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  • Articles  (6,460)
  • Springer  (6,460)
  • American Chemical Society
  • 1995-1999  (6,460)
  • 1997  (6,460)
  • Mathematics  (6,460)
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  • Articles  (6,460)
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  • 1995-1999  (6,460)
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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
    Electronic Resource
    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 
    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/BF02458430
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  • 7
    Electronic Resource
    Electronic Resource
    Dynamical consequences of optimal host feeding on host-parasitoid population dynamics (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 809-831 
    Details
    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
    Electronic Resource
    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
    Electronic Resource
    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 
    Details
    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
    Electronic Resource
    An extremum principle for parabolic competition (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1145-1154 
    Details
    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
    Electronic Resource
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460108
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  • 13
    Electronic Resource
    Electronic Resource
    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.
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    URL: http://dx.doi.org/10.1007/BF02458429
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  • 14
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
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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
    Electronic Resource
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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
    Electronic Resource
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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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    Stability and instability properties of aggregation of single chain amphiphiles into binary mixtures (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 43-61 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    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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    The hydromechanics of hydrocephalus: Steady-state solutions for cylindrical geometry (1997)
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    Bulletin of mathematical biology 59 (1997), S. 295-323 
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    Notes: Abstract Hydrocephalus is a state in which the circulation of cerebrospinal fluid is disturbed. This fluid, produced within the brain at a constant rate, moves through internal cavities in it (ventricles), then exits through passages so that it may be absorbed by the surrounding membranes (meninges). Failure of fluid to move properly through these passages results in the distention of the passages and the ventricles. Ultimately, this distention causes large displacements and distortion of brain tissue as well as an increase of fluid in the extracellular space of the brain (edema). We use a two-phase model of fluid-saturated material to simulate the steady state of the hydrocephalic brain. Analytic solutions for the displacement of brain tissue and the distribution of edema for the annular regions of an idealized cylindrical geometry and small-strain theory are found. The solutions are used for a large-deformation analysis by superposition of the responses obtained for incrementally increasing loading. The effects of structural and hydraulic differences of white and gray brain matter, and the ependymal lining surrounding the venticles, are examined. The results reproduce the characteristic steady-state distribution of edema seen in hydrocephalus, and are compared with experiment.
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    Matching among multiple random sequences (1997)
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    Bulletin of mathematical biology 59 (1997), S. 483-496 
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    Notes: Abstract In searching for strong homologies between multiple nucleic acid or protein sequences, researchers commonly look at fixed-length segments in common to the sequences. Such homologies form the foundation of segment-based algorithms for multiple alignment of protein sequences. The researcher uses settings of “unusualness of multiple matches” to calibrate the algorithms. In applications where a researcher has found a multiple matching word, statistical significance helps gauge the unusualness of the observed match. Previous approximations for the unusualness of multiple matches are based on large sample theory, and are sometimes quite inaccurate. Section 2 illustrates this inaccuracy, and provides accurate approximations for the probability of a common word inR out ofR sequences. Section 3 generalizes the approximation to multiple matching inR out ofS sequences. Section 4 describes a more complex approximation that incorporates exact probabilities and yields excellent accuracy; this approximation is useful for checking the simpler approximations over a range of values.
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    Links between maximum likelihood and maximum parsimony under a simple model of site substitution (1997)
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    Bulletin of mathematical biology 59 (1997), S. 581-607 
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    Notes: Abstract Stochastic models of nucleotide substitution are playing an increasingly important role in phylogenetic reconstruction through such methods as maximum likelihood. Here, we examine the behaviour of a simple substitution model, and establish some links between the methods of maximum parsimony and maximum likelihood under this model.
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    Phase transition from environmental to dynamic determinism in mountain pine beetle attack (1997)
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    Bulletin of mathematical biology 59 (1997), S. 609-643 
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    Notes: Abstract Mountain pine beetle outbreaks are responsible for widespread tree mortality in pine forests throughout western North America. Intensive outbreaks result in significant economic loss to the timber industry and massive changes to the forest habitat. Because of the time and space scales involved in a beetle outbreak, mathematical models are needed to study the evolution of an outbreak. In this paper we present a partial differential equation model of the flight phase of the mountain pine beetle which includes chemotactic responses and tree defense. We present a numerical method for integrating this model and use this method to investigate the relationship between emergence rate, forest demographic and patterns of beetle attack. In particular we look at how emergence rate affects the beetles' ability to successfully attack strong trees, which may be an indicator of an epidemic outbreak.
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    Continuous versus discrete single species population models with adjustable reproductive strategies (1997)
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    Bulletin of mathematical biology 59 (1997), S. 679-705 
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    Notes: Abstract We investigate population models with both continuous and discrete elements. Birth is assumed to occur at discrete instants of time whereas death and competition for resources and space occur continuously during the season. We compare the dynamics of such discrete-continuous hybrid models with the dynamics of purely discrete models where within-season mortality and competition are modelled directly as discrete events. We show that non-monotone discrete single-species maps cannot be derived from unstructured competition processes. This result is well known in the case of fixed reproductive strategies and our results extend this to the case of adjustable reproductive strategies. It is also shown that the most commonly used non-monotone discrete maps can be derived from structured competition processes.
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    Mathematical interpretation of dose-response curves (1997)
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    Bulletin of mathematical biology 59 (1997), S. 747-761 
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    Notes: Abstract The dose-response of an individual organism can be described by a step functions if the organism survives when the dose is below a certain lethal level and dies when this level is exceeded. If, in a population of organism, the lethal dose for an individual has a unimodal distribution, the latter's properties will determine the shape of the population's response in the following manner. If the distribution is symmetric the dose-response curve has a symmetric sigmoid shape when plotted on linear coordinates. The location of the inflection point and the curve's slope around it are determined by the distribution's mode and variance. When the distribution is skewed, the dose-response curve has an asymmetric sigmoid shape which becomes reminiscent of an exponential decay when the distribution is strongly skewed to the right. The population's dose-response curve can be constructed by integration of the step changes over the distribution range. The step function representing the dose-response of an individual organism can be approximate by a Fermi function, and the distribution of an lethal doses can be represented by the Weibull distribution function. When the two functions are combined, the resulting dose-response of the populationS(X)), which is the fraction of survivors after exposure to a doseX, is given by:S(X)=∫ 0 1 [1/{+exp{(X-X c (φ))/a i ]}]dω whereX c (ω)={(1/b)[-ln(1-ω)]}(1/n),n andb being the constants of the Weibull distribution anda i an arbitrarily small number, i.e.a i ≪[X−X c (ϕ)], whose actual magnitude is of little significance. This model can be used to determine the underlying distributions of experimental dose-response relationship. It was applied to published survival data of microorganisms exposed to pulsed electric field, X-ray radiation and ozone to show that the different observed shapes of the dose-response curve, and shifts between them, can be expressed in terms of the correponding distribution parameters, namely the mode, variance and skewness.
