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  • Articles  (9,811)
  • Springer  (9,811)
  • 1995-1999  (9,811)
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  • 1995  (9,811)
  • Mathematics  (7,137)
  • Process Engineering, Biotechnology, Nutrition Technology  (2,327)
  • Nature of Science, Research, Systems of Higher Education, Museum Science  (347)
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  • Articles  (9,811)
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  • 1995-1999  (9,811)
  • 1945-1949
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  • 1
    Electronic Resource
    Electronic Resource
    Hypnosis modelling in neural networks (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 1-20 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the framework of the neural network theory effects similar to hypnotic displays are constructed. They are based on the associative paradigm involving non-linear interaction of excitatory and inhibitory channels with synaptic memory. The non-linearity of long-term memorizing processes may cause effects exhibited by blind spots, which are interpreted as the first stage of hypnosis. More complicated phenomena are discussed in terms of a two-layer network.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458314
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  • 2
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    Dynamics of small autocatalytic reaction networks—II. Replication, mutation and catalysis (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 21-61 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mutation is introduced into autocatalytic reaction networks. The differential equations obtained are neither of repliator-type nor can they be transformed straightway into a linear equation. Examples of low dimensional dynamical systems —n=2, 3 and 4 — are discussed and complete qualitative analysis is presented. Error thresholds known from simple replication-mutation kinetics with frequency independent replication rates occur here as well. Instead of cooperative transitions or higher order phase transitions the thresholds appear here as supercritical or subcritical bifurcations being analogous to first-order phase transitions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458315
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  • 3
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    Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 63-76 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The non-linear behavior of a differential equations-based predator-prey model, incorporating a spatial refuge protecting a consant proportion of prey and with temperature-dependent parameters chosen appropriately for a mite interaction on fruit trees, is examined using the numerical bifurcation code AUTO 86. The most significant result of this analysis is the existence of a temperature interval in which increasing the amount of refuge dynamically destabilizes the system; and on part of this interval the interaction is less likely to persist in that predator and prey minimum population densities are lower than when no refuge is available. It is also shown that increasing the amount of refuge can lead to population outbreaks due to the presence of multiple stable states. The ecological implications of a refuge are discussed with respect to the biological control of mite pests.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458316
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  • 4
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    Optimal root/shoot-partitioning of carbohydrates in plants (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 99-107 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In many applications of control theory on plant growth models biomass maximization is postulated to avoid analytically unsolvable problems while fruit maximization is commonly considered to be a more realistic criterion. In a special case, we are able to compare these criteria. Iwasa and Roughgarden (1984,Theor. Pop. Biol. 25, 78–105) have investigated a certain class of plant growth models using a fruit maximization criterion. They proved that, in the vegetative growth period, the organs follow a certain path of balanced growth. We show that this path remains optimal when biomass maximization is postulated. This underlines the importance of the balanced growth path found by Iwasa and Roughgarden. Furthermore, our result suggests that in the vegetative growth period the biomass maximization criterion is a good approximation of fruit maximization. In another theoretical control investigation, Schultzeet al. (1983,Oecologia 58, 169–177) derived a different type of balanced growth path. We apply the theory of Iwasa and Roughgarden to an improved version of the model of Schulzeet al. This leads to a new description of balanced growth between root and shoot that reflects non-linearities in the water uptake process and constitutes an interesting hypothesis for further experimental testing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458318
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  • 5
    Electronic Resource
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    Ion induced deformation of soft tissue (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 77-98 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper the effects of changing the ion concentration in and around a sample of soft tissue are investigated. The triphasic theory developed by Laiet al. (1990,Biomechanics of Diarthrodial Joints, Vol. 1, Berlin, Springer-Verlag) is reduced to two coupled partial differential equations involving fluid ion concentration and tissue solid deformation. These equations are given in general form for Cartesian, cylindrical and spherical geometries. After solving the two equations quantities such as fluid velocity, fluid pressure, chemical potentials and chemical expansion stress may be easily calculated. In the Cartesian geometry comparison is made with the experimental and theoretical work of Myerset al. (1984,ASME J. biomech. Engng,106, 151–158). This dealt with changing the ion concentration of a salt shower on a strip of bovine articular cartilage. Results were obtained in both free swelling and isometric tension states, using an empirical formula to acount for ion induced deformation. The present theory predicts lower ion concentrations inside the tissue than this earlier work. A spherical sample of tissue subjected to a change in salt bath ion concentration is also considered. Numerical results are obtained for both hypertonic and hypotonic bathing solutions. Of particular interest is the finding that tissue may contract internally before reaching a final swollen equilibrium state or swell internally before finally contracting. By considering the relative magnitude, and also variation throughout the time course of terms in the governing equations, an even simpler system is deduced. As well as being linear the concentration equation in the new system is uncoupled. Results obtained from the linear system compare well with those from the spherical section. Thus, biological swelling situations may be modelled by a simple system of equations with the possibility, of approximate analytic solutions in certain cases.
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    URL: http://dx.doi.org/10.1007/BF02458317
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  • 6
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    Memory capacity in large idiotypic networks (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 109-136 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Many models of immune networks have been proposed since the original work of Jerne [1974,Ann. Immun. (Inst. Pasteur) 125C, 373–389]. Recently, a limited class of models (Weisbuchet al., 1990,J. theor. Biol. 146, 483–499) have been shown to maintain immunological memory by idiotypic network interactions. We examine generalizations of these models when the networks are both large and highly connected to study their memory capacity, i.e. their ability to account for immunization to a large number of random antigens. Our calculations show that in these minimal models, random connectivities with continuously distributed affinities reduce the memory capacity to essentially nil.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458319
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  • 7
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    A kinetic model of coronary reactive hyperemic response to transient ischemia (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 137-156 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restriced inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.
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    URL: http://dx.doi.org/10.1007/BF02458320
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  • 8
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    Kinetic study of an enzyme-catalysed reaction in the presence of novel irreversible-type inhibitors that react with the product of enzymatic catalysis (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 157-168 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the present paper a kinetic study is made of the behaviour of a Michaelis-Menten enzyme-catalysed reaction in the presence of irreversible inhibitors rendered unstable in the medium by their reaction with the product of enzymatic catalysis. A general mechanism involving competitive, non-competitive, uncompetitive and mixed irreversible inhibition with one or two steps has been analysed. The differential equation that describes the kinetics of the reaction is non-linear and computer simulations of its dynamic behaviour are presented. The results obtained show that the systems studied here present kinetic co-operativity for a target enzyme that follows the simple Michaelis-Menten mechanism in its action on the substrate, except in the case of an uncompetitive-type inhibitor.
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    URL: http://dx.doi.org/10.1007/BF02458321
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  • 9
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    Book reviews (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 169-173 
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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/BF02458322
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  • 10
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    On the estimation of alternative pathways of fatty acid oxidation in the liverIn vivo (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 191-203 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The relative contributions of mitochondrial β-oxidation and peroxisomal β-oxidation and peroxisomal ω-oxidation to the oxidation of a given fatty acidin vivo can be quantitated by an isotopic method. The approach requires infusion of a fatty acid labelled on two specific carbon atoms (e.g. [1-14C] and [11-14C] palmitate) to an isotopic steady state, with subsequent isolation and degradation of an acetylated conjugate as a product of the liver cytosolic acetyl CoA pool and of ketone bodies as a product of the liver mitochondrial acetyl CoA pool.
