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  • Springer  (100,817)
  • Elsevier  (91,877)
  • 1985-1989  (192,694)
  • 1950-1954
  • 1986  (99,217)
  • 1985  (93,477)
  • 1
    Electronic Resource
    Electronic Resource
    An equation for flow in the renal proximal tubule (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 29-57 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460061
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  • 2
    Electronic Resource
    Electronic Resource
    Seventeenth Annual Meeting of the Classification Society of North America (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 105-105 
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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/BF02460066
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  • 3
    Electronic Resource
    Electronic Resource
    Editorial: Software Survey Section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    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/BF02460067
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  • 4
    Electronic Resource
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    Dominance of geometric overelastic factors in pulse transmission through arterial branching (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 97-103 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460065
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  • 5
    Electronic Resource
    Electronic Resource
    Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 125-136 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460018
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  • 6
    Electronic Resource
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    Multiple stable equilibria in a predator-prey system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 137-148 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Necessary and sufficient conditions are given for three equilibria to occur in a predatorprey model and conditions are given for two of these to be stable. The existence of two stable equilibria requires predator intraspecific competition for either space or food, and the lower the prey growth rate the stronger this predator self-regulation must be. A prey growth rate that is skewed to the right, the ability of a few predators to survive at low prey densities, and predators with high searching effectiveness, long handling times, and large maximum per capita rate of increase all make two stable equilibria more likely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460019
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  • 7
    Electronic Resource
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    Servocontrol of the heart rate in homeothermic animals: On recognizing butterfly catastrophy models in biology (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 107-124 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Drawing evidence from a variety of cardiovascular studies on the heart rate in homeothermic animals, the author establishes the following thesis. The servocontrol (i.e. the autonomic and reflex control) by the medulla oblongata of the heart (rate) is a negative feedback dynamic which is isomorphic (i.e. ‘diffeomorphic’) to the dyamic underlying the heat rate control in those animals (cf. Kuyk,Bull. math. Biol. 46, 81–102, 1984). In fact, unlike in the heat rate case, the qualitative evidence supporting this thesis can not be fully complemented by quantitative data stemming from experiments, because of a lack of pertinent experiments—which, indeed, should measuresimultaneously the heart rate state parameter and thefour control parameters at the input side of the medulla. The results of some of the existing experiments on animal preparations can nevertheless be adduced to recognize that this dynamic can be graphed by the five-dimensional butterfly catastrophe type. The theory leads to new ways of looking at experiments in the field and/or setting up such experiments in the future.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460017
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  • 8
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    Simulation of cellular compaction and internalization in mammalian embryo development as driven by minimization of surface energy (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 167-187 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model based upon minimization of surface energy is proposed as an explanation for compaction and internalization of cells during mammalian embryo development. The model is used to simulate and graphically display these phenomena on a computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460021
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  • 9
    Electronic Resource
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    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 197-211 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460023
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  • 10
    Electronic Resource
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    Pattern formation and morphogenesis: A reaction-diffusion model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 213-228 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of cellular differentiation and consequent pattern generation during embryonic development has been mathematically investigated with the help of a reaction-diffusion model. It is by now a well-recognized fact that diffusion of micromolecules (through intercellular gap junctions), which is dependent on the spatial parameter (r), serve the purpose of ‘positional information’ for differentiation. Based on this principle the present model has been constructed by coupling the Goodwin-type equations for RNA and protein synthesis with the diffusion process. The homogeneous Goodwin system can exhibit stable periodic solution if the value of the cooperativity as measured by the Hill coefficient (ρ) is greater than 8, which is not biologically realistic. In the present work it has been observed that inclusion of a negative cross-diffusion can drive the system into local instability for any value of ρ and thus a time-periodic spatial solution is possible around the unstable local equilibrium, eventually leading to a definite pattern formation. Inclusion of a negative cross-diffusion thus makes the system biologically realistic. The cross-diffusion can also give rise to a stationary wave-like dissipative structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460024
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  • 11
    Electronic Resource
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    Editorial: Software survey section (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. I 
    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/BF02460027
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  • 12
    Electronic Resource
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    SCoP: An interactive simulation control program for micro- and minicomputers (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 427-441 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A nes software system is described for building simulation programs on micro- and minicomputers. Model equations are written as C subroutines, compiled and linked to the SCoP package to produce a menu-driven, interactive program. The system maintains a database of names, values, and units for all model parameters and variables. Run-time options include several methods for interactive parameter modification and both graphic and tabular outputs, with output values presented as they are calculated. Simulation output values can be compared with experimental data graphically and a companion program SCoPFit is provided for formal optimization of parameter values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459691
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  • 13
    Electronic Resource
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    Global stability of partially closed food-chains with resources (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 455-468 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider the existence and global stability of aq-member equilibrium (1≤q≤n) in partially closed food-chains of lengthn having an abiotic component as resource. We observe that such existence demands bounds of resource supply rate and these bounds are weighted sums of interaction coefficients. Particular results of global sector-stability of partially feasible equilibria of simple food-chains obeying Lotka-Volterra dynamics are shown. Lastly the elasticity of such food-chains when a new species is introduced at the highest trophic level is investigated.
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    URL: http://dx.doi.org/10.1007/BF02462317
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  • 14
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    Global stability in time-delayed single-species dynamics (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 485-492 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Criteria are established for three classes of models of single-species dynamics with a single discrete delay to have a globally asymptotically stable positive equilibrium independent of the length of delay.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462319
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  • 15
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    Predator-prey systems with group defence: The paradox of enrichment revisited (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 493-508 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The main concern of this paper is with survival or extinction of predators in models of predator-prey systems exhibiting group defence of the prey. It is shown that if there is no mutual interference among predators, enrichment could result in their extinction. However, if there is mutual interference, the predator population survives (at least deterministically).
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    URL: http://dx.doi.org/10.1007/BF02462320
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  • 16
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    A class of general stochastic compartmental systems (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 509-523 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper a general class of semi-Markov compartmental systems is studied. Two models for different input processes are analysed. Attention has been paid to the recurrence times associated with each compartment and to the distribution of the number of particles in each compartment. As an example, a three-compartment system is discussed to study the movement between three health states of patients with chronic diseases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462321
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  • 17
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    Optimized homology searches of the gene and protein sequence data banks (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 569-583 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A strategy is presented for searching the gene and protein sequence data banks which combines the use of two previously described algorthms. The implementation of this strategy is thoroughly evaluated with respect to sensitivity, specificity and speed. The establishment of standard benchmarks for comparing programs that rearch the sequence data banks for homology is proposed.
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    URL: http://dx.doi.org/10.1007/BF02462324
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  • 18
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    Receptors and functional linkage in membrane permeability: A quantum mechanical model (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 545-567 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract During functional linkage, ligand receptors are coupled to other receptors and to the cell's metabolic-transport apparatus. The linkage guides the cellular processing of matter, energy and information. Previous conceptions of functional linkage have used the ideas of classical physics appropriate to macroscopic objects. This study presents an initial quantum mechanical model of functional linkage in the case of ligands moving through lipid bilayers and hydrophilic transmembrane channels (‘pores’) of molecular dimensions. On the basis of permeability data, energy surfaces consisting of piecewise-constant potential regions are used to model the lipid bilayers and transmembrane channels. The centre-of-mass wavefunction for a ligand on such energy surfaces is analysed and the permeability coefficients calculated from the wavefunction's transmission characteristics. It is found that quasi-bound states in the several ligand-binding regions of a bilayer or pore system can functionally link to facilitate the passage of the molecule across the permeability barrier. Appearance of the linkage is a sensitive function of the ligand's energy. If the centre-of-mass energies are distributed as in a thermalized fluid, the flux via the quantum functional linkage can equal or exceed that of a classical flux for proton transport through rigid pores in which the intrasite barriers are relatively high (0.25–1 eV) and narrow (0.1–1 Å). The functional linkage plays a less important role in bilayer (rather than pore) energy surfaces and at higher molecular weights. If the ligand-receptor interaction is accompanied by energy transfer to or from ligands, the flux via the quantum functional linkage can equal or exceed the classically expected flux at all relevant ligand molecular weights. These findings are discussed in relation to earlier work and the limitations of the model emphasized.