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    Penetration of host cell lines by bacteria. Characteristics of the process of intracellular bacterial infection (1997)
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    Bulletin of mathematical biology 59 (1997), S. 857-879 
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    Notes: Abstract A model which describes the characteristics of the penetration of the cells by bacteria is presented. Since the process of invasion is preceded necessarily by the step in which the bacteria adhere to the cells, the proposed model is based on the expressions previously derived for the process of adhesion, which allow us to determine the number of attached bacteria under different conditions. Thus, the model considers that invasion occurs irreversibly from attached bacteria to specific receptors located on the cell surface with a rate coefficient=k i so that the invasive capacity in a given bacterium-host cell system is mainly determined by the value of this coefficient. Once internalized, the bacteria can follow three different time courses, namely: 1) intracellular growth is hindered so that the bacteria remain in stationary phase, 2) there is a lag phase during which the bacteria stay in stationary phase before they are able to grow exponentially with a rate coefficient=k c , and 3) the bacteria exhibit a growth exponertial phase as they enter the cells. In turn, the time course followed by extracellular bacteria also has a decisive influence on the process of invasion and, in this regard, unbound bacteria are considered either in stationary or in exponential phase. Expressions for these different situations have been derived, and from them, procedures to determine the levels of bacterial infection and for quantitative invasive data analysis are presented.
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    Virus load and antigenic diversity (1997)
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    Bulletin of mathematical biology 59 (1997), S. 881-896 
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    Notes: Abstract In this paper, we analyse mathematical models for the interaction between virus replication and immune responses. We show that the immune system can provide selection pressure for or against viral diversity. The paper provides new insights into the relationship between virus load (=the abundance of virus in an infected individual) and antigenic diversity. Antigenic variation can increase virus load during infections, but the correlation between load and diversity in comparisons among different infected individuals can be positive or negative, depending on whether individuals differ in their cross-reactive or strain-specific immune responses. We derive two models: our first model applies to any replicating parasite that can escape from immune responses; our second model includes immune function impairment, and specifically describes infections with the human immunodeficiency virus (HIV).
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    On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed (1997)
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    Bulletin of mathematical biology 59 (1997), S. 911-929 
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    Notes: Abstract The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicita priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vasclar indicators. A sum of two inverse Gaussian functions is proposed as an alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models.
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    Bulletin of mathematical biology 59 (1997), S. 1013-1028 
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    Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1029-1046 
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    Notes: Abstract Cultured vascular endothelial cells undergo significant morphological changes when subjected to sustained fluid shear stress. The cells elongate and align in the direction of applied flow. Accompanying this shape change is a reorganization at the intracellular level. The cytoskeletal actin filaments reorient in the direction of the cells' long axis. How this external stimulus is transmitted to the endothelial cytoskeleton still remains unclear. In this article. we present a theoretical model accounting for the cytoskeletal reorganization under the influence of fluid shear stress. We develop a system of integro-partial-differential equations describing the dynamics of actin filaments, the actin-binding proteins, and the drift of transmembrane proteins due to the fluid shear forces applied on the plasma membrane. Numerical simulations of the equations show that under certain conditions, initially randomly oriented cytoskeletal actin filaments reorient in structures parallel to the externally applied fluid shear forces. Thus, the model suggests a mechanism by which shear forces acting on the cell membrane can be transmitted to the entire cytoskeleton via molecular interactions alone.
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    Asymptotic analysis of an epidemic model with primary and secondary infection (1997)
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    Bulletin of mathematical biology 59 (1997), S. 1101-1123 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For many biological systems, the behavior of interest is contained in the evolution of transients rather than in the stability of equilibria. These include systems in which perturbations and interruptions occur on a time scale much shorter than the equilibration time, and those in which any final equilibrium is sensitive to initial conditions. In this article, we examine a model of fungal root disease in a crop involving primary and secondary infection mechanisms. This system is subject to regular interruptions in the form of harvesting and sowing. Using an asymptotic approach in which certain parameter values are assumed to be small, the model can be broken down into a set of simpler subsystems respresenting recognizable biological mechanisms. These linear models can be solved to give closed-form analytical solutions for transient evolution. From this information, it is possible to construct an annual map of disease severity in the crop, and determine the parameter values under which the infection will bulk up or fade out.
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    Qualitative modeling of mechanoelectrical feedback in a ventricular cell (1997)
    Springer
    Bulletin of mathematical biology 59 (1997), S. 1155-1181 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mechanical changes in the heart muscle can influence its electrical properties through a process called mechanoelectrical feedback (MEF). This feedback can operate via changes in calcium dynamics during the cross-bridge cycle or via mechanosensitive (stretch-activated) channels. We present a four-variable ordinary differential equation (ODE) system that caricatures the electrical and mechanical activity of a ventricular cell and their mutual interactions. A three-variable excitable system with restitution properties of the FitzHugh-Nagumo type is coupled to a fourth equation which describes changes in cell length during a lightly loaded contraction. The resulting four-variable system models MEF in a cell and can be incorporated into spatially distributed models for mechanoelectric behavior during wave propagation in the cardiac tissue.