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    URL: http://dx.doi.org/10.1007/BF02460615
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  • 11
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    Correlations of rates of insulin release from islets and plateau fractions for β-cells (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 229-246 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Pancreatic β-cells in intact islets of Langerhans perfused with various glucose concentrations exhibit periodic bursting electrical activity (BEA) consisting of active and silent phases. The fraction of the time spent in the active phase is called the plateau fraction and appears to be strongly correlated with the rate of release of insulin from islets as glucose concentration is varied. Here this correlation is quantified and a theoretical development is presented in detail. Experimental rates of insulin release are correlated with “effective” plateau fractions over a range of glucose concentrations. There are a number of different models for BEA in pancreatic β-cells and a method is developed here to quantify the dependence of a glucose dependent parameter on glucose concentration. As an example, the plateau fractions computed from the Sherman-Rinzel-Keizer model are matched with experimental plateau fractions to obtain a relationship between the model's glucose-dependent parameter, β, and glucose concentration. Knowledge of the relationships between β and glucose concentration and between experimental measurements of rates of insulin release and plateau fractions permits the determination of theoretical rates of insulin release from the model.
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    URL: http://dx.doi.org/10.1007/BF02460617
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  • 12
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    The development of concentration gradients in a suspension of chemotactic bacteria (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 299-344 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract When a suspension of bacterial cells of the speciesBacillus subtilis is placed in a chamber with its upper surface open to the atmosphere complex bioconvection patterns are observed. These arise because the cells: (1) are denser than water; and (2) usually swim upwards, so that the density of an initially uniform suspension becomes greater at the top than the bottom. When the vertical density gradient becomes large enough, an overturning instability occurs which ultimately evolves into the observed patterns. The reason that the cells swim upwards is that they are aerotactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell (N) and oxygen (C) concentrations, and these are solved in the pre-instability phase of development whenN andC depend only on the vertical coordinate and time. Numerical results are obtained for both shallow- and deep-layer chambers, which are intrinsically different and require different mathematical and numerical treatments. It is found that, for both shallow and deep chambers, a thin boundary layer, densely packed with cells, forms near the surface. Beneath this layer the suspension becomes severely depleted of cells. Furthermore, in the deep chamber cases, a discontinuity in the cell concentration arises between this cell-depleted region and a cell-rich region further below, where no significant oxygen concentration gradients develop before the oxygen is fully consumed. The results obtained from the model are in good qualitative agreement with the experimental observations.
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    URL: http://dx.doi.org/10.1007/BF02460620
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  • 13
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    Topological and phenomenological classification of bursting oscillations (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 413-439 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (inMathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.
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    URL: http://dx.doi.org/10.1007/BF02460633
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  • 14
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    Book reviews (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 499-506 
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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/BF02460637
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  • 15
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    Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 461-486 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract To ensure its sustained growth, a tumour may secrete chemical compounds which cause neighbouring capillaries to form sprouts which then migrate towards it, furnishing the tumour with an increased supply of nutrients. In this paper a mathematical model is presented which describes the migration of capillary sprouts in response to a chemoattractant field set up by a tumour-released angiogenic factor, sometimes termed a tumour angiogenesis factor (TAF). The resulting model admits travelling wave solutions which correspond either to successful neovascularization of the tumour or failure of the tumour to secure a vascular network, and which exhibit many of the characteristic features of angiogenesis. For example, the increasing speed of the vascular front, and the evolution of an increasingly developed vascular network behind the leading capillary tip front (the brush-border effect) are both discernible from the numerical simulations. Through the development and analysis of a simplified caricature model, valuable insight is gained into how the balance between chemotaxis, tip proliferation and tip death affects the tumour's ability to induce a vascular response from neighbouring blood vessels. In particular, it is possible to define the success of angiogenesis in terms of known parameters, thereby providing a potential framework for assessing the viability of tumour neovascularization in terms of measurable quantities.
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    URL: http://dx.doi.org/10.1007/BF02460635
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  • 16
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    Nonlinear Approximation by Trigonometric Sums (1995)
    Springer
    The journal of Fourier analysis and applications 2 (1995), S. 29-48 
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    ISSN: 1531-5851
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate the $L_p$ -error of approximation to a function $f\in L_p({\Bbb T}^d)$ by a linear combination $\sum_{k}c_ke_k$ of $n$ exponentials $e_k(x):= e^{i\langle k,x\rangle}=e^{i(k_1x_1+\cdots+k_dx_d)}$ on ${\Bbb T}^d,$ where the frequencies $k\in {\Bbb Z}^d$ are allowed to depend on $f.$ We bound this error in terms of the smoothness and other properties of $f$ and show that our bounds are best possible in the sense of approximation of certain classes of functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s00041-001-4021-8
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  • 17
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    Uniformly Elliptic PDEs with Bounded, Measurable Coefficients (1995)
    Springer
    The journal of Fourier analysis and applications 2 (1995), S. 237-259 
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    ISSN: 1531-5851
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let $L[\,\cdot\,]$ be a nondivergent linear second-order uniformly elliptic partial differential operator defined on functions with domain $\Omega.$ Consider the question, "When is a function u a solution of $L[u] = 0$ on $\Omega$ ?" The naive answer, "u is a solution of $L[u] = 0$ on $\Omega$ if $u\in C^2(\Omega)$ and $L[u](x) = 0$ for all $x\in\Omega,$ " is clearly too limited. Indeed, if the coefficients of L are in $W^{1,2}\cap L^{\infty},$ then L can be rewritten in divergence form for which the notion of a "weak" solution can be applied. In this case there could be infinitely many functions that are "weak" but not classical solutions. More importantly, even if the coefficients of L are just bounded and measurable, the recent results of Krylov permit us to construct "solutions" of $L[u] = 0$ on $\Omega,$ and these "solutions" are generally no better than continuous; the "weak" solutions previously mentioned can be obtained by this construction, too. The preceding discussion provides us with an adequate extrinsic definition of solution (i.e., given a function u we either prove that it is or is not the result of such a construction) that has been used by several authors, but one that is not particularly satisfying or illuminating. Our major contribution in this paper is to show the following. I. There is an intrinsic definition of solution that is equivalent to the extrinsic one. II. Furthermore, the intrinsic definition is just the (now) well-known Crandall-Lions viscosity solution, modified in a natural way to accommodate measurable coefficients.
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    URL: http://dx.doi.org/10.1007/s00041-001-4031-6
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  • 18
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    A Weighted Tauberian Theorem (1995)
    Springer
    The journal of Fourier analysis and applications 2 (1995), S. 397-406 
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    ISSN: 1531-5851
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth. It can be used to study the weighted average of the form $(T^\alpha (\hbox {ln }T)^\beta)^{-1}\int _0^T h(t) \, dt.$
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    URL: http://dx.doi.org/10.1007/s00041-001-4042-3
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  • 19
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    Neuronal growth via hybrid system of self-growing and diffusion based grammar rules: I (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 205-227 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The formation of neuronal networks requires axonal growth towards target neutons. A simple set of grammar rules is introduced to describe axonal growth towards target cells situated both at short and long distances from the growing neuron. Growth for short distances is descrbed by growth following the highest gradient of a chemical compound (which is spread by diffusion from the targets). This approach fails to describe long-distance growth, which is addressed by adopting a graph grammar theory for growing trees. With these rules a flexible tool to draw network of neurons by computer can be developed.
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    URL: http://dx.doi.org/10.1007/BF02460616
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  • 20
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    Interlocking triads of growth control in tumors (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 345-366 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A pair of growth control triads are used to describe coincident tumor growth and liver regeneration after partial hepatectomy. The models are extensions of previous growth control models which describe tumor growth in an unperturbed host (Michelson and Leith, 1991,Bull. math. Biol. 53, 639–656; idem, 1992, Proceedings of the Third International Conference on Communications and Control, Vol. 2, pp. 481–490; idem, 1992,Bull. math. Biol. 55, 993–1011; idem,J. theor. Biol. 169, 327–338). The linkage between the two triads depends upon systemic signals carried by soluble factors, and mathematical descriptors based upon biological first principals are proposed. The sources of the growth factors, their targets and the processing of their signals are investigated. Analyses of equilibrium in the constant coefficients case and simulated growth curves for the dynamic system are presented, and the effects of growth factor-induced mitogenesis and angiogenesis are discussed in particular. A case is made for early and late responses in the coupled control system. The biology of the signal processing paradigm is placed within a new theoretical context and discussed with regard to tumor adaptation, liver differentiation and the development of a tumor hypoxic fraction.