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    URL: http://dx.doi.org/10.1007/BF02462323
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  • 19
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    A nonlinear measure of subalignment similarity and its significance levels (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 617-632 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new measure of subalignment similarity is introduced. Specifically, similaritys(l,c) is defined as the logarithm to the basep of the probability of findingc or fewer mismatches in a subalignment of lengthl, wherep is the probability of a match. Previous algorithms can not use this measure to find locally optimal subalignments because, unlike Needleman-Wunsch and Sellers similarities, this measure is nonlinear. A new pattern recognition algorithm is described for finding all locally optimal subalignments of two nucleotide sequences. The DD algorithm can uses(l, c) or any other reasonable similarity function to assess the relative interest of subalignments. The DD algorithm searches only the diagonal graph, which lacks insertions and deletions. This search strategy greatly decreases the computation time and does not require an arbitrary choice of gap cost. The paths of the resulting DD graph usually draw attention to likely locations for insertions and deletions. A heuristic formula is derived for estimating significance levels fors(l, c) in the context of the lengths of the two aligned sequences. The DD algorithm has been used to find interesting subalignments between the nucleotide sequences for human and murine interleukin 2.
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    URL: http://dx.doi.org/10.1007/BF02462327
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  • 20
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    Locally optimal subalignments using nonlinear similarity functions (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 633-660 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Nonlinear similarity functions are often better than linear functions at distinguishing interesting subalignments from those due to chance. Nonlinear similarity functions useful for comparing biological sequences are developed. Several new algorithms are presented for finding locally optimal subalignments of two sequences. Unlike previous algorithms, they may use any reasonable similarity function as a selection criterion. Among these algorithms are VV-1, which finds all and only the locally optimal subalignments of two sequences, and CC-1, which finds all and only the weakly locally optimal subalignments of two sequences. The VV-1 algorithm is slow and interesting only for theoretical reasons. In contrast, the CC-1 algorithm has average time complexityO(MN) when used to find only very good subalignments.
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    URL: http://dx.doi.org/10.1007/BF02462328
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  • 21
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    Adaptability: The significance of variability from molecule to ecosystem (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 701-703 
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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/BF02462331
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  • 22
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    Convergence in a resource-based competition system (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 681-699 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A resource-based competition model of two consumer species and one resource species is formulated in the form of a Lotka-Volterra system. The competition involves both exploitation and interference. By a method of asymptotic estimates, sufficient conditions are derived for the three species system to converge ast→∞ to an equilibrium point with all three species present; a generalization of the result forn≥2 and single resource species is indicated. The strong form of equilibrium perisistence of the three species consumer-resource system is achieved by the ability of each of the consumer species to exploit the resource and interfere with others in such a way which will avoid exclusion by the other.
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    URL: http://dx.doi.org/10.1007/BF02462330
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  • 23
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    A survey of linear singular systems (1986)
    Springer
    Circuits, systems and signal processing 5 (1986), S. 3-36 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.
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    URL: http://dx.doi.org/10.1007/BF01600184
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  • 24
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    An isoclinal approach to the comparative statics of biological communities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 59-75 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An understanding of the comparative statics of biological communities is important both as a means of explaining the long-term effects of changes in environmental conditions, and as a framework for viewing community time trajectories. A general formulation of community dynamics is presented here which, given full information about a particular community's dynamic behavior, describes the impact of a change in environmental conditions on the community steady state. However, since such full information is often lacking in studies of biological communities, various approaches to partial information analysis of comparative statics are presented and compared, including a generalized protocol for isocline analysis. The suggested isocline protocol is shown to be a useful tool for both full and partial information analyses, as well as for both general and partial equilibrium studies.
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    URL: http://dx.doi.org/10.1007/BF02460062
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  • 25
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    An interpretation of Fujita's frequency diagrams in phyllotaxis (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 77-86 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Fujita's diagrams in phyllotaxis, showing the frequencies of divergence angles as a function of these angles for low phyllotactic patterns such as (2, 1) and (3, 2), which are approximately normal curves centered at the limitdivergence angle of 137.51°, are shown to be puzzling when compared to results and observations in the field. An analysis of these diagrams is proposed, in the context of Fujita's methodology, of data from other sources, of a mathematical theorem on lattices, and of the contact pressure theory of phyllotaxis.
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    URL: http://dx.doi.org/10.1007/BF02460063
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  • 26
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    Existence of steady-state probability distributions in multilocus models for genotype evolution (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 87-95 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.
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    URL: http://dx.doi.org/10.1007/BF02460064
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    Transient phase kinetics of activation of human plasminogen (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 149-166 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Equations for the time-dependent concentrations of all species involved in the general mechanism of human plasminogen activation proposed by Wohlet al. (J. biol. Chem. 255, 2005–2013, 1980) have been derived. These equations are valid for the whole course of the reaction: for both the transient phase and the steady state. In addition, we compare our results with the ones obtained by the above-mentioned authors for the steady state assuming rapid equilibrium conditions. Finally, we propose a method for the determination of all velocity constants.
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    URL: http://dx.doi.org/10.1007/BF02460020
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  • 28
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    Interval graphs and maps of DNA (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 189-195 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A special class of interval graphs is defined and characterized, and an algorithm is given for their construction. These graphs are motivated by an important representation of DNA called restriction maps by molecular biologists. Circular restriction maps are easily included.
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    URL: http://dx.doi.org/10.1007/BF02460022
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  • 29
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    On mathematical modeling of critical variables in cancer treatment (goals: Better understanding of the past and better planning in the future) (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 253-278 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Over the past 25 years stepwise improvement in the cure of disseminated cancers has been good, fair or very poor depending on the particular cancer one is discussing. “Cancer chemotherapy provides variably effective treatment for the majority of forms of human cancer and curative treatment for some 12 categories.” We have been slow to gain and learn how to apply quantitative information on the biologic phenomena that underlie the responsiveness, or lack of responsiveness, of many different cancers to single drugs and combinations of drugs delivered in different ways. I am of the opinion that continuing development and integration of rational biomathematical models based on principles already identified, and testing them for compatibility with much already available experimental and clinical data, will lead to models that will help in planning more effective treatment regimens for cancers now classified as moderately refractory or very refractory to chemotherapy. Some of the critical variables are considered briefly. My advice, for what it is worth, is “try to be sure that the biologic concepts that you use in modeling are almost as good as the arithmetic.”
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    URL: http://dx.doi.org/10.1007/BF02459681
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    Physiological pharmacokinetics (1986)
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    Bulletin of mathematical biology 48 (1986), S. 309-322 
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    Notes: Abstract A discussion of the bases of physiological pharmacokinetics is followed by a brief review of the fundamental mass balance equations of the models. Some examples are outlined, together with a listing of published reviews which give many more references and detailed examples. Finally, some thoughts on future research directions are presented.