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    Compactness properties of locally compact groups (1997)
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    Transformation groups 2 (1997), S. 119-135 
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    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Compactness propertiesC n andC P n for locally compact groupsG are introduced generalizing the finiteness propertiesF n andF P n for discrete groups. The propertyC 1 resp.C 2 is equivalent withG having a compact set of generators, resp. having a compact presentation. Some basic properties of the compactness propertiesC n are shown. A local-global principle is proved by the second named author in the adjacent paper of this volume.
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    Workload planning in small lot printed circuit board assembly (1997)
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    OR spectrum 19 (1997), S. 147-157 
    Details
    ISSN: 1436-6304
    Keywords: Key words: production ; scheduling ; printed circuit board assembly ; modelling ; linear programming ; aggregational error ; decision support ; Schlüsselwörter: Produktion ; Ablaufplanung ; Leiterplattenbestückung ; Modellierung ; lineare Programmierung ; Aggregationsfehler ; Entscheidungsunterstützung ; S′jm = Sjm ; SFj(r)(12)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Bei der Kleinserienmontage von Leiterplatten besteht das Problem der Einlastungsplanung darin, ein Tagesprogramm an Produktionsaufträgen zusammenzustellen, die gemeinsam in das Produktionssystem eingeschleust werden. Jeder Produktionsauftrag entspricht einem bestimmten Leiterplattentyp. Wechselt man bei der automatischen Bestückung von Leiterplatten zu einem neuen Leiterplattentyp, so fallen erhebliche Rüstzeiten an, die davon abhängen, wie viele Bauteilezuführungen im Magazin der Bestückungsautomaten ausgewechselt werden müssen. Zur Unterstützung dieses Entscheidungsproblems werden zwei unterschiedliche Modelle der linearen Optimierung entwickelt. Die beiden Modelle unterscheiden sich vor allem durch ihren Aggregationsgrad und ihren Rechenaufwand. Zur Verringerung des Aggregationsfehlers wird ein auf der Fuzzy-Set-Theorie beruhender Ansatz zur Abschätzung der bei automatischen SMD-Bestückungsautomanten auftretenden Rüstzeiten entwickelt. Hierbei wird als industrielles Anwendungsbeispiel die Leiterplattenbestückung in einem bedeutenden Elektronikunternehmen betrachtet. Die durchgeführte numerische Untersuchung zeigt, daß das hochaggregierte Fuzzy-LP-Modell zu hinreichend genauen Lösungen führt und erheblich geringeren Rechenaufwand verursacht als ein detaillierteres LP-Modell. Außerdem wird die praktische Eignung des Fuzzy-LP-Modells für den Einsatz innerhalb eines interaktiven Entscheidungsunterstützungssystems verdeutlicht.
    Notes: Abstract. The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.
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    A capacity-oriented hierarchical approach to single-item and small-batch production planning using project-scheduling methods (1997)
    Springer
    OR spectrum 19 (1997), S. 77-85 
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    ISSN: 1436-6304
    Keywords: Single-item and small-batch production ; make-to-order production ; hierarchical planning ; project scheduling ; Einzel- und Kleinserienfertigung ; Kundenauftragsfertigung ; Hierarchische Planung ; Projektplanung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Die meisten in der Praxis eingesetzten Produktionsplanungs- und Steuerungssysteme (PPS-Systeme) besitzen den Nachteil, daß weder eine hierarchische Planung mit Rückkopplungen ermöglicht wird, noch die Ressourcenbeschränkungen auf allen Planungsstufen beachtet werden. Außerdem sind PPS-Systeme meist nicht auf die Anforderungen verschiedener Organisations- und Fertigungstypen, z.B. der Fertigung kleiner Stückzahlen, zugeschnitten. Wir behandeln einen Ansatz für die hierarchische Planung von Einzel- und Kleinserienfertigung bei Kundenauftragsfertigung unter Berücksichtigung beschränkter Ressourcen. Insbesondere werden die Stufen der kapazitierten Hauptproduktionsprogrammplanung, der mehrstufigen Losgrößenplanung, der Termin- und Kapazitätsplanung sowie der Maschinenbelegungsplanung betrachtet, wobei das Niveau der Produkt- und Ressourcenaggregation jeweils von Stufe zu Stufe abnimmt. Die meisten Optimierungsprobleme, die hierbei auf den einzelnen Planungsstufen auftreten, können als ressourcenbeschränkte Projektplanungsprobleme modelliert werden.
    Notes: Abstract Most production planning and control (PPC) systems used in practice have an essential weakness in that they do not support hierarchical planning with feedback and do not observe resource constraints at all production levels. Also, PPC systems often do not deal with particular types of production, for example, low-volume production. We propose a capacity-oriented hierarchical approach to single-item and small-batch-production planning for make-to-order production. In particular, the planning stages of capacitated master production scheduling, multi-level lot sizing, temporal and capacity planning, and shop floor scheduling are discussed, where the degree of aggregation of products and resources decreases from stage to stage. It turns out that the optimization problems arising at most stages can be modelled as resourceconstrained project scheduling problems.
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    Workload planning in small lot printed circuit board assembly (1997)
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    OR spectrum 19 (1997), S. 147-157 
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    ISSN: 1436-6304
    Keywords: production ; scheduling ; printed circuit board assembly ; modelling ; linear programming ; aggregational error ; decision support ; Produktion ; Ablaufplanung ; Leiterplattenbestückung ; Modellierung ; lineare Programmierung ; Aggregationsfehler ; Entscheidungsunterstützung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Bei der Kleinserienmontage von Leiterplatten besteht das Problem der Einlastungsplanung darin, ein Tagesprogramm an Produktionsaufträgen zusammenzustellen, die gemeinsam in das Produktionssystem eingeschleust werden. Jeder Produktionsauftrag entspricht einem bestimmten Leiterplattentyp. Wechselt man bei der automatischen Bestückung von Leiterplatten zu einem neuen Leiterplattentyp, so fallen erhebliche Rüstzeiten an, die davon abhängen, wie viele Bauteilezuführungen im Magazin der Bestückungsautomaten ausgewechselt werden müssen. Zur Unterstützung dieses Entscheidungsproblems werden zwei unterschiedliche Modelle der linearen Optimierung entwickelt. Die beiden Modelle unterscheiden sich vor allem durch ihren Aggregationsgrad und ihren Rechenaufwand. Zur Verringerung des Aggregationsfehlers wird ein auf der Fuzzy-Set-Theorie beruhender Ansatz zur Abschätzung der bei automatischen SMD-Bestückungsautomanten auftretenden Rüstzeiten entwickelt. Hierbei wird als industrielles Anwendungsbeispiel die Leiterplattenbestückung in einem bedeutenden Elektronikunternehmen betrachtet. Die durchgeführte numerische Untersuchung zeigt, daß das hochaggregierte Fuzzy-LP-Modell zu hinreichend genauen Lösungen führt und erheblich geringeren Rechenaufwand verursacht als ein detaillierteres LP-Modell. Außerdem wird die praktische Eignung des Fuzzy-LP-Modells für den Einsatz innerhalb eines interaktiven Entscheidungsunterstützungssystems verdeutlicht.
