, systems and signal processing 16 (1997), S. 455-473 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper generalizes a recent result onsimple factorization of 2-variable (2-v) polynomials to simple andgroup factorization ofn-variate (n-v), (n≥3) polynomials. The emphasis is on developing a reliablenumerical technique for factorization. It is shown that simple as well as group factorization can be achieved by performing singular value decomposition (SVD) on certain matrices obtained from the coefficients of the givenn-v polynomial expressed in a Kronecker product form. For the polynomials that do not have “exact” simple and/or group factors, the concepts of approximate simple and group factorization are developed. The use of SVD leads to an elegant solution of an approximaten factorization problem. Several nontrivial examples are included to illustrate the results presented in this paper.
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    URL: http://dx.doi.org/10.1007/BF01198062
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    A sequentially operated periodic FIR filter for perfect reconstruction (1997)
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    Circuits, systems and signal processing 16 (1997), S. 475-486 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a sequentially operated periodic FIR filter to perform the functions of multirate filter banks for perfect reconstruction. This filter consists of an analysis filter and a synthesis filter. Each of these filters has a single-input/single-output FIR filter with periodically time-varying coefficients and a sequentially operated multichannel sampling scheme. As a result, the proposed filter can offer considerable improvements in computation and implementation. For the design of the filter, we provide a necessary and sufficient condition for perfect reconstruction in terms of the blocked transfer matrices and give a design procedure.
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    Design of linear-phase, FIR integrators of degreer, r=1, 2, 3,..., for midband frequency range (1997)
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    Circuits, systems and signal processing 16 (1997), S. 537-545 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper a novel analytical technique for designing linear-phase, FIR integrators of first degree has been proposed by taking the optimality criteria of maximal flatness (in the Butterworth sense) of the amplitude response, at midband frequency:ω=π/2. Mathematical formulas to compute exact weights for the design of first-degree integrators (i.e., frequency response 1/(jω)) have been derived. Thereafter, the design has been extended to approximate linear-phase integrators for any generic degreer, r〉1. The performance characteristics of the first-, second- and third-degree integrators have been given to highlight the efficacy of the designs. The suggested designs are particularly suitable for the midband frequency range of operations.
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    Design of IIR digital notch filters (1997)
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    Circuits, systems and signal processing 16 (1997), S. 415-427 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A method is presented for the design of notch filters with specified notch frequency Ω0 and 3-dB rejection bandwidthB t, using a first-order real all-pass filter, wherein the only coefficient is used to control the notch frequency. To control the bandwidth, use is made of a new amplitude change function (ACF), and it is shown that given notch filter specifications can be exactly met thereby. Also, using the ACF, it is shown that stability of the second-order notch filter designs can be improved along with the noise gain.
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    When is the stability of a nonlinear input-output system robust? (1997)
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    Circuits, systems and signal processing 16 (1997), S. 487-505 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider a general nonlinear input-output system governed by operator equations that relate the system's input, state, and output, all of which are in extended spaces. It is assumed that the system variables are separated. Our results give conditions under which the stability of the nominal system is robust; i.e., it is not destroyed by any sufficiently small admissible perturbation of the system. Theorem 1 deals with the case when by stability we mean theincremental stability. Theorem 3 concerns the*-stability; i.e., the case when the stability is essentially the boundedness of the transmission operator. Moreover, in Theorem 2 it is shown that, under certain conditions, the incremental stability of the nominal system implies insensitivity. Basically, our results show that if the operators describing the nominal system are well behaved, and the transition from the nominal system to the perturbed system is not abrupt, then the nominal system stability is robust. The applications of the results are illustrated by several examples.
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    A separation theorem for finite-precision digital systems (1997)
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    Circuits, systems and signal processing 16 (1997), S. 107-119 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract For models of zero-input direct-form digital filters implemented in fixed-point digital hardware it is known that if saturation arithmetic is used and stability holds when the quantization is ignored, then the amplitude of all limit cycles can be made arbitrarily small by making the bound on the magnitude of the quantization sufficiently small. In that sense the effects of quantization and overflow can be considered separately. Recently, this proposition was extended to the case in which the input need not be zero. Here we give a result to the effect that quantization and overflow can be considered separately for a much more general class of discrete-time systems, and we give as an example an application of this result to systems governed by state equations.