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    Cell kinetics simulation languages (1986)
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    Bulletin of mathematical biology 48 (1986), S. 323-336 
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    Notes: Abstract The use of stochastic simulation languages in cell kinetics research is discussed. Two special purpose simulation languages; CELLSIM and CELLGROW are described and example problems are presented.
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    Chemical carcinogenesis and toxicity models: Matching complexity to objectives (1986)
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    Bulletin of mathematical biology 48 (1986), S. 293-307 
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    Notes: Abstract Mathematical models predicting tissue doses of chemical toxicants can be either highly complex or simple, depending upon the end results needed. As an example of a highly complex mathematical model, the Miller Model of the distribution of reactive gases in human and animal lungs is described. The Miller Model accounts for the convection, the radial and axial diffusion, and the chemical reactions of gases as an inhaled breath passes down the airways. The geometry and physiology of human and animal lungs are used to calculate the convection and diffusion likely in each generation or bifurcating series of airways commencing with the trachea and extending 24 generations in humans. The chemical reactivity of ozone, an air pollutant, is accounted for by simulating second-order chemical reactions with the fluid lining materials of the lung and tissue biological molecules. The flux of ozone into three compartments (pulmonary tissue, overlying liquid layer and capillary blood) in each generation of the lung is calculated to provide molecular doses of ozone reaching each region of the lung. These results of calculated molecular dose are then used to construct dose-response curves for a variety of biological endpoints. A much simpler model is also described which recognizes the saturable or Michaelis-Menten type of kinetics controlling the removal of nickelous ion (nickel) from the lung. This model is used to calculate the chronic lung burden of the human lung for occupational, environmental and cigarette smoking exposure scenarios. In both the complex Miller Model and the simpler nickel lung burden model, the results can be used to calculate molecular doses at the potential site of action of these environmental chemicals and to unify a wide variety of studies. The predictions made are more likely to be valid since multiple investigators using a variety of animal species have participated in generation of the primary data. As a methodology, mathematical modeling based on physiological, physicochemical and anatomical principles provides a means of eliminating non-scientific considerations from the important process of regulating and recognizing toxic or cancer causing chemicals in the human environment.
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    Kinetic simulation of anticancer drug effects on metabolic pathway fluxes: Two case studies (1986)
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    Bulletin of mathematical biology 48 (1986), S. 337-351 
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    Notes: Abstract This paper presents a brief review of applications of kinetic simulation of multi-enzyme networks to the study of antimetabolite drugs used as anticancer agents. Kinetic models consist of systems of nonlinear differential equations that describe changes in concentrations of cellular metabolites with respect to time. Such models have been used to predict the effect of changes in activity of enzymes, or changes in enzyme kinetic parameters, on sensitivity to inhibition. Kinetic simulation has provided insight into several aspects of the biochemical pharmacology of antimetabolites, including drug sensitivity and resistance, and drug-drug interactions. Two specific studies are described in detail. The first concerns the importance of the ratio of competing enzymes in determining the selectivity of inhibitors of one of the competing enzymes, studied by a simple model. The second case study examines the effect of alternative biosynthetic pathways, thede novo and salvage pathways of pyrimidine nucleotide biosynthesis, on the selectivity of antipyrimidine drugs, as studied by a detailed model of 27 reactions of pyrimidine metabolism.
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    Cancer chemotherapy: Optimal control using the Verhulst-Pearl equation (1986)
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    Bulletin of mathematical biology 48 (1986), S. 381-404 
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    Notes: Abstract General (deterministic) ordinary differential equations for the representation of cancer growth are presented when the growth is perturbed due to the action of a chemotherapeutic agent. The Verhulst-Pearl equation is introduced as a particular example of a growth equation applicable to human tumors. An optimal control problem with general performance criterion and state equation is formulated and shown to possess a novel feedback control relationship. This relationship is used in two continuous drug delivery problems involving the Verhulst-Pearl equation.
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    Use of the circuit simulation program SPICE2 for analysis of the metabolism of anticancer drugs (1986)
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    Bulletin of mathematical biology 48 (1986), S. 353-380 
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    Notes: Abstract Complex networks of biological processes are analogous to electrical circuits. For each step in a biological or electrical network, flow is dependent on the driving force and the conductivity of the step. The relationship between biological flows and their driving forces can therefore be expressed as relationships between analogous currents and voltages. The time dependence of approach to equilibrium or a steady state is determined by the rates of depletion of material in various compartments. Electrical capacitance is therefore analogous to compartment volume. Once these generalized concepts of flow, force and capacitance are recognized, it becomes clear that computer programs designed for analysis of electrical circuits may be used for simulation of biological networks. A set of simple mathematical descriptions of the individual steps and a diagram showing how the steps are arranged with respect to each other are all that is necessary to perform a simulation; there is no need for computer programming skills or differential equations. The use of SPICE2 for simulation of the cellular and plasma pharmacokinetics of cytosine arabinoside (araC) is described as an example. A network model is developed which considers cellular pharmacokinetics (membrane transport, intracellular phosphorylation and dephosphorylation), and plasma pharmacokinetics following infusions of araC.
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    Future directions in computer simulation (1986)
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    Bulletin of mathematical biology 48 (1986), S. 405-415 
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    Notes: Abstract Developments in computer hardware and software are making significant improvements in the availability of simulation for biomedical researchers. This paper reviews past and present techniques for digital computer simulation and looks at improvements likely in the near future. In the area of hardware, personal computers are making computing and simulation more widely available and at the same time, supercomputers and special-purpose numerical processors are making it possible to solve larger problems. Software developments for simulation are reducing the time, effort and special skills required to produce a simulation program. A new hierarchical linker is proposed to make it easy to synthesize a global model by combining existing submodels. In the more distant future, computer models may be constructed graphically and with the assistance of intelligent programs capable of analysis and information retrieval.
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    Strategies for computer modeling (1986)
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    Bulletin of mathematical biology 48 (1986), S. 417-426 
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    Notes: Abstract Modeling is a ubiquitous and often misunderstood enterprise in which data from diverse disciplines are analyzed by techniques from other diverse disciplines in an attempt to confirm or falsify a set of hypotheses about the real world. Guidelines are offered for designing models to match the goals of modeling biological systems. Techniques for the construction and interpretation of models are discussed. The requirements for credibility of models are detailed, and tests are suggested for their validation.
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    First Conference of the International Federation of Classification Societies (1986)
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    Bulletin of mathematical biology 48 (1986), S. 453-453 
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    Conference retrospective: An appropriate modeling infrastructure for cancer research (1986)
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    Bulletin of mathematical biology 48 (1986), S. 443-452 
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    Notes: Abstract Presentations and discussions at the symposium illustrate some general issues in biomedical modeling for cancer research. Given the motivations for modeling and assumptions concerning who should be involved in the modeling process, one can identify some basic needs to be met in supports to modelers. These concern both the models themselves and ways of presenting them to users. In conclusion, some thoughts are offered on economic and educational issues that may affect the infusion of modeling into biomedical research.
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    Editorial: Software survey section (1986)
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    Bulletin of mathematical biology 48 (1986), S. I 
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    Some properties of solutions of the semi-state model for nonlinear nonstationary systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 109-123 
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    Notes: Abstract Certain properties of solutions similar to set invariance, set attractivity, boundedness, BIBO stability, etc. are investigated for the semistate model $$P(t)\dot x = M(t,x)x + D(t,x)u,y = q(t,x,u).$$ For systems considered, it is assumed that the reduction to a normal form of lower order is not possible. Using the direct method of Liapunov, the properties of solutions are investigated without actual knowledge of solutions.