    Notes: Abstract The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.
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    Palletmanager/cargomanager (1997)
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    OR spectrum 19 (1997), S. 177-180 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Resümee Mit Hilfe beider Programme kann ein breites Spektrum von industriellen Anwendungsproblemen der Paletten- und Containerbeladung sowie der Gestaltung von Packstückdimensionen effizient gelöst werden. Die Rechenzeiten liegen bei einem modernen PC im Bereich weniger Sekunden. Dabei sind die Programme sowohl an formalen Optimalitätskriterien ausgerichtet als auch an den vielfältigen praktischen Anforderungen, die in unterschiedlichen Anwendungssituationen auftreten können. Der Anwender erhält eine umfassende Lösungspräsentation sowie die Möglichkeit, zahlreiche Druckprotokolle unterschiedlicher Inhalte zu erstellen. Hinsichtlich der Druckprotokolle wäre eine weiterführende individuelle Gestaltungsmöglichkeit wünschenswert. Für künftige Versionen sollten die Entwicklung einer benutzerfreundlichen, grafikorientierten Programmoberfläche mit Mausbedienung sowie Online-Hilfen und Kontextmenüs angestrebt werden, damit der ohne Zweifel vorhandenen funktionalen Leistungsfähigkeit der Programme auch ein entsprechender Bedienkomfort zur Seite gestellt wird.
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    Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing (1997)
    Springer
    OR spectrum 19 (1997), S. 87-96 
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    ISSN: 1436-6304
    Keywords: Key words: Dynamic multi-item multi-level capacitated lotsizing ; mathematical programming models ; Schlüsselwörter: Dynamische mehrstufige Mehrprodukt-Losgrößenprobleme ; Modelle der mathematischen Programmierung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Das dynamische mehrstufige Mehrprodukt-Losgrößenproblem läßt sich als gemischt-ganzzahliges Optimierungsproblem mit einem Kürzeste-Wege-Modell abbilden. Ein besonderer Vorteil dieser Modellformulierung liegt in der sehr scharfen unteren Schranke der zugehörigen LP-Relaxation. Als nachteilig erweist sich jedoch einerseits der unverhältnismäßig hohe Rechenaufwand zur Lösung der LP-Relaxation mit Standardsoftware der mathematischen Programmierung sowie andererseits die mit der Periodenanzahl quadratisch wachsende Variablenanzahl, die die Lösbarkeit von Probleminstanzen mit vielen Perioden stark einschränkt. Zur Behebung der genannten Nachteile wird in dem vorliegenden Aufsatz eine Modifikation des ursprünglichen Kürzesten-Wege-Modells vorgeschlagen. Diese neue Modellformulierung erlaubt es dem Anwender einen Kompromiß zwischen der Modellgröße und der Schärfe der zugehörigen LP-Relaxation zu finden. Hierzu ist ein Vorschauhorizont τ vom Anwender zu definieren. Zusätzlich wird ein iteratives Verfahren beschrieben, das den minimalen Vorschauhorizont τ bestimmt, bei dem die schärfste untere Schranke erreicht wird. Neben theoretischen Erkenntnissen werden auch die Ergebnisse umfangreicher Testrechnungen vorgestellt.
    Notes: Abstract. The shortest route representation of the dynamic multi-item multi-level capacitated lotsizing problem is appealing due to the tight bound provided by its Linear Programming (LP) relaxation. However, it suffers from two main drawbacks: Firstly, even solving the LP relaxation of problem instances with up to 16 time periods and 40 items with standard mathematical programming software might require a prohibitive amount of computer time. Secondly, the quadratic growth of the number of variables with the number of periods restricts the solution of problem instances with many periods. Both drawbacks will be addressed in this paper by proposing reformulations of the original shortest route model. Especially we will introduce a model formulation which allows the user to find a tradeoff between model size and tightness of the lower bound obtained by the LP relaxation by specifying the number of look ahead periods τ. Furthermore, we will provide an iterative procedure for determining those look ahead periods which result in the tightest LP relaxation. Theoretical insights as well as computational results are provided, too.
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    Kapazitätsanpassung bei simultaner Losgrößen- und Reihenfolgeplanung (1997)
    Springer
    OR spectrum 19 (1997), S. 251-260 
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    ISSN: 1436-6304
    Keywords: Sortenfertigung ; Prozeßindustrie ; Losgrößenplanung ; Reihenfolgeplanung ; Batch production ; flow process industry ; lotsizing ; scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract The paper considers the effect of capacity adaptations for the Economic Lot Scheduling Problem. A heuristic is presented which shows how to compute simultaneously lot sizes, schedules and capacity requirements for medium term planning. The results are evaluated with respect to the optimal solution of the Continuous Setup Lotsizing Problem.
    Notes: Zusammenfassung Der vorliegende Beitrag erweitert das Planungsmodell des „Economic Lot Scheduling“ Problems um den für die Praxis in der Mittelfristplanung wichtigen Aspekt der Kapazitätsanpassung. Es wird eine Heuristik vorgestellt, die simultan Losgrößen, Reihenfolgen und die Kapazitätsanpassung bestimmt. Die Ergebnisse der Heuristik werden mit Hilfe der Optimallösung des „Continuous Setup Lotsizing“ Problems überprüft.