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    URL: http://dx.doi.org/10.1007/BF02460621
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  • 21
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    Optimal population stabilization and control using the Leslie matrix model (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 381-399 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider the problem of optimal stabilization and control of populations which follow the Leslie model dynamics, within state space and control systems theory and methodology. Various types of culling strategies are formulated and introduced into the Leslie model as control inputs, and their effect on global asymptotic stability is investigated. Our new approach provides answers to several unexplored problems. We show that in general it is possible to achieve a desired stable equilibrium population level, through the design of a class ofshifted-proportional stabilizing culling policies. Further, we formulate general non-linear constrained opitmization problems, for obtaining the cost-optimal policy among this generally infinite class of such stabilizing policies. The theoretical findings are illustrated through the solution of the problem over an infinite planning horizon for a numerical example. A comparative study of the costs and dynamic effects of various culling strategies also supports the mathematical results.
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    URL: http://dx.doi.org/10.1007/BF02460631
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  • 22
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    A data assimilation technique applied to a predator-prey model (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 593-617 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new approach for data assimilation, which is based on the adjoint method, but allows the computer code for the adjoint to be constructed directly from the model computer code, is described. This technique is straightforward and reduces the chance of introducing errors in the construction of the adjoint code. Implementation of the technique is illustrated by applying it to a simple predator-prey model in a model fitting mode. A series of identical twin numerical experiments are used to show that this data assimilation approach can successfully recover model parameters as well as initial conditions. However, the ease with which these values are recovered is dependent on the form of the model equations as well as on the type and amount of data that are available. Additional numerical experiments show that sufficient coefficient and parameter recoveries are possible even when the assimilated data contain significant random noise. Thus, for biological systems that can be described by ecosystem models, the adjoint method represents a powerful approach for estimating values for little-known biological parameters, such as initial conditions, growth rates, and mortality rates.
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    URL: http://dx.doi.org/10.1007/BF02460785
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  • 23
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    Building activity and longevity of queenless groups of the Oriental hornet,Vespa orientalis (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 441-460 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The effect of group size on behavioral parameters of the Oriental hornet,Vespa orientalis, was assessed experimentally under laboratory conditions. Hornet groups of various sizes (ranging from 1 to 100 individuals per group) comprised of young individuals (0–24 hr of age) devoid of a queen were placed in artificial breeding boxes (ABBs). The following three quantitative parameters were evaluated: the amount and rate of building as a function of the number of hornets in the group, the rate of oviposition as, related to group size and the longevity of hornets as a function of their group size. The probability for the occurrence of these events was similarly considered and additional behavioral parameters were only assessed qualitatively. Results of this investigation revealed a relation between the three mentioned quantitative behavioral parameters and the number of hornets per group. The number of hornets per group was positively related to the extent of building, the number of cells built by a group is $$2\pi \sqrt {group size} $$ , but negatively related to the rate of building. As for the delay of building, a non-monotone relation was found. The relation between number of hornets per group and the oviposition delay was found to be non-monotone; the number of hornets per group and their longevity were found to be inversely related. Discrepanices were recorded on the very small (1–2 individuals) or very large (100 individuals) hornet groups.
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    Fuzzy classification of nucleotide sequences and bacterial evolution (1995)
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    Bulletin of mathematical biology 57 (1995), S. 527-537 
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    Notes: Abstract A new method for reconstructing evolutionary relationship among bacteria by use of rRNA sequence data is proposed. The method is based on the concept of fuzzy classification of probabilitiesp(i), p(i/j) andp(i/j*) (i=A,G,C,U) of each sequence. The resulting partition tree shares common features of previous works but has some new peculiarities.
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    Book reviews (1995)
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    Bulletin of mathematical biology 57 (1995), S. 619-630 
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    Gyrotaxis: Interaction between algae and flagellates (1995)
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    Bulletin of mathematical biology 57 (1995), S. 631-650 
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    Notes: Abstract We describe the behaviour of motile microorganisms (e.g. flagellates) attracted by “gyrotaxis” to a sinking, non-motile particle (e.g. an algal cell). The model is based on the application of Stokes' solution for the flow field around the settling cell. The volume within which the flagellate is attracted to the sinking particle is determined from the trajectories of the flagellate. The model of gyrotaxis has several applications; these include the colonization of sinking marine snow particles with motile microoganisms and suspension feeding by protozoa.
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    Effect of dimensionality on Lotka-Volterra predator-prey dynamics: Individual based simulation results (1995)
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    Bulletin of mathematical biology 57 (1995), S. 507-526 
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    Notes: Abstract The effect of varying habitat dimensionality on the dynamics of a model predator-prey system is examined using an individual-based simulation. The general results are that in one dimension fluctuations in abundance of prey and predators occur over a large range of spatial scales (extinctions occur over many spatial scales). In two dimensions (and low mobilities of prey and predators) the dynamics become more predictably periodic at local scales and constant at larger scales due to statistical stabilization. In three dimensions, the model can become “phase-locked” with prey and predators displaying oscillations in abundance over large spatial scales.
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    Dicarboxylic acid fluxes during gluconeogenesis. No channelling of mitochondrial oxalacetate (1995)
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    Bulletin of mathematical biology 57 (1995), S. 557-568 
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    Notes: Abstract A rather complete model of the gluconeogenic pathway was used, with the known separate pools of mitochondrial and cytosolic oxalacetate, malate and aspartate. The fumarase, malate dehydrogenase and glutamate oxalacetate transaminase reactions were assumed to be isotopically actively reversible, but none at isotopic equilibrium. Malate was assumed to exchange actively between the mitochondrial and cytosol, while aspartate exchange was more limited, in agreement with the known electrogenic nature of aspartate export from the mitochondria. This model was fit to14C data obtained in hepatocyte studies, and to the whole rat14C data obtained by Heath and Rose (Biochem J. 227, 851–876, 1985). The latter data were easily fit to our model, when a single mitochondrial oxalacetate pool was assumed. However, invoking two mitochondrial oxalacetate pools, as proposed by Heath and Rose, with the oxalacetate formed via pyruvate carboxylase preferentially channelled to gluconeogenesis, could not be fit with the known differences in scrambling in glucose and glutamate produced from L[3-14C]lactate.
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    Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells (1995)
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    Bulletin of mathematical biology 57 (1995), S. 569-591 
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    Notes: Abstract Oscillatory secretion of insulin has been observed in many different experimental preparations ranging from pancreatic islets to the whole pancreas. Here we examine the mathematical features underlying a possible model for oscillatory secretion from the perifused, insulin-secreting cell line, HIT-15. The model includes the kinetics of uptake of glucose by GLUT transporters, the rate of glucose metabolism within the cell, and the effect of glucose on the rate of insulin secretion. Putative feedback by insulin on the rate of glucose transport into the cells is treated phenomenologically and leads to insulin oscillations similar to those observed experimentally in HIT cells. The resulting set of ordinary differential equations is simplified by time-scale analysis to a two-variable set of ordinary differential equations. Because of this simplification we can explore, in great detail, the characteristics of the oscillations and their sensitivity to parameter variation using phase plane analysis.
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    Sperm motility in the presence of boundaries (1995)
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    Bulletin of mathematical biology 57 (1995), S. 679-699 
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    Notes: Abstract The fluid dynamics of sperm motility near both rigid and elastic walls is studied using the immersed boundary method. Simulations of both single and interacting organisms are presented. In particular, we find that nearby organisms originally undulating with a 90° phase shift may adjust their relative swimming velocities and phase-lock. Comparisons with previous analytical results are also discussed. The tendency of a near-wall to attract organisms is demonstrated.