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    Multiple time scales for nonlinear systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 153-169 
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    Notes: Abstract In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form $$\dot x = A( \in )x$$ (cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.
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    A model for cooperative ligand binding at complementary sites of DNA (1986)
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    Bulletin of mathematical biology 48 (1986), S. 21-27 
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    Notes: Abstract The process of cooperative binding of ligands to DNA has been classified into different modes. An additional mode of cooperative interaction amongst ligands binding at sites on complementary strands has been emphasised. A statistical mechanical method has been applied to obtain an analytical expression for the fraction of nucleotide sites bound. Theoretical Scatchard plots have been drawn and analysed.
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    Model for chemotactic bacterial bands (1986)
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    Bulletin of mathematical biology 48 (1986), S. 1-19 
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    Notes: Abstract Suspensions of chemotactic bacteria develop spatial and temporal structures in response to an initial inhomogeneity in the medium. A theoretical model is presented for the analysis of spatial and temporal evolution of bacterial bands in response to several attractants. Applications of the model to various experimental cases give good agreement between theory and observation. The theoretical analysis provides further insight to the mechanisms governing band formation and band migration.
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    Pointwise bounds for a nonlinear heat conduction model of the human head (1986)
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    Bulletin of mathematical biology 48 (1986), S. 229-236 
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    Notes: Abstract The theory of maximum principles is applied to a nonlinear differential equation representing a heat conduction model of the human head to obtain accurate analytical upper and lower bounding curves.
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    1986 Gordon Research Conference on Theoretical Biology and Biomathematics (1986)
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    Bulletin of mathematical biology 48 (1986), S. 237-237 
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    Guest editors’ foreword (1986)
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    Bulletin of mathematical biology 48 (1986), S. 239-240 
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    The role of simulation in biomathematical modeling (1986)
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    Bulletin of mathematical biology 48 (1986), S. 241-251 
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    Notes: Abstract This paper is a general introduction to the field of biomathematical modeling. Biomathematical modeling is divided into three parts: the derivation of models, the fitting of models to data, and the simulation of data from models. This paper focuses on the simulation of data from models. The uses of simulation, the potential users of simulation, and simulation software are described.
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    A stochastic model for the origin and treatment of tumors containing drug-resistant cells (1986)
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    Bulletin of mathematical biology 48 (1986), S. 279-292 
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    Notes: Abstract A stochastic model for the chemotherapy of experimental tumors is presented. The focus of this model is on the presence of drug-resistant mutants and their influence on eventual treatment outcome. Equations are derived for the joint probability-generating function for the number of chemo-sensitive and chemo-resistant cells. The model is extended to two drugs and it is shown how the model may be used to make deductions regarding the optimum scheduling of therapy.
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    Software survey section (1986)
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    Bulletin of mathematical biology 48 (1986), S. I 
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    The wiring-in of neural nets revisited (1986)
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    Bulletin of mathematical biology 48 (1986), S. 661-680 
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    Notes: Abstract Earlier and some recent ideas about the possible modes of specification of the wiring-in of nervous systems are reviewed in the light of older and several recent experiments, and some new ideas are suggested. It is argued that certain general principles, notably the postulated ‘principle of alternative matching’ (PALMA) and a suggested and related ‘kaleidoscopic effect’ (KALEF), as well as the notion of an ‘extracellular guidance network’ (ECGN), are in good agreement with recent and older findings concerning axonal guidance during neural wiring-in. It seems possible that by means of genetically programmed processes, neurons become systematically combinatorially labelled to such a degree that possibly all neurons areuniquely specified, as regards the combination oftypes of cell labels they make. Yet, there remains considerable freedom as regards the modes of arrangements of cell labels within cell surface membranes and the KALEF permits to overcome apparent difficulties that confronted earlier versions of the cell labelling hypotheses (cf. Edelman,Science 219, 450–457, 1983, for mention of such difficulties). Apart from label specification, neural development seems to depend on trophic factors, which are also essential for the maintenance of the developed nervous system. The systematic programmes for cell labelling, apart from generating all the required neurons, also produces inappropriate neurons and synaptic connections. These are got rid of by systematic cell death and/or atrophy of inappropriate synapses and/or elimination of inappropriate axon collaterals. The resulting neural net seems then very specifically wired-in for each species, apparently without redundant neurons.
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    Persistence and global stability in a predator-prey model consisting of three prey genotypes with fertility differences (1986)
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    Bulletin of mathematical biology 48 (1986), S. 469-484 
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    Notes: Abstract A model of a predator-prey interaction, where the prey population consists of three genotypes with random mating and continuous, nonlinear birth and death processes with fertility differences, is proposed. Sufficiency conditions giving the existence of a globally stable equilibrium on one of the coordinate planes are given. This extends results of Freedman and Waltman [J. Math. Biol. 6, 367–374 (1978) andRocky Mountain J. Math. 12, 779–784 (1982)]. In addition, conditions are derived which guarantee the persistence of all components of the populations.
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    Heterogeneous organ models (1986)
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    Bulletin of mathematical biology 48 (1986), S. 525-543 
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    Notes: Abstract A theoretical study is made of three organ flow models with heterogeneity of capillary transit times. A new parametrization of Rose and Goresky's Model III facilitates in many cases a reduction to Goresky's Model II, accomplished by a special time shift. The shift parameter $$\tau _{c_z } = \tau _{c_m } - t_{APP} /b$$ defined here is critical in this analysis of Model III. A new expression of the series for outflow concentration in Model III is given and proves useful in examining the model as an operator and in relating it to Models I and II. A result on parameter optimization is given: if $$\tau _{c_z } \geqslant 0$$ then Model III cannot fit better than Model II. This is applied to some data from Rose and Goresky [Circulation Res. 39, 541–544 (1976)] and raises a new question about their model. A heart model of Levin and Bassingthwaighte based on regional flow measurement is shown to be a discretized generalization of Model II.
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    Diffusion effect on stability of Lotka-Volterra models (1986)
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    Bulletin of mathematical biology 48 (1986), S. 585-601 
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    Notes: Abstract This paper analyses the diffusion effect on stability in Lotka-Volterra systems for a patch-type environment. Applying the extended stability theorem of LaSalle, some classes of patches for which the diffusion does not affect the system's stability are drawn. Further, complicated dynamical behaviours in two-prey, one-predator diffusion models are given when the patch does not belong to the above classes.
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    Optimal sequence alignment using affine gap costs (1986)
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    Bulletin of mathematical biology 48 (1986), S. 603-616 
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    Notes: Abstract When comparing two biological sequences, it is often desirable for a gap to be assigned a cost not directly proportional to its length. If affine gap costs are employed, in other words if opening a gap costsv and each null in the gap costsu, the algorithm of Gotoh (1982,J. molec. Biol. 162, 705) finds the minimum cost of aligning two sequences in orderMN steps. Gotoh's algorithm attempts to find only one from among possibly many optimal (minimum-cost) alignments, but does not always succeed. This paper provides an example for which this part of Gotoh's algorithm fails and describes an algorithm that finds all and only the optimal alignments. This modification of Gotoh's algorithm still requires orderMN steps. A more precise form of path graph than previously used is needed to represent accurately all optimal alignments for affine gap costs.