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    Buchbesprechungen (1997)
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    OR spectrum 19 (1997), S. 284-284 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    Buchbesprechungen (1997)
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    OR spectrum 19 (1997), S. 294-295 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    Dank den Referenten (1997)
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    OR spectrum 19 (1997), S. 296-296 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
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    Genetische Modellierung von Künstlichen Neuronalen Netzen (1997)
    Springer
    OR spectrum 19 (1997), S. 285-293 
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    ISSN: 1436-6304
    Keywords: Künstliche Neuronale Netze ; Genetischer Algorithmus ; Kreditwürdigkeitsprüfung ; Konfigurationsproblem ; Artificial neural nets ; genetic algorithm ; credit evaluation ; configuration problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract Artificial neural nets (ANN) have been applied successfully to various classification problems like credit evaluation etc. While the ANN-specific learning strategies and algorithms are independent from the application domain and the problem instance, the configuration of an ANN is a design and decision problem which should take into account the specific problem domain (i.e. credit evaluation) and the specific instantiation (i.e. given set of indicators). In this article we show how to apply “Genetic modeling” to this configuration problem, i.e. we show how suitable ANN-configurations can be constructed in an evolutionary manner using a genetic algorithm. We report on empirical results for the application to the configuration of LVQ-ANN for credit evaluation.
    Notes: Zusammenfassung Künstliche Neuronale Netze (KNN) haben sich für eine automatisierte Klassifikation, wie sie etwa bei der Kreditwürdigkeitsprüfung durchzuführen ist, als Alternative zu klassischen statistischen Methoden etabliert. Während die KNN-Typ-spezifischen Lernverfahren, wie etwa das Back-Propagation-Verfahren bei Multi-Layer-Perceptron-Netzen dabei anwendungsdomänenunabhängig und auch instanzunabhängig definiert sind, stellt die Konfiguration des spezifischen KNN für eine konkrete Anwendung ein Entscheidungsproblem dar, das jeweils in Abhängigkeit der Anwendungsdomäne (Kreditwürdigkeitsprüfung) und der konkreten Instanz (unternehmenspezifische Kennzahlensysteme) zu lösen ist. Für dieses Konfigurationsproblem, das in der Literatur noch nicht umfassend behandelt wurde, wird in dieser Arbeit mit dem “Genetic Modeling” ein Ansatz vorgestellt, bei dem eine passende Netzkonfiguration mittels eines Genetischen Algorithmus ebenfalls aus historischem Wissen “gelernt” wird. Wir berichten über erste empirische Ergebnisse beim Einsatz zur Kreditwürdigkeitsprüfung mittels LVQ-KNN.
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    Risk as a primitive: a survey of measures of perceived risk (1997)
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    OR spectrum 19 (1997), S. 235-250 
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    ISSN: 1436-6304
    Keywords: Key words: Risk judgement, perceived risk, axiomatic measures of risk ; Schlüsselwörter Risikobeurteilung, wahrgenommenes Risiko, axiomatische Risikomaße
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Risiko ist ein Konzept, das bei der Behandlung vieler volks- oder betriebswirtschaftlicher Probleme eine wesentliche Rolle spielt. Üblicherweise wird Risiko im Rahmen des traditionellen Erwartungsnutzenmodells behandelt, bei dem es nur indirekt über die Form der Nutzenfunktion erfaßt wird. Der Zweck von Nutzenfunktionen besteht aber darin, Präferenzen zu modellieren. In diesem Aufsatz wird ein Überblick über solche Ansätze gegeben, die Risikowahrnehmungen direkt modellieren. Nach einer kurzen Darstellung naiver Risikomaße, die aus der früheren ökonomischen Literatur bekannt sind, werden neuere theoretische und empirische Konzepte präsentiert.
    Notes: Abstract. The concept of risk is essential to many problems in economics and business. Usually, risk is treated in the traditional expected utility framework where it is defined only indirectly through the shape of the utility function. The purpose of utility functions, however, is to model preferences. In this paper, we review those approaches which directly model risk judgements. After a short review of naive risk measures used in earlier economic literature, we present recent theoretical and empirical developments.
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    Zur Abweichungsanalyse im operativen, modellgestützten Controlling (1997)
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    OR spectrum 19 (1997), S. 273-283 
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    ISSN: 1436-6304
    Keywords: Schlüsselwörter: Abweichungsanalyse ; Controlling ; Key words: Deviation analysis ; controlling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Abstract. Systems of economic ratios are very important in the field of operative controlling. Functional equations of economic quantities may be analyzed by comparing actual current values of these variables with planned values or values of a previous period using methods of deviation analysis. In this paper different methods of deviation analysis are compared. They are based on conditions, which should be satisfied by methods used to determine the effects on a depending quantity caused by the change of its components. In some aspects these conditions are different from conditions for methods of deviation analysis used in cost accounting. Based on an approximation of the temporal change of economic quantities a new method of deviation analysis is developed. This concept satisfies all conditions formulated at the beginning of the paper.
    Notes: Zusammenfassung. Große Bedeutung im operativen Controlling haben Kennzahlensysteme. Dabei auftretende funktionale Zusammenhänge zwischen den Kennzahlen lassen sich unter Nutzung der Methoden der Abweichungsanalyse analysieren, indem Soll- und Ist-Werte oder Angaben verschiedener zeitlicher Perioden miteinander verglichen werden. Gegenstand dieser Arbeit ist ein Vergleich verschiedener Konzepte der Abweichungsanalyse. Dazu werden Kriterien formuliert, deren Erfüllung für die Nutzung der betreffenden Methoden im Controlling und für eine möglichst einfache und eindeutige Interpretation der Ergebnisse wünschenswert erscheint. Aus der Sicht der Kennzahlensysteme ergeben sich dabei teilweise andere Anforderungen als die in der Kostenrechnung diskutierten Bedingungen. Für die Analyse der zeitlichen Entwicklung wird ein neues Konzept der Abweichungsanalyse entwickelt, das allen geforderten Kriterien genügt.