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    Image restoration using a conjugate gradient-based adaptive filtering algorithm (1997)
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    Circuits, systems and signal processing 16 (1997), S. 197-206 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new two-dimensional (2D) sample-based conjugate gradient (SCG) algorithm is developed for adaptive filtering. This algorithm is based on the conjugate gradient method of optimization and therefore has a fast convergence characteristic. The SCG is computationally simpler than the recursive least squares (RLS) algorithm. The SCG algorithm with the equation-error and output-error methods is investigated for application in image restoration. Simulation results show that the new algorithm significantly outperforms existing algorithms in the restoration of noisy images.
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    Row Straightening via local interactions (1997)
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    Circuits, systems and signal processing 16 (1997), S. 287-305 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A number of agents can arrange themselves equidistantly in a row via a sequence of adjustments, based on a simple “local” interaction. The convergence of the configuration to the desired one is exponentially fast. A similarity is shown between this phenomenon and the dynamics of pulse propagation along a distributedRC line, and a conjecture is made concerning the evolution of a similar system with a probabilistic rule of behavior.
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    Generic properties of combinatory maps: Neutral networks of RNA secondary structures (1997)
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    Bulletin of mathematical biology 59 (1997), S. 339-397 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract Random graph theory is used to model and analyse the relationship between sequences and secondary structures of RNA molecules, which are understood as mappings from sequence space into shape space. These maps are non-invertible since there are always many orders of magnitude more sequences than structures. Sequences folding into identical structures formneutral networks. A neutral network is embedded in the set of sequences that arecompatible with the given structure. Networks are modeled as graphs and constructed by random choice of vertices from the space of compatible sequences. The theory characterizes neutral networks by the mean fraction of neutral neighbors (λ). The networks are connected and percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value (λ〉λ*). Below threshold (λ〈λ*), the networks are partitioned into a largest “giant” component and several smaller components. Structure are classified as “common” or “rare” according to the sizes of their pre-images, i.e. according to the fractions of sequences folding into them. The neutral networks of any pair of two different common structures almost touch each other, and, as expressed by the conjecture ofshape space covering sequences folding into almost all common structures, can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared to data obtained by folding large samples of RNA sequences. Differences are explained in terms of specific features of RNA molecular structures.
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    Host-parasite dynamics and the evolution of host immunity and parasite fecundity strategies (1997)
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    Bulletin of mathematical biology 59 (1997), S. 427-450 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract We explore evolutionarily stable co-evolution of host-macroparasite interactions in a discrete-time two-species population dynamics model, in which the dynamics may be stable, cyclic or chaotic. The macroparasites are assumed to harm host individuals through decreased reproductive output. Hosts may develop costly immune responses to defend themselves against parasites. Parasites compete with conspecifics by adjusting their fecundities. Overall, the presence of both parasites and the immune response in hosts produces more stable dynamics and lower host population sizes than that observed in the absence of the parasites. In our evolutionary analyses, we show that maximum parasite fecundity is always an evolutionarily stable strategy (ESS), irrespective of the type of population interaction, and that maximum parasite fecundity generally induces a minimum parasite population size through over-exploitation of the host. Phenotypic polymorphisms with respect to immunity in the host species are common and expected in ESS host strategies: the benefits of immunication depend on the frequency of the immune hosts in the population. In particular, the steady-state proportions of immune hosts depend, in addition to all the parameters of the parasite dynamics only on the cost of immunity and on the virulence of parasites in susceptible hosts. The implicit ecological dynamics of the host-parasite interaction affect the proportion of immune host individuals in the population. Furthermore, when changes in certain population parameters cause the dynamics of the host-parasite interaction to move from stability to cyclicity and then to chaos, the proportion of immune hosts tends to decrease; however, we also detected counter-examples to this result. As a whole, incorporating immunological and genetic aspects, as well as life-history trade-offs, into host-macroparasite dynamics produces a rich extension to the patterns observed in the models of ecological interactions and epidemics, and deserves more attention than is currently the case.