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    A semistate approach to feedback stabilization of neutral delay systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 69-85 
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    Notes: Abstract In this paper we consider derivative feedback in a semistate framework for the problem of stabilizing the neutral root chains for a class of neutral delay-differential equations where the difference operator (orD-operator) is unstable. Recent work has shown that such systems cannot be stabilized by state feedback alone[3], [13], [16]. In addition, we consider the problem of using derivative feedback to eliminate all neutral root chains entirely, thus turning the closed loop system into a retarded delay system. By representing neutral delay-differential systems as semistate systems over a polynomial ring of delay operators, both of the above problems are shown to be reducible to the following question: Given matricesD,B over a commutative ringR, when does there exist a matrixM also overR such thatD+BM isR-unimodular? In the case of commensurable point delays our results are applications of some recent results on the simultaneous stabilization problem [19], and we give a constructive procedure for computing the required feedback law. In the case of noncommensurable delays we give a sufficient condition for the existence of suitable feedback for the above problems.
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    A geometric characterization of the reachable and the controllable subspaces of descriptor systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 37-48 
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    Notes: Abstract The concepts of {A,E,R(B)} and restricted {E,A,R(B)} invariance are introduced. The reachable subspace of a descriptor system is shown to be the supremal {A,E,R(B)}invariant subspace contained in the least restricted {E,A,R(B)} subspace of Rn. Algorithms to compute the reachable subspace of a descriptor system $$E\dot x = Ax + Bu$$ in terms ofE,A andB are given. A new proof of the feedback invariance of the reachable subspace is presented.
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    On one-leg methods for differential-algebraic equations (1986)
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    Circuits, systems and signal processing 5 (1986), S. 87-95 
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    Notes: Abstract One-leg methods for general differential-algebraic equations are analyzed. Sufficient stability conditions are formulated for transferable differential-algebraic equations. A natural scaling is proposed to obtain matrices with uniformly bounded condition in the linear systems to be solved.
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    On digital smoothing filters: A brief review of closed form solutions and two new filter approaches (1986)
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    Circuits, systems and signal processing 5 (1986), S. 187-210 
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    Notes: Abstract The concept of smoothing noisy data using appropriate polynomials turns out to be equivalent to the application of suitable nonrecursive digital filters having the following properties: They process the data in such a way that the moments are conserved up to a desired order while the energy of their impulse response is minimum. Flatness constraints of their frequency response at Ω=0 are equivalent to the moment condition. By using orthogonal polynomials, an explicit solution is known from the literature. A second approach which uses a special decomposition also yields closed form solutions. The realization is simplified, especially in the case where a large number of moments is supposed to be conserved.
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    Decoupling and pole-zero assignment of singular systems with dynamic state feedback (1986)
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    Circuits, systems and signal processing 5 (1986), S. 49-68 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper refers to the problem of designing a linear state feedback dynamic controller for single-input, single-output decoupling of linear, time-invariant, singular systems. Sufficient conditions are established for the state-feedback decoupling problem to have a solution. In the case where the system satisfies these conditions, the class of controller matrices which decouple the system is given. Finally a method is presented for pole-zero placement in the decoupled singular system and a structure is described for the realization of the generalized transfer function matrices.
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    A characterization of semistate systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 125-137 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    URL: http://dx.doi.org/10.1007/BF01600191
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    Semistate implementation: Differentiator example (1986)
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    Circuits, systems and signal processing 5 (1986), S. 171-183 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract It is shown that the semistate equations can be transformed via a linear transformation into a form which is useful for physical realizations. The result is applied to the example of a semistate described differentiator which is then realized through an op-amp circuit composed of integrators.
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    Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade (1986)
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    Circuits, systems and signal processing 5 (1986), S. 227-259 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We formulate and prove a theorem which gives a rigorous theoretical justification for the use of describing functions to predict the existence of limit cycles in a multiple nonlinear feedback system and to predict the stability properties of these limit cycles. Our approach uses the classical sinusoidal-input describing function and the theory of integral manifolds. We demonstrate the applicability of our result by means of two specific examples.
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    Chaos generation using binary hysteresis (1986)
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    Circuits, systems and signal processing 5 (1986), S. 321-341 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The design of a continuous-time system suitable for electronic circuit realization for integrated circuit generation of chaotic responses is presented. The system is second order and is based upon an unstable oscillator with state-space trajectories that are fed back into themselves, and stabilized, via the use of binary hysteresis. The chaotic nature of the signals is guaranteed by a theorem of Li and Yorke through the generation of a period-three return map. Experimental results are given that verify the design.
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    Some results concerning the abstract degenerate nonlinear equationD t Mu(t) +Lu(t)=f(t, Ku(t)) (1986)
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    Circuits, systems and signal processing 5 (1986), S. 261-274 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We apply some abstract existence results, proved in Sections 1 and 2 of the paper, to some cases of the following problem (P), formally stated as (P) $$\left\{ \begin{gathered} D_t \left( {Mu\left( t \right)} \right) + Lu\left( t \right) = f\left( {t,Ku\left( t \right)} \right) 0〈 t \leqslant \tau \hfill \\ Mu\left( t \right) \to u_0 as t \to 0 + \hfill \\ \end{gathered} \right.$$ whereK,L,M are linear and/is a nonlinear term. The unknown functionu is required to lie in various functional spaces.
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    Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part I: Conservation laws (1986)
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    Circuits, systems and signal processing 5 (1986), S. 279-319 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper is the first in a two part sequence which studies nonlinear networks, containing capacitor-only cutsets and/or inductor-only loops from the geometric coordinate-free point of view of differentiable manifolds. Given such a nonlinear networkN, with °0 equal to the sum of the number of independent capacitor-only cutsets and the number of independent inductor-only loops, we establish the following: (i) circuit theoretic sufficient conditions to guarantee that the set Σ0, of equilibrium points is a δ0-dimensional submanifold of the state space Σ ofN; (ii) circuit theoretic sufficient conditions for the condition thatN has δ0 independent conservation laws and hence that through each pointσ of the state space Σ ofN, there passes a codimension δ0 invariant submanifold ∑ σ * of the network dynamics; (iii) circuit theoretic sufficient conditions to guarantee that the manifolds ∑ σ * and Σ0 intersect transversely.
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    A note on the genericity of simultaneous stabilizability and pole assignability (1986)
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    Circuits, systems and signal processing 5 (1986), S. 371-387 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we study the genericity of simultaneous stabilizability, simultaneous strong stabilizability, and simultaneous pole assignability, in linear multivariable systems. The main results of the paper had been previously established by Ghosh and Byrnes using state-space methods. In contrast, the proofs in the present paper are based on input-output arguments, and are much simpler to follow, especially in the case of simultaneous and simultaneous strong stabilizability. Moreover, the input-output methods used here suggest computationally reliable algorithms for solving these two types of problems. In addition to the main results, we also prove some lemmas on generic greatest common divisors which are of independent interest.
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    Synthesis of arbitrary digital transfer functions using allpass-based structures derived via LBR two-pair extraction procedure (1986)
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    Circuits, systems and signal processing 5 (1986), S. 343-370 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The implementation of a digital filter transfer function with all transmission zeros on the unit circle is developed via the synthesis of an appropriate allpass function. The synthesis procedure is based on the “LBR-extraction” approach. The resulting structure is in the form of a doubly terminated cascade of lossless (LBR) two-pairs, with each two-pair realizing a single real or a pair of complex transmission zeros. The Concepts of complete and partial “1” removals, and “1” shifting are introduced and utilized during the synthesis process. The resulting structures have several properties in common with the Gray and Markel lattice filters, but do not require tap coefficients for numerator realization. The building blocks used in this paper are similar to those in certain wave-digital filters and orthogonal filters.