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    Contributions of memory B cells to secondary immune response (1995)
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    Bulletin of mathematical biology 57 (1995), S. 713-731 
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    Notes: Abstract The secondary immune response is one of the most important features of immune systems. During the secondary immune response, the immune system can eliminate the antigen, which has been encountered by the individual during the primary invasion, more rapidly and efficiently. Both T and B memory cells contribute to the secondary response. In this paper, we only concentrate on the functions of memory B cells. We explore a model describing the memory contributed by the specific long-lived clone which is maintained by continued stimulation with a small amount of antigens sequestered on the surfaces of the follicular dendritic cells (FDC). The behavior of the secondary response provided by the model can be compared with experimental observations. The model shows that memory B cells indeed play an important role in the secondary response. It is found that a single memory cell in a long-lived clone may not be long-lived. In the present note, the influences of relevant parameters on the secondary response are also explored.
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    Reproduction rate, feeding process, and liebig limitations in cell populations—II (1995)
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    Bulletin of mathematical biology 57 (1995), S. 749-782 
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    Notes: Abstract A biological system consisting of a population of cells suspended in a liquid substrate is considered. The general problem addressed in the paper is the derivation of the kinetic pattern of population growth as a statistical effect of a very large number of elementary interactions between a single cell and the molecules of nutrient in substrate. Solution of the problem is obtained in the form of equation expressing the population growth ratec as a function of substrate concentration,C s. The analytical expression derived is applied to a real bacterial population (Escherichi coli) and kinetic patterns are theoretically computed. The major findings, expressed roughly, without nuances, are: (i) the concentration of nutrient at the cell membrane,C c, can only be equal to either 0 (for theC s below some threshold valueC *) orC s (forC s〉C *); (ii) the Michaelis-Menten-Monod kinetics observed in experiments is an artifact: the pure (not contaminated by foreign factors) dependence ofc onC s is actually such that the functionc=c(C s) has practically linear increase whenC s〈C *, and is constant,c=c(C *)=const, whenC s〉C *; (iii) the Liebig principle is strictly fulfilled: up to a feasible accuracy of observation, under no circumstances can population growth be limited (controlled) by more than one substrate component—replacement of a limiting component for another one is an instant event rather than a gradual process.
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    Idiotypic regulation of B cell differentiation (1995)
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    Bulletin of mathematical biology 57 (1995), S. 841-881 
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    Notes: Abstract We study the equilibrium properties of idiotypically interacting B cell clones in the case where only the differentiation of B cells is affected by idiotypic interactions. Furthermore, we assume that clones may recognize and be stimulated by self antigen in the same fashion as by antiantibodies. For idiotypically interacting pairs of non-autoreactive clones we observe three qualitatively different dynamical regimes. In the first regime, at small antibody production an antibody-free fixed point, the virgin state, is the only attractor of the system. For intermediate antibody production, a symmetric activated state replaces the virgin state as the only attractor of the system. For large antibody production, finally, the symmetric activated state gives way to two asymmetric activated states where one clone suppresses the other clone. If one or both clones in the pair are autoreactive there is no virgin state. However, we still observe the switch from an almost symmetric activated state to two asymmetric activated states. The two asymmetric activated states at high antibody production have profoundly different implications for a self antigen which is recognized by one of the clones of the pair. In the attractor characterized by high autoantibody concentration the self antigen is attacked vigorously by the immune system while in the opposite steady state the tiny amount of autoantibody hardly affects the self antigen. Accordingly, we call the first state the autoimmune state and the second the tolerant state. In the tolerant state the autoreactive clone is down-regulated by its anti-idiotype providing an efficient mechanism to prevent an autoimmune reaction. However, the antibody production required to achieve this anti-idiotypic control of autoantibodies is rather large.
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    The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models (1995)
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    Bulletin of mathematical biology 57 (1995), S. 899-929 
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    Notes: Abstract It is widely believed, following the work of Connor and Stevens (1971,J. Physiol. Lond. 214, 31–53) that the ability to fire action potentials over a wide frequency range, especially down to very low rates, is due to the transient, potassium A-current (I A). Using a reduction of the classical Hodgkin-Huxley model, we study the effects ofI A on steady firing rate, especially in the near-threshold regime for the onset of firing. A minimum firing rate of zero corresponds to a homoclinic bifurcation of periodic solutions at a critical level of stimulating current. It requires that the membrane's steady-state current-voltage relation be N-shaped rather than monotonic. For experimentally based genericI A parameters, the model does not fire at arbitrarily low rates, although it can for the more atypicalI A parameters given by Connor and Stevens for the crab axon. When theI A inactivation rate is slow, we find that the transient potassium current can mediate more complex firing patterns, such as periodic bursting in some parameter regimes. The number of spikes per burst increases asg A decreases and as inactivation rate decreases. We also study howI A affects properties of transient voltage responses, such as threshold and firing latency for anodal break excitation. We provide mathematical explanations for several of these dynamic behaviors using bifurcation theory and averaging methods.
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    Fractals in science (1995)
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    Bulletin of mathematical biology 57 (1995), S. 939-941 
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    Coping with chaos: Analysis of chaotic data and the exploitation of chaotic systems (1995)
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    Bulletin of mathematical biology 57 (1995), S. 945-946 
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    On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 65-107 
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    Notes: Abstract Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in ℂn and on domains of finite type in ℂ2. Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.
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    Irregular Sampling in Wavelet Subspaces (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 181-189 
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    Notes: Abstract As a particular wavelet subspace, the Paley-Wiener space $B_{\pi}$ has both regular and irregular sampling theorems. A regular sampling theorem in general wavelet subspaces has been established for several years. In this paper, we discuss the irregular sampling problem in wavelet subspaces.
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    Autocorrelation Functions as Translation Invariants in L1 and L2 (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 217-225 
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    Notes: Abstract The Adler-Konheim theorem [Proc. Amer. Math. Soc. 13 (1962), 425-428] states that the collection of nth-order autocorrelation functions ${\cal M} = \{M^n(\cdot): n=1,2,\dots\}$ is a complete set of translation invariants for real-valued L1 functions on a locally compact abelian group. It is shown here that there are proper subsets of ${\cal M}$ that also form a complete set of translation invariants, and these subsets are characterized. Specifically, a subset is complete if and only if it contains infinitely many even-order autocorrelation functions. In addition, any infinite subset of $\cal M$ is complete up to a sign. While stated here for functions on $\cal R,$ the proofs presented hold for functions on any locally compact abelian group that is not compact, in particular, on ${\cal R}^n$ and the integer lattice ${\cal Z}^n.$
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    Fourier Inequalities and Moment Subspaces in Weighted Lebesgue Spaces (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 49-64 
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    Notes: Abstract For $k \in {\Bbb N}, k \not= 0,$ define ${\cal F}_kf(\gamma) = \int_{{\Bbb R}^n} f(t)R_k(-2i \pi \gamma.t) \, dt, n\geq 1,$ where $R_k(i\lambda) = e^{i\lambda} - \sum^{k-1}_{j=0} \left(i \lambda \right)^{j} / \left(j~!\right).$ Pointwise estimates and weighted inequalities describing the local Lipschitz continuity of ${\cal F}_kf$ are established. Sufficient conditions are found for the boundedness of ${\cal F}_k$ from $L^p_v$ into $L^q_\mu,$ and a spherical restriction property is proved. A study of the moment subspaces of $L^p_v$ is next developed in the one-variable case, for $1 〈 p 〈 \infty, v$ locally integrable, $v 〉 0$ a.e. It includes a decomposition theorem and a complete classification of all possible sequences of moment subspaces in $L^p_v.$ Characterizations are also given for each class. Applications related to the approximation and decomposition of ${\cal F}_k$ are discussed.