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    Pattern formation in systems with one spatially distributed species (1997)
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    Bulletin of mathematical biology 59 (1997), S. 533-549 
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    Topics: Biology , Mathematics
    Notes: Abstract We describe a three-species mechanism for spatial pattern formation in which only one species spatially moves. We show that a bifurcation to traveling or standing waves occurs. We contrast this mechanism for pattern formation with the better known cases where more than one species moves.
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    Dynamics of cellular homeostasis: Recovery time for a perturbation from equilibrium (1997)
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    Bulletin of mathematical biology 59 (1997), S. 451-481 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract In the collecting ductin vivo, the principal cell encounters a wide range in luminal flow rate and luminal concentration of NaCl. As a consequence, there are substantial variations in the transcellular fluxes of Na+ and Cl−, conditions which would be expected to perturb cell volume and cytosolic concentrations. Several control mechanisms have been identified which can potentially blunt these perturbations, and these entail cellular regulation of the luminal membrane Na+ channel and peritubular membrane K+ and Cl− channels. To illustrate the impact of these regulated channels, a mathematical model of the principal cell of the rat cortical collecting duct has been developed, in which ion channel permeabilities are either constant or regulated. In comparison to the model with fixed permeabilities, the model with regulated channels demonstrates enhanced cellular homeostasis following steady-state variation in luminal NaCl. However, in the transient response to a cytosolic perturbation, the difference in recovery time between the models is small. An approximate analysis is presented which casts these models as dynamical systems with constant coefficients. Despite the presence of regulated ion channels, concordance of each model with its linear approximation is verified for experimentally meaningful perturbations from the reference condition. Solution of a Lyapunov equation for each linear system yields a matrix whose application to a perturbation permits explicit estimation of the time to recovery. Comparison of these solution matrices for regulated and non-regulated cells confirms the similarity of the dynamic response of the two models. These calculations suggest that enhanced homeostasis by regulated channels may be protective, without necessarily hastening recovery from cellular perturbations.
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    Cannibalism in an age-structured predator-prey system (1997)
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    Bulletin of mathematical biology 59 (1997), S. 551-567 
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    Topics: Biology , Mathematics
    Notes: Abstract Recently, Kohlmeier and Ebenhöh showed that cannibalism can stabilize population cycles in a Lotka-Volterra type predator-prey model. Population cycles in their model are due to the interaction between logistic population growth of the prey and a hyperbolic functional response. In this paper, we consider a predator-prey system where cyclic population fluctuations are due to the age structure in the predator species. It is shown that cannibalism is also a stabilizing mechanism when population oscillations are due to this age structure. We conclude that in predator-prey systems, cannibalism by predators can stabilize both externally generated (consumer-resource) as well as internally generated (agestructure) fluctuations.
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    Two classes of the aminoacyl-tRNA synthetases in correspondence with the Codon path cube (1997)
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    Bulletin of mathematical biology 59 (1997), S. 645-648 
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    Topics: Biology , Mathematics
    Notes: Abstract Codon corresponding amino acids within the Codon path cube exist in a strict relation to two classes of enzymes aminoacyl-tRNA synthetases.
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    Cycle-time and residence-time density approximations in a stochastic model for circulatory transport (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1-22 
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    Topics: Biology , Mathematics
    Notes: Abstract The concentration of a drug in the circulatory system is studied under two different elimination strategies. The first strategy—geometric elimination—is the classical one which assumes a constant elimination rate per cycle. The second strategy—Poisson elimination—assumes that the elimination rate changes during the process of elimination. The problem studied here is to find a relationship between the residence-time distribution and the cycle-time distribution for a given rule of elimination. While the presented model gives this relationship in terms of Laplace-Stieltjes transform, the aim here is to determine the shapes of the corresponding probability density functions. From experimental data, we expect positively skewed, gamma-like distributions for the residence time of the drug in the body. Also, as some elimination parameter in the model approaches a limit, the exponential distribution often arises. Therefore, we use laguerre series expansions, which yield a parsimonious approximation of positively skewed probability densities that are close to a gamma distribution. The coefficients in the expansion are determined by the central moments, which can be obtained from experimental data or as a consequence of theoretical assumptions. The examples presented show that gamma-like densities arise for a diverse set of cycle-time distributions and under both elimination rules.