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    Generalized solutions of semistate equations and stability (1986)
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    Circuits, systems and signal processing 5 (1986), S. 391-403 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, solvability and stability of nonlinear, time-varying semistate equations is discussed. It is shown that generalized solutions exist in a vicinity of an equilibrium. Moreover, results on a Liapunov-like (uniform, asymptotic) stability are given.
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    Approximating linearizations for nonlinear systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 419-433 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Given a nonlinear control system $$\dot x(t) = f(x(t)) + \sum\limits_{i = 1}^m {u_i (t)g_i (x(t))}$$ on ℝ n and a pointx 0 in ℝ n , we want to approximate the system nearx 0 by a linear system. Of course, one approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that we should construct a linear approximation based on Lie bracket matching atx 0. In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, we show that there is a coordinate system for ℝ n nearx 0 in which these two types of linearizations agree. We indicate the importance of this agreement by examining the time responses of the nonlinear system and its linear approximation and comparing the lower-order kernels in Volterra expansions of each.
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    A new approach to Hurwitz polynomials in several variables (1986)
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    Circuits, systems and signal processing 5 (1986), S. 405-417 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The theory of scattering and related types of Hurwitz polynomials, as well as the role of these polynomials in the theory of multidimensional passive circuits, have been established in previous publications. In the present paper a new approach is developed by means of which the previous results on scattering Hurwitz polynomials can be obtained in a more compact and systematic fashion.
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    Approximation of nonlinear systems having outputs (1986)
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    Circuits, systems and signal processing 5 (1986), S. 465-479 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Suppose we have a nonlinear system with output $$\begin{gathered} \dot x = f(x) + g(x)u, \hfill \\ y = h(x), \hfill \\ \end{gathered}$$ an open setO of state spaceR n , and a positive integerk. We find conditions onf,g, andh so that for eachx 0 ε O there is ann-dimensional affine linear system, which depends onx 0 but not onu, having the property that the output time responses (starting at the statex 0 of the original nonlinear system and this approximating linear system agree through orderk for any admissable controlu. Several possible applications of our results are examined.
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    Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part II: Symmetries (1986)
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    Circuits, systems and signal processing 5 (1986), S. 435-448 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper is the last in a two-part sequence which studies nonlinear networks, containing capacitor-only cutsets and/or inductor-only loops, from the geometric coordinate-free point of view of the theory of differentiable manifolds. For such circuits, it is shown that (subject to certain assumptions) there is a naturally defined Lie group action of $$\mathbb{R}^{\delta _0 }$$ on the state space ∑ ofN, whereδ 0 is the sum of the number of independent capacitor-only cutsets and the number of independent inductor-only loops. Circuit theoretic sufficient conditions on the reactive constitutive relations are derived for the circuit dynamics to be invariant under this Lie group action.
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    Stability of nonlinear systems with three time scales (1986)
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    Circuits, systems and signal processing 5 (1986), S. 449-464 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We study the asymptotic stability of a singularly perturbed nonlinear time-invariant systemS ɛv , which has three vastly different time scales. The systemS ɛv is approximated by three simpler systems over different time intervals. We give a straightforward proof of the fact that the asymptotic stability ofS ɛv is guaranteed when the equilibrium points of the three simpler systems are exponentially stable and when the parametersɛ andν are sufficiently small.
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    Index two linear time varying singular systems of differential equations (1986)
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    Circuits, systems and signal processing 5 (1986), S. 97-107 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Linear time varying singular systems of differential equations of the formA(t)x′(t) + B(t)x(t)=f(t) whereA(t) is singular and the system has index at most two are considered. Recent results on their analytic solution are improved on. Examples are given that show these results are not easily extended.
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    Global analyticity of a geometric decomposition for linear singularly perturbed systems (1986)
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    Circuits, systems and signal processing 5 (1986), S. 139-152 
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    Notes: Abstract A geometric decomposition is developed for linear, time-invariant singularly perturbed systems of a general form. The decomposition is shown to be determined by a mappingd between two real analytic manifolds, the range ofd being a manifold of canonical forms. Our main result establishes analyticity ofd over its entire domain.
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    Recursive estimation of two-dimensional processes with application to image processing (1986)
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    Circuits, systems and signal processing 5 (1986), S. 211-226 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A low order quarter-plane-causal recursive model is presented to represent the class of 2-D stationary Gaussian processes with power spectra matrices factorable into a quarter-plane-causal and anti-causal parts. This model is used to develop a technique for obtaining optimal 2-D recursive estimators. The approach taken here is similar to Attasi's [8], with no commutability condition imposed on the model. Circumventing this condition allows the modeling of the 2-D processes to be achieved with fewer parameters, and enables one to find the solutions to the problems of “blur” and “color noise” which are inherent in most image degraded images. Some simulated examples illustrate these points.
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    Some comments on Wolfe's ‘away step’ (1986)
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    Mathematical programming 35 (1986), S. 110-119 
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    ISSN: 1436-4646
    Keywords: Convex programming ; Frank-Wolfe algorithm
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    Topics: Computer Science , Mathematics
    Notes: Abstract We give a detailed proof, under slightly weaker conditions on the objective function, that a modified Frank-Wolfe algorithm based on Wolfe's ‘away step’ strategy can achieve geometric convergence, provided a strict complementarity assumption holds.
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    Announcement: Euro VIII - the eighth European conference on operational research (1986)
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    Mathematical programming 35 (1986), S. 125-125 
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    Topics: Computer Science , Mathematics
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    Improved asymptotic analysis of the average number of steps performed by the self-dual simplex algorithm (1986)
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    Mathematical programming 35 (1986), S. 140-172 
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    Keywords: Probabilistic analysis ; self-dual simplex ; spherical symmetry
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    Notes: Abstract In this paper we analyze the average number of steps performed by the self-dual simplex algorithm for linear programming, under the probabilistic model of spherical symmetry. The model was proposed by Smale. Consider a problem ofn variables withm constraints. Smale established that for every number of constraintsm, there is a constantc(m) such that the number of pivot steps of the self-dual algorithm,ρ(m, n), is less thanc(m)(lnn) m(m+1) . We improve upon this estimate by showing thatρ(m, n) is bounded by a function ofm only. The symmetry of the function inm andn implies thatρ(m, n) is in fact bounded by a function of the smaller ofm andn.
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    A finite characterization ofK-matrices in dimensions less than four (1986)
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    Mathematical programming 35 (1986), S. 17-31 
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    Keywords: Linear complementarity problem ; K-matrix ; Q 0-matrix ; finite characterization ; Q-matrix
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    Notes: Abstract The class of realn × n matricesM, known asK-matrices, for which the linear complementarity problemw − Mz = q, w ≥ 0, z ≥ 0, w T z =0 has a solution wheneverw − Mz =q, w ≥ 0, z ≥ 0 has a solution is characterized for dimensionsn 〈4. The characterization is finite and ‘practical’. Several necessary conditions, sufficient conditions, and counterexamples pertaining toK-matrices are also given. A finite characterization of completelyK-matrices (K-matrices all of whose principal submatrices are alsoK-matrices) is proved for dimensions 〈4.
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    Binary group and Chinese postman polyhedra (1986)
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    Mathematical programming 34 (1986), S. 1-33 
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    Keywords: Polyhedra ; Chinese Postman ; Binary Group Problems ; Binary Matroids ; Blocking Clutters
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    Notes: Abstract A new proof of the characterization of the Chinese postman polyhedra is given. In developing this proof, a theorem of Gomory about homomorphic lifting of facets for group polyhedra is generalized to subproblems. Some results for the Chinese postman problem are generalized to binary group problems. In addition, a connection is made between Fulkerson's blocking polyhedra and a blocking pair of binary group problems. A connection is also developed between minors and lifting of facets for group problems.