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    Designing Multiresolution Analysis-type Wavelets and Their Fast Algorithms (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 135-159 
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    Notes: Abstract Often, the Dyadic Wavelet Transform is performed and implemented with the Daubechies wavelets, the Battle-Lemarie wavelets, or the splines wavelets, whereas in continuous-time wavelet decomposition a much larger variety of mother wavelets is used. Maintaining the dyadic time-frequency sampling and the recursive pyramidal computational structure, we present various methods for constructing wavelets ψwanted, with some desired shape and properties and which are associated with semi-orthogonal multiresolution analyses. We explain in detail how to design any desired wavelet, starting from any given multiresolution analysis. We also explicitly derive the formulae of the filter bank structure that implements the designed wavelet. We illustrate these wavelet design techniques with examples that we have programmed with Matlab routines.
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    Weil Multipliers (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 191-215 
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    Notes: Abstract This paper studies a class of linear operators on spaces of functions of one real variable, which correspond to multiplication by a measurable function under the Weil transform $\Theta.$ These operators are called Weil multipliers, and arise out of the authors' study of Gabor series and radar ambiguity functions. Representation theory provides a natural class of Weil multipliers: the set of doubly periodic functions with absolutely convergent Fourier series, ${\bf A}({\bf T}^2).$ It will be proved that functions in ${\bf A}({\bf T}^2)$ are $L^p$ multipliers for all $1 \leq p \leq 2$ and, therefore, define bounded linear endomorphisms of ${\bf L}^p({\bf R}).$ Also, we record the fact that the Wiener lemma tells us something about the orbit structure of these multipliers acting on function spaces on the Heisenberg nilmanifold. Linear maps that correspond to multiplication by a function under a unitary conjugacy have a particularly simple spectral decomposition, which yields an approximation theory for these operators and provides insight into the foundation of the authors' previous work on approximate orthonormal bases. Finally, the problem of inversion of a multiplier will be analyzed for smooth functions that have a specified structure near their zeros.
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    On the Uniqueness in the Inverse Conductivity Problem (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 227-235 
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    Notes: Abstract Let $\Omega$ be a smooth domain in R2 containing a polygon D. The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered. We show that D is uniquely determined from boundary measurements corresponding two appropriately chosen Neumann datas.
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    Haar Type Orthonormal Wavelet Bases in R2 (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 1-14 
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    Notes: Abstract K.-H. Grochenig and A. Haas asked whether for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn. They proved that this is the case when the dimension n = 1. This article shows that this is also the case when the dimension n = 2.
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    On the Reproducing Formula of Calderon (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 15-28 
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    Notes: Abstract Let $1 〈 p 〈 \infty, h \in L_p ({\Bbb R}),$ and $f \in L_{p^\prime} ({\Bbb R}).$ Under certain conditions on $h,$ we shall prove that $\int_y^\infty (h_t \ast f)(x)\,dt/t$ converges nontangentially to $f(x_0)$ at $(x_0,0)$ for $a.a.\, x_0.$
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    On the allometric growth of tissues in fruits (1995)
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    Bulletin of mathematical biology 57 (1995), S. 487-498 
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    Notes: Abstract This paper deals with the relative growth of three different fruit tissues. Their morphogenetic periods and the mathematical constraints involved are described, and more precisely, the paper shows an allometric relationship (Y=nX m ) between the widths (X, Y) of the main tissues in stone fruits such as cherries, peaches and prunes. The mathematical relationships between the growth of the mesocarp and of the endocarp of somePrunus fruits are described, and it is proved that before the formation of the embryo, growth is allometric, in agreement with conclusions drawn from some experimental data. However, according to another study, the growth of the mesocarp and of the endocarp are ruled by autocatalytic and monomolecular functions, before as well as after the formation of the embryo. In this case, it is proved that if allometry exits in stone fruits, it can only be anantiometry (m=−1). To solve the dilemma, two main alternatives are proposed and discussed. We conclude that, while allometry is established on reasonable grounds before the formation of the embryo, after the formation of the embryo the mesocarp and endocarp evolve independently since a center for the coordination of growth no longer exists, and each tissue can grow according to its own independent rules.
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    Reliable segmentation by successive bifurcation (1995)
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    Bulletin of mathematical biology 57 (1995), S. 539-556 
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    Notes: Abstract In many organisms, a reliable number of segments is produced even though important properties of the region involved, especially its size at the time of pattern formation, are apparently not specified with sufficient precision. We show that this can be readily accomplished if segmentation occurs through a sequence of bifurcations rather than all at once, and we provide evidence from developmental studies that indicates that this is typically what actually occurs. Our results strongly suggest that where patterns are formed reliably, this generally happens in stages rather than by the setting up in advance of a complete prepattern.
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    Estimates from Below for Lebesgue Constants (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 287-301 
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    Notes: Abstract Estimates from below for the norms of linear means of multiple Fourier series are obtained. These means are given by some function λ and generalize the well-known Bochner-Riesz means. Sharpness of these estimates is established. The assumptions on λ are rather weak and of local character. Our results contain as particular cases a number of earlier published results. Proofs are based on the authors' new results on asymptotics of the Fourier transform of piecewise-smooth functions. Some applications of the results obtained are given, namely, orders of growth of the Lebesgue constants for "ovals" and "hyperbolic crosses" are evaluated and sharp conditions on the modulus of smoothness of a function are given, for this function to be approximated by the linear means.
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    High-Order Orthonormal Scaling Functions and Wavelets Give Poor Time-Frequency Localization (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 415-426 
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    Topics: Mathematics
    Notes: Abstract For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the time-frequency windows tend to infinity as n → ∞. This class includes those of Battle-Lemarie and Daubechies. In addition, if the scaling functions have at least asymptotic linear phase, then we prove that they converge to the "sinc" function and their corresponding orthonormal wavelets converge to the "difference" of two sinc functions.
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    Nonperiodic Sampling of Bandlimited Functions on Unions of Rectangular Lattices (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 435-452 
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    Notes: Abstract It is shown that a function $f\in L^p[-R,R], 1\le p〈\infty,$ is completely determined by the samples of $\hat f$ on sets $\Lambda=\cup_{i=1}^m\{n/2r_i\}_{n\in{\bf Z}}$ where $R=\sum r_i,$ and $r_i/r_j$ is irrational if $i\ne j,$ and of $\hat f^{(j)}(0) \mbox{ for } j=1,\ldots,m-1.$ If $f\in C^{m-2-k}[-R,R],$ then the samples of $\hat f$ on $\Lambda$ and only the first k derivatives of $\hat f$ at 0 are required to determine f completely. Higher dimensional analogues of these results, which apply to functions $f\in L^p[-R,R]^d$ and $C^{m-2-k}[-R,R]^d,$ are proven. The sampling results are sharp in the sense that if any condition is omitted, there exist nonzero $f\in L^p[-R,R]^d$ and $C^{m-2-k}[-R,R]^d$ satisfying the rest. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials that are not Riesz bases for $L^2[-R,R].$ A signal processing application in which such sampling sets arise naturally is described in detail.
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    Hardy Spaces on the Plane and Double Fourier Transforms (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 487-505 
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    Notes: Abstract We provide a direct computational proof of the known inclusion ${\cal H}({\bf R} \times {\bf R}) \subseteq {\cal H}({\bf R}^2),$ where ${\cal H}({\bf R} \times {\bf R})$ is the product Hardy space defined for example by R. Fefferman and ${\cal H}({\bf R}^2)$ is the classical Hardy space used, for example, by E.M. Stein. We introduce a third space ${\cal J}({\bf R} \times {\bf R})$ of Hardy type and analyze the interrelations among these spaces. We give simple sufficient conditions for a given function of two variables to be the double Fourier transform of a function in $L({\bf R}^2)$ and ${\cal H}({\bf R} \times {\bf R}),$ respectively. In particular, we obtain a broad class of multipliers on $L({\bf R}^2)$ and ${\cal H}({\bf R}^2),$ respectively. We also present analogous sufficient conditions in the case of double trigonometric series and, as a by-product, obtain new multipliers on $L({\bf T}^2)$ and ${\cal H}({\bf T}^2),$ respectively.