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    Evolution of shape in oligocene and mioceneNotocarinovalva (Ostracoda, Crustacea): A multivariate statistical study (1997)
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    Bulletin of mathematical biology 59 (1997), S. 63-87 
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    Topics: Biology , Mathematics
    Notes: Abstract Largely due to L. F. Bookstein, geometric morphometrics has been developed as an amalgamation of techniques drawn from mathematical statistics, non-Euclidean geometry and computer graphics, applied to labelled points (landmarks) and the biological images upon which they are registered. A tool of fundamental importance is the method of interpolation known as the thin-plate spline. Bookstein's sample-oriented procedure of relative warps, applied to data composed of coordinate pairs observed on eight landmarks on three samples of two species of fossil marine ostracods (bivalved microcrustacean),Notocarinovalva airella andN. yulecartensis, separated in time, is used to obtain weight matrices, which, when appropriately partitioned, constitute the familiar data matrices of multivariate statistical analysis. Standard multivariate statistical analysis of samples may be carried out in the tangent space to shape space at the Procrustes average shape. Linear discriminant function scores were used for assessing, approximately, the evolutionary relevance of shape change and change in size (based on standard distance measures) in the species from the upper and lower Oligocene and lower middle Miocene of Victoria, Australia. The findings indicate that a small, though consistent, change in non-uniform shape of the carapace has taken place. The analysis indicates that the evolution in shape of the carapace could have been caused by random genetic drift in moderately large populations, tempered by weak selection.
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    Book reviews (1997)
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    Bulletin of mathematical biology 59 (1997), S. 197-204 
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    Topics: Biology , Mathematics
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    Isologous diversification: A theory of cell differentiation (1997)
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    Bulletin of mathematical biology 59 (1997), S. 139-196 
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    Topics: Biology , Mathematics
    Notes: Abstract An isologous diversification theory for cell differentiation is proposed, based on simulations of interacting cells with biochemical networks and the cell division process following consumption of some chemicals. According to the simulations of the interaction-based dynamical systems model, the following scenario of the cell differentiation is proposed. (1) Up to some threshold number, divisions bring about almost identical cells with synchronized biochemical oscillations. (2) As the number is increased, the oscillations lose synchrony, leading to groups of cells with different phases of oscilaations. (3) Amplitudes of oscillation and averaged chemical compositions start to differ by groups of cells. The differentiated behavior of states is transmitted to daughter cells. (4) Recursivity is formed so that the daughter cells keep the identical chemical character. This “memory” is made possible through the transfer of initial conditions. (5) Successive differentiation proceeds. The mechanism of tumor cell formation, origin of stem cells, anomalous differentiation by transplantations, apoptosis and other features of cell differentiation process are also discussed, with some novel predictions.
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    On the origin of tiger bush (1997)
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    Bulletin of mathematical biology 59 (1997), S. 263-294 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We propose a model which describes the dynamics of vast classes of terrestrial plant communities growing in arid or semi-arid regions throughout the world. On the basis of this model, we show that the vegetation stripes (tiger bush) formed by these communities result from an interplay between short-range cooperative interactions controlling plant reproduction and long-range self-inhibitory interactions originating from plant competition for environmental resources. Isotropic as well as anisotropic environmental conditions are discussed. We find that vegetation stripes tend to orient themselves in the direction parallel or perpendicular with respect to a direction of anisotropy depending on whether this anisotropy influences the interactions favouring or inhibiting plant reproduction; furthermore, we show that ground curvature is not a necessary condition for the appearance of arcuate vegetation patterns. In agreement within situ observations, we find that the width of vegetated bands increases when environmental conditions get more arid and that patterns formed of stripes oriented parallel to the direction of a slope are static, while patterns which are perpendicular to this direction exhibit an upslope motion.
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    A two-backbone polymer model for interphase chromosome geometry (1997)
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    Bulletin of mathematical biology 59 (1997), S. 325-337 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A polymer model for the overall geometric structure of a human chromosome during the G0/G1 portion of cell-cycle interphase is constructed, based on fluorescencein situ hybridization data on distances between defined genomic sequences. The model consists of flexible giant loops, averaging about 6 million base pairs, with two random-walk backbones; it involves essentially three parameters. Numerical results based on properly selected values of parameters fit the data well.
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