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    On box totally dual integral polyhedra (1986)
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    Mathematical programming 34 (1986), S. 48-61 
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    Keywords: Total Dual Integrality ; Hilbert Basis ; Polyhedra
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    Notes: Abstract Edmonds and Giles introduced the class of box totally dual integral polyhedra as a generalization of submodular flow polyhedra. In this paper a geometric characterization of these polyhedra is given. This geometric result is used to show that each TDI defining system for a box TDI polyhedron is in fact a box TDI system, that the class of box TDI polyhedra is in co-NP and is closed under taking projections and dominants, that the class of box perfect graphs is in co-NP, and a result of Edmonds and Giles which is related to the facets of box TDI polyhdera.
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    Facet inequalities from simple disjunctions in cutting plane theory (1986)
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    Mathematical programming 34 (1986), S. 72-83 
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    Keywords: Cutting Planes ; Disjunctive Programming
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    Notes: Abstract The duality between facets of the convex hull of disjunctive sets and the extreme points of reverse polars of these sets is utilized to establish simple rules for the derivation of all facet cuts for simple disjunctions, namely, elementary disjunctions in nonnegative variables. These rules generalize the cut generation procedure underlying polyhedral convexity cuts with negative edge extensions. The latter are also shown to possess some interesting properties with respect to a biextremal problem that maximizes the distance, from the origin, of the nearest point feasible to the cut. A computationally inexpensive procedure is given to generate facet cuts for simple disjunctions which are dominant with respect to any specified preemptive ordering of variables.
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    Convergence of an annealing algorithm (1986)
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    Mathematical programming 34 (1986), S. 111-124 
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    Keywords: Global Optimization ; Stochastic Optimization ; Annealing ; Metropolis Method ; NP ; Hill Climbing ; Local Improvement
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems, including NP-hard combinatorial problems such as the travelling salesman, Steiner trees and others. There is an appealing physical analogy for its operation, but a more formal model seems desirable. In this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1. We also show that there are cases where convergence takes exponentially long—that is, it is no better than a deterministic method. We study how the convergence rate is affected by the form of the problem. Finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of ‘practical’ confidence in the solution.
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    A competitive (dual) simplex method for the assignment problem (1986)
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    Mathematical programming 34 (1986), S. 125-141 
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    ISSN: 1436-4646
    Keywords: Assignment Problem ; Dual Method ; Signature ; Linear Programming ; Simplex Method ; Pivoting ; Average Behavior
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    Notes: Abstract “Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling.” - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974). A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx ij 〈 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx ij is shown to converge in at most ( 2 n-1 ) pivots, and at most O(n 3) time, and it is argued that on average the number of pivots is at mostn logn.
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    Network design problem with congestion effects: A case of bilevel programming (1986)
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    Mathematical programming 34 (1986), S. 142-162 
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    ISSN: 1436-4646
    Keywords: Network Design ; Bilevel Programming ; Variational Inequalities ; Stackelberg Games
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    Notes: Abstract Recently much attention has been focused on multilevel programming, a branch of mathematical programming that can be viewed either as a generalization of min-max problems or as a particular class of Stackelberg games with continuous variables. The network design problem with continuous decision variables representing link capacities can be cast into such a framework. We first give a formal description of the problem and then develop various suboptimal procedures to solve it. Worst-case behaviour results concerning the heuristics, as well as numerical results on a small network, are presented.
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    A method of linearizations for linearly constrained nonconvex nonsmooth minimization (1986)
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    Mathematical programming 34 (1986), S. 175-187 
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    ISSN: 1436-4646
    Keywords: Primary 65K05 ; Secondary 90C25 ; Nonsmooth Optimization ; Nondifferentiable Programming ; Linearly Constrained Minimization ; Descent Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A readily implementable algorithm is given for minimizing a (possibly nondifferentiable and nonconvex) locally Lipschitz continuous functionf subject to linear constraints. At each iteration a polyhedral approximation tof is constructed from a few previously computed subgradients and an aggregate subgradient, which accumulates the past subgradient information. This aproximation and the linear constraints generate constraints in the search direction finding subproblem that is a quadratic programming problem. Then a stepsize is found by an approximate line search. All the algorithm's accumulation points are stationary. Moreover, the algorithm converges whenf happens to be convex.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580582
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    First announcement and call for papers: International conference on stochastic programming (1986)
    Springer
    Mathematical programming 34 (1986), S. 248-249 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580591
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    Sensitivity theorems in integer linear programming (1986)
    Springer
    Mathematical programming 34 (1986), S. 251-264 
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    ISSN: 1436-4646
    Keywords: Integer Linear Programming ; Chvátal Rank ; Cutting Planes ; Sensitivity Analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right-hand-side vector. Among our results, we show that, for any optimal solution to a linear program max{wx: Ax≤b}, the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixA. Using this, we strengthen several integer programming ‘proximity’ results of Blair and Jeroslow; Graver; and Wolsey. We also show that the Chvátal rank of a polyhedron {x: Ax≤b} can be bounded above by a function of the matrixA, independent of the vectorb, a result which, as Blair observed, is equivalent to Blair and Jeroslow's theorem that ‘each integer programming value function is a Gomory function.’
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582230
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  • 91
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    The Manne-Chao-Wilson algorithm for computing competitive equilibria: A modified version and its implementation (1986)
    Springer
    Mathematical programming 34 (1986), S. 302-332 
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    ISSN: 1436-4646
    Keywords: Generalized Programming ; Competitive Equilibria ; Economic Modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a modification of the Manne-Chao-Wilson algorithm for computing competitive equilibria and discuss some of its convergence properties. Numerical experiments involving models with up to 100 price responsive agents are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582233
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  • 92
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    Affirmative action algorithms (1986)
    Springer
    Mathematical programming 34 (1986), S. 292-301 
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    ISSN: 1436-4646
    Keywords: Selection Rules ; Linear Programming ; Linear Complementarity ; Network Flows
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Affirmative action is a new variety of selection rule which employs historical information to favor the choice of elements that have not been selected in the past. We categorize three implementations of this principle and discuss their application to the simplex method, to Bard-type schemes for the linear complementarity problem, and to augmenting path methods for network flow problems. We present analytical and computational results, and some open questions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582232
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  • 93
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    Linear complementarity problems with an invariant number of solutions (1986)
    Springer
    Mathematical programming 34 (1986), S. 265-291 
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    ISSN: 1436-4646
    Keywords: Linear Complementarity Problems ; Complementary Cones ; Invariant Number of Solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper studies the class INS of all realn × n matricesM for which the linear complementarity problem (q, M) has exactlyk solutions—k depending only onM—for all realn-vectorsq interior to the coneK(M) of vectors for which (q, M) has any solution at all. This generalizes the results in Cottle and Stone (1983) which deal with the subclassU in INS wherek equals one. After the first two sections of this paper, which introduce the problem and background material, we move on to examine necessary conditions for a matrixM to be in INS (Section 3) and sufficient conditions under whichM will be in INS (Section 4). Section 5 deals with the possible values whichk may have. Section 6 discusses related results concerning the geometry of linear complementarity problems. Finally, Section 7 deals with some known and new matrix classes which are in INS.