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    On Higher Riesz Transforms for Gaussian Measures (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 583-596 
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    Notes: Abstract Given an n × n matrix B, positive definite and symmetric, let LB be the differential operator in Rn given by $L_B=\frac{1}{2}\Delta -Bx\cdot \mbox{grad}_x.$ A class of higher Riesz transforms associated with LB is defined by means of higher gradients of order k. It is shown that these transformations are bounded in the space $L^p,\ 1〈p〈\infty,$ with respect to the measure that makes LB selfadjoint. The constants obtained are independent of the dimension n and depend only on k,p, and the number of different eigenvalues of the matrix B. The proof of the results uses an extension of the Littlewood-Paley-Stein theory of square functions to the vector-valued case and inequalities previously proved by one of the authors in the context of the Riesz transforms of order one.
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    A Search for Best Constants in the Hardy-Littlewood Maximal Theorem (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 473-486 
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    Notes: Abstract Let $Mf(x) = \sup(1/2r)\int^{x+r}_{x-r} |f(t)|\;dt$ be the centered maximal operator on the line. Through a numerical search procedure, we have conjectural best constants for the weak-type 1-1 estimate (3/2) and the Lp estimate (the constant B(p,1) such that $M(|x|^{-1/p}) = B(p,1)|x|^{-1/p}).$ We prove that these constants are lower bounds for the best constants and discuss the numerical evidence for the conjectures.
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    On Strongly Interacting Internal Solitary Waves (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 507-517 
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    Notes: Abstract The Cauchy problem and global well-posedness for a mathematical model of the strong interaction of two-dimensional, long, internal gravity waves propogating on neighboring pycnoclines in a stratified fluid have been studied by Bona, Ponce, Saut, Tom, and others. We show that global well-posedness occurs even when the initial data is rough.
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    Biorthogonal Smooth Local Trigonometric Bases (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 109-133 
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    Notes: Abstract In this paper we discuss smooth local trigonometric bases. We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases. These allow natural representations of constant and, sometimes, linear components. We study and compare their approximation properties and applicability in data compression. This is illustrated with numerical examples.
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    Multiresolution Analysis and Multivariate Approximation of Smooth Signals in CB(Rd (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 161-180 
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    Notes: Abstract In this paper we derive rates of approximation for a class of linear operators on $C_B({\bf R}^d)$ associated with a multiresolution analysis $\{ V_n\}_{n\in{\bf Z}}.$ We show that for a uniformly bounded sequence of linear operators $\{T_n\}_{n\in{\bf Z}}$ satisfying $T_n f\equiv f$ on the subspace $V_n\cap C_B({\bf R}^d),$ a lower bound for the approximation order is determined by the number of vanishing moments of a prewavelet set. We consider applications to extensions of generalized projection operators as well as to sampling series.
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    Approximation of Distribution Spaces by Means of Kernel Operators (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 261-286 
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    Notes: Abstract We investigate conditions on kernel operators in order to provide prescribed orders of approximation in the Triebel-Lizorkin spaces. Our approach is based on the study of the boundedness of integral kernel operators and extends the Strang-Fix theory, related to the approximation orders of principal shift-invariant spaces, to a wide variety of spaces.
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    A Generalized Sampling Theorem with the Inverse of an Arbitrary Square Summable Sequence as Sampling Points (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 303-314 
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    Notes: Abstract In this article a generalized sampling theorem using an arbitrary sequence of sampling points is derived. The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points tn = an + b if n = 0, 1, 2, ... and tn = an + c if n = 0, -1, -2, ..., where a, b, c are arbitrary constants. The reconstruction formula is derived explicitly in the form of a sampling series expansion. When a = 1, b = 0 = c, the famous Whittaker-Shannon-Kotel'nikov sampling theorem is obtained as a special case.
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    An Uncertainty Principle for Eigenfunction Expansions (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 427-433 
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    Notes: Abstract In this paper, we extend a theorem of Hardy’s on Fourier transform pairs to: (a) a noncompact-type Riemannian symmetric space of rank one, with respect to the eigenfunction expansion of the invariant Laplacian; (b) a compact Riemannian manifold with respect to the eigenfunction expansion of a positive elliptic operator; and (c) Rn with respect to Hermite and Laguerre expansions.
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    Frame Analysis of Irregular Periodic Sampling of Signals and Their Derivatives (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 453-471 
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    Topics: Mathematics
    Notes: Abstract Given a bandlimited signal, we consider the sampling of the signal and some of its derivatives in a periodic manner. The mathematical concept of frames is utilized in the analysis of the properties of the sequence of sampling functions. The frame operator of this sequence is expressed as a matrix-valued function multiplying a vector-valued function. An important property of this matrix is that the maximum and minimum eigenvalues are equal (in some sense) to the upper and lower frame bounds. We present a method for finding the dual frame and, thereby, a method for reconstructing the signal from its samples. Using the matrix approach we prove that the sequence of sampling functions is always complete in the cases of critical sampling and oversampling. A sufficient condition for the sequence of sampling functions to constitute a frame is derived. We show that if no sampling of the signal itself is involved, the sampling is not stable and cannot be stabilized by oversampling. Examples are considered, and the frame bounds in the case of sampling of the signal and its first derivative are calculated explicitly. Finally, the matrix approach can be similarly applied to other problems of signal representation.
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    On Bernstein's Inequality and Kahane's Ultraflat Polynomials (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 519-582 
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    Notes: Abstract The investigation of $ L^q $ norm Bernstein inequalities $(0〈q\leq \infty ), $ for polynomials with unimodular coefficients, leads to unexpected results. Some phenomena here upset our intuition. This paper closely revisits the ultraflat polynomials whose existence was conjectured by Littlewood in 1966 and proved by Kahane in 1980. A major role in this study is also played by arbitrary ultraflat polynomials, that is, including those that are not necessarily obtained by variations or refinements of Kahane's method.
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    Functions with Time and Frequency Gaps (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 611-614 
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    Notes: Abstract We present an explicit, straightforward construction of smooth integrable functions with prescribed gaps around the origin in both time and frequency domain.
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    Perturbation of a circadian rhythm by single and periodic signals and its mathematical simulation (1995)
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    Bulletin of mathematical biology 57 (1995), S. 175-189 
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    Topics: Biology , Mathematics
    Notes: Abstract Adaptive characteristics of circadian rhythm are based on their capacity to be synchronized by external signals, particularly light signals. The effect of both single and periodic light signals on the electroretinogram (ERG) circadian rhythm in crayfish is studied. In a previous work (Lara-Aparicioet al., Bull math. Biol. 55, 97–110, 1993) we developed a mathematical model simulating the emergence of the ERG circadian rhythm during the ontogeny of the crayfish. In the present work we have tested the familiar wave-shift behaviour of an oscillator with a single limit cycle. Two new facts, not present in a simpler model, now appear, which simulate adequately the experimental results, i.e. the presence of a transient stage and the shape of the perturbed wave which changes according to the characteristics of the external light signals.
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    Dynamical behaviour of biological regulatory networks—I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state (1995)
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    Bulletin of mathematical biology 57 (1995), S. 247-276 
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    Notes: Abstract In the field of biological regulation, models dictated by expreimental work are usually complex networks comprising intertwined feedback loops. In this paper the biological roles of individual positive loops (multistationarity, differentiation) and negative loops (homeostasis, with or without oscillations, buffering of gene dosage effect) are discussed. The relationship between feedback loops and steady states is then clarified, and the problem: “How can one conveniently disentangle complex networks?” is then considered. Initiated long ago, logical descriptions have been generalized from various viewpoints; these developments are briefly discussed. The recent concept of the loop-characteristic state, defined as the logical state located at the level of the thresholds involved in the loop, together with its application, are then presented. Biological applications are also discussed.