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    Simple optimal replenishment and disposal policies for a product recovery system with leadtimes (1997)
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    OR spectrum 19 (1997), S. 111-122 
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    ISSN: 1436-6304
    Keywords: Key words: Stochastic inventory control, remanufacturing, disposal, dynamic programming, decision rules ; Schlüsselwörter Stochastisches Lagerhaltungsproblem, Wiederverwendung, Entsorgung, Dynamische Programmierung, Entscheidungsregeln
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Es wird ein Lagerhaltungsproblem mit stochastischer Nachfrage betrachtet, bei dem Produkte nach Gebrauch wieder zurückgegeben werden können. Diese gebrauchten Güter, deren Rückfluß ebenfalls stochastischer Natur ist, können entweder nach entsprechender Aufarbeitung wiederverwendet oder müssen entsorgt werden. Außer durch Wiederaufarbeitung kann die Versorgung mit marktfähigen Produkten durch Neubeschaffung erfolgen. Es wird davon ausgegangen, daß nur proportionale Kosten für die einzelnen Aktivitäten auftreten und daß sowohl Wiederaufarbeitung als auch reguläre Beschaffung mit festen Durchlaufzeiten bzw. Lieferzeiten verbunden sind. Es wird für den Fall periodischer Kontrolle gezeigt, wie die optimale Entscheidungsregel für Beschaffung, Aufarbeitung und Entsorgung mit Hilfe der stochastischen dynamischen Programmierung untersucht werden kann. Dabei wird der entscheidende Einfluß von Durchlauf- und Lieferzeit auf die Komplexität der Entscheidungsregel herausgearbeitet. Schließlich wird gezeigt, für welche Situationen optimale Regeln einfacher Struktur abgeleitet werden können.
    Notes: Abstract. The paper addresses a problem of product recovery management where a single product is stocked in order to fulfill a stochastic demand of customers who may return products after usage, thus generating also stochastic product returns. The material flow can be controlled by procuring new products on the one hand, and by remanufacturing or disposal of returned items on the other. A situation is considered where all costs are proportional and where remanufacturing as well as procurement needs a fixed deterministic leadtime which can be different for both activities. For periodic review control it is shown how the optimal decision rules for procurement, remanufacturing and disposal can be evaluated by exploiting the functional equations of a dynamic programming formulation. The serious impact of leadtimes on the complexity of the control rule is elaborated, and it is demonstrated for which leadtime situations simple optimal policies can be derived.
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    URL: http://dx.doi.org/10.1007/BF01545510
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    Palletisation efficiency as a criterion for product design (1997)
    Springer
    OR spectrum 19 (1997), S. 139-145 
    Details
    ISSN: 1436-6304
    Keywords: Key words: Packing ; pallet loading ; product design. ; Schlüsselwörter: Packprobleme ; Palettenbeladung ; Produktgestaltung.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Der Artikel befaβt sich mit der Frage, wie bei der Gestaltung eines Produkts oder seiner Verpackung die Auswirkungen auf den Nutzungsgrad von Paletten berücksichtigt werden können. Die dabei eingenommene Perspektive ist die umgekehrte der üblichen: an Stelle einer Bewertung vorab bestimmter Alternativen betrachtet der Artikel das Problem, die Wahlmöglichkeiten zu identifizieren, die dem Designer zur Verfügung stehen, wenn ein bestimmter Nutzungsgrad der Palette erreicht werden soll. Zusätzlich zu mehreren algorithmischen Problemstellungen werden verschiedene praktische Aspekte des Problems erörtert. Die Ergebnisse zweier Fallstudien dienen als konkrete Bezugspunkte für alle Teile des Artikels.
    Notes: Abstract. The paper is concerned with the question of how implications for palletisation efficiency may be taken into account in the product/packaging design process. The perspective from which this topic is approached is the reverse of that usually adopted: rather than dealing with an evaluation of pre-determined design alternatives, the paper considers the problem of identifying the options open to the designer if a given palletisation efficiency target is to be achieved. In addition to a number of algorithmic issues various practical aspects of the problem are also discussed. The results of two case studies provide a concrete frame of reference throughout the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01545515
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  • 90
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    Buchbesprechungen (1997)
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    OR spectrum 19 (1997), S. 130-130 
    Details
    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01545512
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  • 91
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    Simple optimal replenishment and disposal policies for a product recovery system with leadtimes (1997)
    Springer
    OR spectrum 19 (1997), S. 111-122 
    Details
    ISSN: 1436-6304
    Keywords: Stochastic inventory control ; remanufacturing ; disposal ; dynamic programming ; decision rules ; Stochastisches Lagerhaltungsproblem ; Wiederverwendung ; Entsorgung ; Dynamische Programmierung ; Entscheidungsregeln
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Es wird ein Lagerhaltungsproblem mit stochastischer Nachfrage betrachtet, bei dem Produkte nach Gebrauch wieder zurückgegeben werden können. Diese gebrauchten Güter, deren Rückfluß ebenfalls stochastischer Natur ist, können entweder nach entsprechender Aufarbeitung wiederverwendet oder müssen entsorgt werden. Außer durch Wiederaufarbeitung kann die Versorgung mit marktfähigen Produkten durch Neubeschaffung erfolgen. Es wird davon ausgegangen, daß nur proportionale Kosten für die einzelnen Aktivitäten auftreten und daß sowohl Wiederaufarbeitung als auch reguläre Beschaffung mit festen Durchlaufzeiten bzw. Lieferzeiten verbunden sind. Es wird für den Fall periodischer Kontrolle gezeigt, wie die optimale Entscheidungsregel für Beschaffung, Aufarbeitung und Entsorgung mit Hilfe der stochastischen dynamischen Programmierung untersucht werden kann. Dabei wird der entscheidende Einfluß von Durchlauf- und Lieferzeit auf die Komplexität der Entscheidungsregel herausgearbeitet. Schließlich wird gezeigt, für welche Situationen optimale Regeln einfacher Struktur abgeleitet werden können.