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    URL: http://dx.doi.org/10.1007/BF01582231
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    Call for nominations: The 1985 Lanchester Prize (1986)
    Springer
    Mathematical programming 34 (1986), S. 370-371 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582237
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  • 95
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    Efficient dual simplex algorithms for the assignment problem (1986)
    Springer
    Mathematical programming 34 (1986), S. 372-372 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582238
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  • 96
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    An extrapolation method for the efficient composition of maps with applications to non-linear oscillations (1986)
    Springer
    Computing 36 (1986), S. 343-354 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Bestimmung von Iterierten hoher Ordnung von Abbildungen in der Nähe der Identität ist ein wichtiges Problem in der Theorie nichtlinearer Schwingungen. Unter Verwendung von Methoden aus der Asymptotischen Analysis wird eine effiziente Extrapolationsmethode abgeleitet und angewendet, insbesondere auf die sogenannten Lorenz-Gleichungen.
    Notes: Abstract The determination of high order iterates of near identity maps is a problem of considerable interest in the theory of non-linear oscillations. Using tools from Asymptotic Analysis we derive an efficient extrapolation method and apply it in various situations, and in particular to the Lorenz equations.
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    URL: http://dx.doi.org/10.1007/BF02240209
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    Quadrature rules for Prandtl's integral equation (1986)
    Springer
    Computing 37 (1986), S. 31-42 
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    ISSN: 1436-5057
    Keywords: Primary 65D32 ; secondary 65R20 ; Cauchy principal value integral ; singular integral equations ; quadrature rules ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit konstruieren wir eine interpolatorische Quadraturformel der Form $$\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 \frac{{f'(x)}}{{y - x}}dx \approx \sum\limits_{i = 1}^n {w_{ni} (y)f(x_{ni} )} ,$$ wobeif(x)=(1−x)α(1+x)β f 0(x), α, β〉0, und {xni} dien Nullstellen des Chebyshevpolynomsn-ten Grades vom ersten TypT n (x) sind. Ferner geben wir ein Konvergenzergebnis an und untersuchen das Verhalten der Größe $$ \sum\limits_{i = 1}^n {|w_{ni} (y)|} $$ , fürn→∞.
    Notes: Abstract In this paper we construct an interpolatory quadrature formula of the type $$\mathop {\rlap{--} \smallint }\limits_{ - 1}^1 \frac{{f'(x)}}{{y - x}}dx \approx \sum\limits_{i = 1}^n {w_{ni} (y)f(x_{ni} )} ,$$ wheref(x)=(1−x)α(1+x)β f o(x), α, β〉0, and {x ni} are then zeros of then-th degree Chebyshev polynomial of the first kind,T n (x). We also give a convergence result and examine the behavior of the quantity $$ \sum\limits_{i = 1}^n {|w_{ni} (y)|} $$ asn→∞.
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    URL: http://dx.doi.org/10.1007/BF02252732
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    Performance evaluations of recursive and iterative algorithms for the Towers of Hanoi problem (1986)
    Springer
    Computing 37 (1986), S. 93-102 
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    ISSN: 1436-5057
    Keywords: 68NO5 ; 68Q25 ; Towers of Hanoi ; performance evaluation ; algorithm ; iteration ; recursion ; binary number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird ein Satz über die Bezihung zwischen den Türmen von Hanoi und den Binärzahlen bewiesen. Aus diesem Satz folgt ein Algorithmus für das Problem der Türme von Hanoi. Die Komplexitätsabschätzungen aller existierenden rekursiven und iterativen Algorithmen für das Problem der Türme von Hanoi zeigen, daß der angegebene iterative Algorithmus der effizienteste in Bezug auf Laufzeit und Speicherplatz ist. Schließlich wird gezeigt, daß die Binärdarstellung von Zahlen den Status allern-Scheiben in jedem Schritt vollständig charakterisiert.
    Notes: Abstract A theorem concerning the relation between the Towers of Hanoi and the binary numbers is proven in this paper. From this theorem, an algorithm for the Towers of Hanoi problem follows. The performance evaluations of all existing recursive and iteative algorithms for the Towers of Hanoi problem show that the above iterative algorithm is the most efficient one in terms of time and space. Finally, it is shown that the binary representation of numbers completely characterizes the status of alln discs in each step.
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    URL: http://dx.doi.org/10.1007/BF02253184
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    Explicit monotone iterations providing upper and lower bounds for finite element solution with nonlinear radiation boundary conditions (1986)
    Springer
    Computing 37 (1986), S. 137-149 
    Details
    ISSN: 1436-5057
    Keywords: 65N30 ; 65H10 ; Nonlinear radiation cooling problem ; finite element solution ; explicit monotone iterations ; upper and lower bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit beobachten wir das explizite monotone Iterationsverfahren von finiten Elementlösungen für das Radiationskühlungsproblem mit nichtlinearen Randbedingungen. Bei diesem Iterationsverfahren ergeben sich obere und untere Schranken, und eine Konvergenz kann nachgewiesen werden. An einigen numerischen Beispielen wird die Brauchbarkeit gezeigt.
    Notes: Abstract In this paper we consider explicit monotone iterations of the finite element solutions for the radiation cooling problem with the nonlinear boundary conditions. These iterations provide upper and lower bounds, and convergence proofs are given. Finally, we give some numerical examples to demonstrate the effectiveness.
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    URL: http://dx.doi.org/10.1007/BF02253187
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    On the globalization of Wilson-type optimization methods by means of generalized reduced gradient methods (1986)
    Springer
    Computing 37 (1986), S. 151-169 
    Details
    ISSN: 1436-5057
    Keywords: 90C30 ; 65K05 ; Nonlinear programming algorithms ; hybrid algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur Bestimmung von Kuhn-Tucker-Punkten nichtlinearer Optimierungsaufgaben wird ein hybrides numerisches Verfahren vorgestellt. Ausgangspunkt der Betrachtungen sind die in diesem Journal erschienenen Arbeiten von Best/Bräuninger/Ritter/Robinson und Kleinmichel/ Richter/Schönefeld, in denen verschiedene lokal überlinear konvergente Verfahren mit einer Strafmethode kombiniert werden, so daß sich für die so entstehenden Verfahren auch die globale Konvergenz nachweisen läßt. Als Beispiel dafür, daß das zugrunde liegende Kopplungsprinzip auf eine Reihe weiterer global konvergenter Verfahren angewendet werden kann, wird ein lokales Verfahren vom Wilson-Typ initialisiert durch ein Verfahren der zulässigen Richtungen, welches unter Benutzung reduzierter Gradienten arbeitet. In beiden Phasen des Verfahrens treten gleichartige Ersatzprobleme in Form spezieller quadratischer Optimierungsaufgaben auf. Daher sind im Gegensatz zu den oben angeführten Arbeiten ausschließlich lineare Gleichungssysteme zu lösen. Unter den üblichen Voraussetzungen läßt sich für das Gesamtverfahren die globale und lokal überlineare Konvergenz zeigen.
    Notes: Abstract For solving nonlinear optimization problems, i.e. for the determination of Kuhn-Tucker points a numerical method is proposed. The considerations continue investigations of Best/ Bräuninger/Ritter/Robinson and Kleinmichel/Richter/Schönefeld. In these papers (published in this journal) different local methods are combined with a penalty method in such a way that global convergence can be guaranteed. In order to show that the basic principle of coupling is applicable to a number of further globally convergent methods a local Wilson-type method is now initialized by a feasible direction method that uses reduced gradients. In both phases of the method similar subproblems (special quadratic programs) occur. Therefore, in contrast to the papers mentioned above systems of linear equations have to be solved exclusively. Under usual assumptions the algorithm is shown to be globally and superlinearly convergent.
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    URL: http://dx.doi.org/10.1007/BF02253188
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