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    Five surprising properties of parsimoniously colored trees (1995)
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    Bulletin of mathematical biology 57 (1995), S. 367-375 
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    Notes: Abstract Trees with a coloration of their leaves have an induced “length” which forms the basis of the widely used maximum parsimony method for reconstructing evolutionary trees in biology. Here we describe five unexpected properties of this length function, including refinements of earlier results.
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    Dynamical behaviour of biological regulatory networks—II. Immunity control in bacteriophage lambda (1995)
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    Bulletin of mathematical biology 57 (1995), S. 277-297 
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    Notes: Abstract A number of bacterial and viral genes take part in the decision between lysis and lysogenization in temperate bacteriophages. In the lambda case, at least five viral genes (cI, cro, cII, N and cIII) and several bacterial genes are involved. Several attempts have been made to model this complex regulatory network. Our approach is based on a logical method described in the first paper of the series which formalizes the interactions between the elements of a regulatory network in terms of discrete variables, functions and parameters. In this paper two models are described and discussed, the first (two-variable model) focused on cI and cro interactions, the second (four-variable model) considering, in addition, genes cII and N. The treatment presented emphasizes the roles of positive and negative feedback loops and their interactions in the development of the phage. The role of the loops between cI and cro, and of cI on itself (which both have to be positive loops) was discovered earlier; this group's contribution to this aspect mainly deals with the possibility of treating these loops as parts of a more extended network. In contrast, the role of the negative loop of cro on itself had apparently remained unexplained. We realized that this loop buffers the expression of genes cro itself, cII, O and P against the inflation due to the rapid replication of the phage. More generally negative auto-control of a gene appears an efficient way to render its expression insensitive (or less sensitive) to gene dosage, whereas a simple negative control would not provide this result.
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    Phyllotaxis: A systemic study in plant morphogenesis (1995)
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    Bulletin of mathematical biology 57 (1995), S. 377-379 
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    The stabilizing role of cannibalism in a predator-prey system (1995)
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    Bulletin of mathematical biology 57 (1995), S. 401-411 
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    Notes: Abstract Cannibalism can have a stabilizing effect in a predator-prey system. Contrary to the intuitive expectation cannibalism of the predator leads to an increase of the standing stocks of both, prey and predator.
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    A universal bifurcation diagram for seasonally perturbed predator-prey models (1995)
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    Bulletin of mathematical biology 57 (1995), S. 701-712 
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    Notes: Abstract The bifurcations of a periodically forced predator-prey model (the chemostat model), with a prey feeding on a limiting nutrient, are numerically detected with a continuation technique. Eight bifurcation diagrams are produced (one for each parameter in the model) and shown to be topologically equivalent. These diagrams are also equivalent to those of the most commonly used predator-prey model (the Rosenzweig-McArthur model). Thus, all basic modes of behavior of the two main predator-prey models can be explained by means of a single bifurcation diagram.
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    A theoretical explanation of “Concomitant resistance” (1995)
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    Bulletin of mathematical biology 57 (1995), S. 733-747 
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    Notes: Abstract Concomitant resistance is a tumor growth dynamic which results when the growth of a second tumor implant is inhibited by the presence of the first. Recently, we modeled tumor growth in the presence of a regenerating liver after partial hepatectomy (Michelson and Leith,Bull. Math. Biol. 57, 345–366, 1995), with an interlocking pair of growth control triads to account for the accelerated growth observed in both tissues. We also modeled tumor dormancy and recurrence as a dynamic equilibrium achieved between proliferating and quiescent subpopulations. In this paper those studies are extended to initially model the concomitant resistance case. Two interlocking model systems are proposed. In one an interactive competition between the tumor implants is described, while in the other purely proportional growth inhibition is described. The equilibria and dynamics of each system when the coefficients are held constant are presented for three subcases of model parameters. We show that the dynamic called concomitant resistance can be real or apparent, and that if the model coefficients are held constant, the only way to truly achieve concomitant resistance is by forcing one of the tumors into total quiescence. If this is the true state of the inhibited implant, then a non-constant recruitment signal is required to insure regrowth when the inhibitor mass is excised. We compare these theoretical results to a potential explanation of the phenomenon provided by Prehn (Cancer Res. 53, 3266–3269, 1993).
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    The mathematics of radiation target analyses (1995)
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    Bulletin of mathematical biology 57 (1995), S. 883-898 
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    Notes: Abstract Radiation target theory has been extended to complex biochemical systems. Mathematical analyses are presented for multiple forms of biological active proteins, for the presence of large inhibitors or activators, for compounds which regulate rate or affinity and for multipe-step reactions. Several predictions of these models have been verified experimentally.
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    Theoretical models in biology: The origin of life, the immune system, and the brain (1995)
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    Bulletin of mathematical biology 57 (1995), S. 935-937 
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    Chaos in dynamical systems (1995)
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    Bulletin of mathematical biology 57 (1995), S. 943-944 
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    Models for embryonic periodicity (1995)
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    Bulletin of mathematical biology 57 (1995), S. 947-948 
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    Density and diffusion limited aggregation in membranes (1995)
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    Bulletin of mathematical biology 57 (1995), S. 651-677 
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    Notes: Abstract Aggregation of membrane molecules is a crucial phenomenon in developing organisms, a classic example being the aggregation of post-synaptic receptors during synaptogenesis. Our understanding of the molecular events involved is improving, but most models of the aggregation or concentration process do not address binding events on the molecular level. An exception is the study of diffusion limited aggregation, in which the aggregation process is simulated on a molecular level. In this analysis, however, important physical parameters such as molecular size, diffusion constant and initial density are not addressed. Thus no predictions about the rate at which such aggregates will form is possible. In the present work the model of diffusion limited aggregation is extended to incorporate these parameters and make the corresponding predictions.
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    An alternative derivation of Fuxman's threshold result (1995)
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    Bulletin of mathematical biology 57 (1995), S. 783-786 
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    Building a structured model of a complex pharmacokinetic system with time delays (1995)
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    Bulletin of mathematical biology 57 (1995), S. 787-808 
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    Topics: Biology , Mathematics
    Notes: Abstract This paper presents a description of the procedure for building a structured model of a complex pharmacokinetic system on using its transfer function. The example employed is that of the pharmacokinetic system based on gentamicin plasma concentrations after intravenous and intratracheal administration to guinea pigs, describing the pathway of the drug into the systemic circulation after the extravascular injection mentioned. The structured model selected consisted of a submodel of a proportional linear subsystem, two submodels of simple linear dynamic subsystems with time constants of 0.135±0.065 hr (95% I.C.) and 0.052±0.288 hr, submodels of parallel subsystems with time delays of 0.254±0.046 hr and 1.135±0.288 hr, connected in serial. Two estimates of the mean residence time of the total amount of gentamicin in the system, i.e. 0.347 and 0.335 hr, were obtained, based on the system frequency and structured model, respectively. From the methodological point of view, our paper demonstrates the efficiency of combination of modelling in the frequency and in the time domain, designed to facilitate studies of pharmacokinetic systems.
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    Deduction of pulmonary microvascular hematocrit from indicator dilution curves (1995)
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    Bulletin of mathematical biology 57 (1995), S. 931-933 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    Dynamics and bifurcations of two coupled neural oscillators with different connection types (1995)
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    Bulletin of mathematical biology 57 (1995), S. 809-840 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.
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    Life in moving fluids: The physical biology of Flow (1995)
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    Bulletin of mathematical biology 57 (1995), S. 949-951 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
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    Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree (1995)
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    The journal of Fourier analysis and applications 2 (1995), S. 597-610 
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    ISSN: 1531-5851
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    Topics: Mathematics
    Notes: Abstract For any fixed $\varepsilon 〉 0$ we construct an orthonormal Schauder basis $\{p_\mu\}_{\mu=0}^{\infty}$ for C[-1,1] consisting of algebraic polynomials $p_\mu$ with $\deg p_\mu \le (1+\varepsilon) \mu .$ The orthogonality is with respect to the Chebyshev weight.