    Notes: Abstract The paper addresses a problem of product recovery management where a single product is stocked in order to fulfill a stochastic demand of customers who may return products after usage, thus generating also stochastic product returns. The material flow can be controlled by procuring new products on the one hand, and by remanufacturing or disposal of returned items on the other. A situation is considered where all costs are proportional and where remanufacturing as well as procurement needs a fixed deterministic leadtime which can be different for both activities. For periodic review control it is shown how the optimal decision rules for procurement, remanufacturing and disposal can be evaluated by exploiting the functional equations of a dynamic programming formulation. The serious impact of leadtimes on the complexity of the control rule is elaborated, and it is demonstrated for which leadtime situations simple optimal policies can be derived.
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    URL: http://dx.doi.org/10.1007/BF01545510
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  • 92
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    Two new heuristic algorithms for the maximal planar layout problem (1997)
    Springer
    OR spectrum 19 (1997), S. 131-137 
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    ISSN: 1436-6304
    Keywords: Facility layout planning ; planar graphs ; heuristics ; numerical experiments ; Layout-Planung ; Innerbetriebliche Standortplanung ; Planare Graphen ; Heuristiken ; Numerische Experimente
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Das Nachbarschaftsproblem bildet ein zentrales Problem der innerbetrieblichen Standortplanung. Da es sich um ein NP-vollständiges Problem handelt, sind Heuristiken erforderlich, um große Problemausprägungen zu behandeln. In der vorliegenden Arbeit werden zwei neue Heuristiken für das Nachbarschaftsproblem vorgestellt, die zu einer speziellen Klasse von Eröffnungsverfahren, den sog. Triangulation Expansion Heuristics, gehören. Die Lösungsqualität und der Rechenzeitbedarf der Verfahren werden auf der Grundlage umfangreicher numerischer Experimente untersucht. Dabei erweist sich eine Heuristik gegenüber den bisher besten in der Literatur beschriebenen Verfahren (Eades et al. 1982, Leung 1992) als überlegen.
    Notes: Abstract The adjacency problem is an important subproblem in facility layout planning. It is known to be NP-complete, so heuristics are required to solve “large” problem instances. In this paper two new heuristics for the adjacency problem are introduced which belong to a special class of constructive methods called Triangulation Expansion Heuristics. Extensive numerical experiments have been carried out in order to evaluate the proposed methods in terms of computing times and solution quality. It has been found that at least one method is clearly superior to the best methods proposed in the literature so far (Eades et al. 1982, Leung 1992).
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    URL: http://dx.doi.org/10.1007/BF01545513
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    A capacity-oriented hierarchical approach to single-item and small-batch production planning using project-scheduling methods (1997)
    Springer
    OR spectrum 19 (1997), S. 77-85 
    Details
    ISSN: 1436-6304
    Keywords: Key words: Single-item and small-batch production ; make-to-order production ; hierarchical planning ; project scheduling ; Schlüsselwörter: Einzel- und Kleinserienfertigung ; Kundenauftragsfertigung ; Hierarchische Planung ; Projektplanung
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. Die meisten in der Praxis eingesetzten Produktionsplanungs- und Steuerungssysteme (PPS-Systeme) besitzen den Nachteil, daß weder eine hierarchische Planung mit Rückkopplungen ermöglicht wird, noch die Ressourcenbeschränkungen auf allen Planungsstufen beachtet werden. Außerdem sind PPS-Systeme meist nicht auf die Anforderungen verschiedener Organisations- und Fertigungstypen, z.B. der Fertigung kleiner Stückzahlen, zugeschnitten. Wir behandeln einen Ansatz für die hierarchische Planung von Einzel- und Kleinserienfertigung bei Kundenauftragsfertigung unter Berücksichtigung beschränkter Ressourcen. Insbesondere werden die Stufen der kapazitierten Hauptproduktionsprogrammplanung, der mehrstufigen Losgrößenplanung, der Termin- und Kapazitätsplanung sowie der Maschinenbelegungsplanung betrachtet, wobei das Niveau der Produkt- und Ressourcenaggregation jeweils von Stufe zu Stufe abnimmt. Die meisten Optimierungsprobleme, die hierbei auf den einzelnen Planungsstufen auftreten, können als res-sourcenbeschränkte Projektplanungsprobleme modelliert werden.
    Notes: Abstract. Most production planning and control (PPC) systems used in practice have an essential weakness in that they do not support hierarchical planning with feedback and do not observe resource constraints at all production levels. Also, PPC systems often do not deal with par-ticular types of production, for example, low-volume production. We propose a capacity-oriented hierarchical approach to single-item and small-batch-production planning for make-to-order production. In particular, the planning stages of capacitated master production scheduling, multi-level lot sizing, temporal and capacity planning, and shop floor scheduling are discussed, where the degree of aggregation of products and resources decreases from stage to stage. It turns out that the optimization problems arising at most stages can be modelled as resource-constrained project scheduling problems.
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    URL: http://dx.doi.org/10.1007/BF01545504
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    Location and layout planning (1997)
    Springer
    OR spectrum 19 (1997), S. 181-194 
    Details
    ISSN: 1436-6304
    Keywords: Discrete and continuous location planning ; warehouse location and center problems ; layout planning ; quadratic assignment and maximal planar graph problem ; Diskrete und kontinuierliche betriebliche Standortplanung ; Warehouse Location- und Zentrenprobleme ; innerbetriebliche Standortplanung ; quadratisches Zuordnungsproblem ; Bestimmung maximaler planarer Graphen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Der Beitrag gibt einen Überblick über quantitative Ansätze zur Lösung betriebswirtschaftlicher Standortplanungsprobleme. Es wird zwischen betrieblicher und innerbetrieblicher Standortplanung unterschieden. Abhängig von der zu verfolgenden Zielsetzung und von den zu beachtenden Nebenbedingungen ergibt sich v.a. bei der betrieblichen Standortplanung eine Vielzahl unterschiedlicher Probleme. Zu den wichtigsten Problemstellungen der diskreten und kontinuierlichen betrieblichen Standortplanung (z.B. Warehouse Location-, Zentren-, Location Routing- und Competitive Location-Probleme) werden Grundmodelle beschrieben und Hinweise auf neue Lösungsverfahren gegeben. Auch verallgemeinerte Modelle und neueste Entwicklungen werden skizziert. Im Rahmen der innerbetrieblichen Standortplanung (Layoutplanung) stellen wir das quadratische Zuordnungsproblem und verschiedene graphentheoretische Ansätze sowie geeignete Lösungsverfahren vor.
    Notes: Abstract This paper gives a review on quantitative methods for microeconomic location planning which can be subdivided into facility location and layout planning. Depending on different objectives and restrictions, there is a large variety of problems, especially in the field of facility location planning. Basic models arising in discrete and continuous facility location planning (e.g., warehouse location, center, location routing, competitive location problems), as well as corresponding solution methods, are presented. Generalized models and recent developments in these fields are outlined. Within layout planning, the quadratic assignment problem and graph-theoretic concepts are considered.
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    URL: http://dx.doi.org/10.1007/BF01545586
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    An exact algorithm for project scheduling with multiple modes (1997)
    Springer
    OR spectrum 19 (1997), S. 195-203 
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    ISSN: 1436-6304
    Keywords: Project management/scheduling ; discrete resource-resource and time-resource tradeoffs ; mode and delay alternatives ; branch-and-bound ; dominance rules ; computational results ; Projektmanagement/-planung ; diskrete Ressourcen-Ressourcen- und Zeit-Ressourcen-Tradeoffs ; Modus- und Delay-Alternativen ; Branch-and-Bound ; Dominanzregeln ; Rechenergebnisse
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir betrachten eine Erweiterung des klassischen Resource-Constrained Project Scheduling Problems (RCPSP), die die Abbildung von Ressourcen-Ressourcen- und Zeit-Ressourcen-Tradeoffs ermöglicht. Damit ist der Projektplaner in der Lage, für jeden Vorgang des Projekts mehrere Ausführungsalternativen (Modi) anzugeben. Der von uns vorgestellte Algorithmus ist eine Verallgemeinerung des derzeit schnellsten Branch-and-Bound-Verfahrens für das RCPSP von Demeulemeester und Herroelen. Wir erweitern deren Konzept der Delay-Alternativen um sogenannte Modus-Alternativen. Die Enumeration wird mit Hilfe von Dominanzregeln beschleunigt. Schließlich fassen wir unsere Rechenergebnise zusammen, in denen wir unser Verfahren mit dem derzeit schnellsten aus der Literatur bekannten Algorithmus vergleichen.
    Notes: Abstract We consider an extension of the classical resource-constrained project scheduling problem (RCPSP), which covers discrete resource-resource and time-resource tradeoffs. As a result a project scheduler is permitted to identify several alternatives or modes of accomplishment for each activity of the project. The solution procedure to be presented is a considerable generalization of the branch-and-bound algorithm proposed by Demeulemeester and Herroelen, which is currently the most powerful method for optimally solving the RCPSP. More precisely, we extend their concept of delay alternatives by introducing mode alternatives. The basic enumeration scheme is enhanced by dominance rules which increase the performance of the algorithm. We then report on our computational results obtained from the comparison with the most rapid procedure reported in the literature.
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    URL: http://dx.doi.org/10.1007/BF01545587
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    LINGO Rezensenten: K. Haase, R. Kolisch, Kiel (1997)
    Springer
    OR spectrum 19 (1997), S. 1-4 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01539798
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    LINGO (1997)
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    OR spectrum 19 (1997), S. 1-4 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Resümee LINGO ist ein ausgereiftes und leicht bedienbares Progamm zur Modellierung und Lösung linearer und nichtlinearer Optimierungsprobleme. Die Robustheit des Programms, die schnell erlernbare Modellierungssprache und das didaktisch hervorragend aufgebaute Handbuch machen LINGO zu einem wertvollen Hilfsmittel in der quantitativ orientierten Betriebswirtschaftslehre. Während die (Kern-)Funktionalität in der DOS- und in der WINDOWS-Version identisch ist, sei dem Anwender jedoch die WINDOWS-Version empfohlen, da diese eine sichere Handhabung von Dateien erlaubt und zudem eine Entwicklungsoberfläche bietet.
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    URL: http://dx.doi.org/10.1007/BF01539798
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    Buchbesprechung (1997)
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    OR spectrum 19 (1997), S. 22-22 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01539801
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  • 99
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    On the complexity of two machine job-shop scheduling with regular objective functions (1997)
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    OR spectrum 19 (1997), S. 5-10 
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    ISSN: 1436-6304
    Keywords: Job-shop ; polynomial algorithm ; Job-Shop ; polynomialer Algorithmus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Für das Zweimaschinen-Job-Shop-Problem ohne Arbeitsunterbrechnungen und den Zielfunktionen Σf i bzw. maxf i , wobei dief i monotone Funktionen der Fertigstellungszeiten der Jobsi sind, werden für den Fall fester Jobanzahlen polynomiale Algorithmen angegeben. Dies beantwortet insbesondere die bislang offene Frage nach dem Komplexitätsstatus des obigen Problems für die ZielfunktionenL max, Σw i U i , und Σw i U. Schließlich zeigen wir, daß das Problem mit beliebiger regulärer Zielfunktion ebenfalls polynomial lösbar ist.
    Notes: Abstract For the nonpreemptive two machine job-shop scheduling problem with a fixed number of jobs and objective functions Σf i and maxf i , wheref i are nondecreasing functions of the finish times of jobsi, polynomial algorithms are presented. This answers previous open questions about the complexity status of the corresponding problems with objective functionsL max, Σw i U i , and Σw i U. We generalize these results by showing that the problem with any regular criterion can be solved in polynomial time.
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    URL: http://dx.doi.org/10.1007/BF01539799
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    Buchbesprechung (1997)
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    OR spectrum 19 (1997), S. 30-30 
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    ISSN: 1436-6304
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01539803
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