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    A numerical approach to optimization problems with variational inequality constraints (1995)
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    Mathematical programming 68 (1995), S. 105-130 
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    ISSN: 1436-4646
    Keywords: primary 49B34 ; secondary 90C31 ; 93C30 ; Variational inequalities ; Sensitivity analysis ; Generalized Jacobian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Optimization problems with variational inequality constraints are converted to constrained minimization of a local Lipschitz function. To this minimization a non-differentiable optimization method is used; the required subgradients of the objective are computed by means of a special adjoint equation. Besides tests with some academic examples, the approach is applied to the computation of the Stackelberg—Cournot—Nash equilibria and to the numerical solution of a class of quasi-variational inequalities.
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    A cutting plane algorithm for convex programming that uses analytic centers (1995)
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    Mathematical programming 69 (1995), S. 1-43 
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    ISSN: 1436-4646
    Keywords: Mathematical programming ; Cutting planes ; Analytic center
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    Notes: Abstract Anoracle for a convex setS ⊂ ℝ n accepts as input any pointz in ℝ n , and ifz ∈S, then it returns ‘yes’, while ifz ∉S, then it returns ‘no’ along with a separating hyperplane. We give a new algorithm that finds a feasible point inS in cases where an oracle is available. Our algorithm uses the analytic center of a polytope as test point, and successively modifies the polytope with the separating hyperplanes returned by the oracle. The key to establishing convergence is that hyperplanes judged to be ‘unimportant’ are pruned from the polytope. If a ball of radius 2−L is contained inS, andS is contained in a cube of side 2 L+1, then we can show our algorithm converges after O(nL 2) iterations and performs a total of O(n 4 L 3+TnL 2) arithmetic operations, whereT is the number of arithmetic operations required for a call to the oracle. The bound is independent of the number of hyperplanes generated in the algorithm. An important application in which an oracle is available is minimizing a convex function overS.
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    A cutting plane method from analytic centers for stochastic programming (1995)
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    Mathematical programming 69 (1995), S. 45-73 
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    ISSN: 1436-4646
    Keywords: Cutting plane ; Stochastic programming ; Analytic center ; Interior-point method
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    Topics: Computer Science , Mathematics
    Notes: Abstract The stochastic linear programming problem with recourse has a dual block-angular structure. It can thus be handled by Benders' decomposition or by Kelley's method of cutting planes; equivalently the dual problem has a primal block-angular structure and can be handled by Dantzig-Wolfe decomposition—the two approaches are in fact identical by duality. Here we shall investigate the use of the method of cutting planes from analytic centers applied to similar formulations. The only significant difference form the aforementioned methods is that new cutting planes (or columns, by duality) will be generated not from the optimum of the linear programming relaxation, but from the analytic center of the set of localization.
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    A continuation method for monotone variational inequalities (1995)
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    Mathematical programming 69 (1995), S. 237-253 
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    ISSN: 1436-4646
    Keywords: Variational inequality ; Nonlinear complementarity ; Nonlinear programming ; Continuation method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a continuation method for monotone variational inequality problems based on a new smooth equation formulation. The existence, uniqueness and limiting behavior of the path generated by the method are analyzed.
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    About strongly polynomial time algorithms for quadratic optimization over submodular constraints (1995)
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    Mathematical programming 69 (1995), S. 269-309 
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    ISSN: 1436-4646
    Keywords: Quadratic programming ; Submodular constraints ; Kuhn-Tucker conditions ; Lexicographically optimal flow ; Parametric maximum flow
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    Notes: Abstract We present new strongly polynomial algorithms for special cases of convex separable quadratic minimization over submodular constraints. The main results are: an O(NM log(N 2/M)) algorithm for the problemNetwork defined on a network onM arcs andN nodes; an O(n logn) algorithm for thetree problem onn variables; an O(n logn) algorithm for theNested problem, and a linear time algorithm for theGeneralized Upper Bound problem. These algorithms are the best known so far for these problems. The status of the general problem and open questions are presented as well.
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    Worst-case comparison of valid inequalities for the TSP (1995)
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    Mathematical programming 69 (1995), S. 335-349 
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    Keywords: Polyhedral combinatorics ; Valid inequalities ; Travelling salesman ; Worst-case analysis
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    Notes: Abstract We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst-case improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor greater than 10/9. The corresponding factor for the class of clique tree inequalities is 8/7, while it is 4/3 for the path configuration inequalities.
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    Solution of and bounding in a linearly constrained optimization problem with convex, polyhedral objective function (1995)
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    Mathematical programming 70 (1995), S. 1-16 
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    ISSN: 1436-4646
    Keywords: Stochastic programming ; Polyhedral functions ; Simplicial functions
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    Topics: Computer Science , Mathematics
    Notes: Abstract A dual method is presented to solve a linearly constrained optimization problem with convex, polyhedral objective function, along with a fast bounding technique, for the optimum value. The method can be used to solve problems, obtained from LPs, where some of the constraints are not required to be exactly satisfied but are penalized by piecewise linear functions, which are added to the objective function of the original problem. The method generalizes an earlier solution technique developed by Prékopa (1990). Applications to stochastic programming are also presented.
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    The curvature integral and the complexity of linear complementarity problems (1995)
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    Mathematical programming 70 (1995), S. 107-122 
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    ISSN: 1436-4646
    Keywords: Linear complementarity problem ; Predictor—corrector algorithm ; Complexity analysis ; Central trajectory ; Curvature integral ; Interior-point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we propose a predictor—corrector-type algorithm for solving the linear complementarity problem (LCP), and prove that the actual number of iterations needed by the algorithm is bounded from above and from below by a curvature integral along the central trajectory of the problem. This curvature integral is not greater than, and possibly smaller than, the best upper bound obtained in the literature to date.
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    Directional derivatives of the solution of a parametric nonlinear program (1995)
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    Mathematical programming 70 (1995), S. 159-172 
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    ISSN: 1436-4646
    Keywords: Parametric nonlinear programming ; Directional differentiability ; B-derivative ; Piecewise smooth function ; Nonunique multipliers ; Degeneracy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a parametric nonlinear optimization problem subject to equality and inequality constraints. Conditions under which a locally optimal solution exists and depends in a continuous way on the parameter are well known. We show, under the additional assumption of constant rank of the active constraint gradients, that the optimal solution is actually piecewise smooth, hence B-differentiable. We show, for the first time to our knowledge, a practical application of quadratic programming to calculate the directional derivative in the case when the optimal multipliers are not unique.
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    On the equivalence of nonlinear complementarity problems and least-element problems (1995)
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    Mathematical programming 70 (1995), S. 191-200 
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    Keywords: Strictly pseudomonotone map ; Z-map ; Complementarity problem ; Least element problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Strictly pseudomonotoneZ-maps operating on Banach lattices are considered. Equivalence of complementarity problems and least-element problems is established under certain regularity and growth conditions. This extends a recent result by Riddell (1981) for strictly monotoneZ-maps to the pseudomonotone case. Some other problems equivalent to the above are discussed as well.
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    Primal—dual methods for linear programming (1995)
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    Mathematical programming 70 (1995), S. 251-277 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Barrier methods ; Interior-point methods
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    Topics: Computer Science , Mathematics
    Notes: Abstract Many interior-point methods for linear programming are based on the properties of the logarithmic barrier function. After a preliminary discussion of the convergence of the (primal) projected Newton barrier method, three types of barrier method are analyzed. These methods may be categorized as primal, dual and primal—dual, and may be derived from the application of Newton's method to different variants of the same system of nonlinear equations. A fourth variant of the same equations leads to a new primal—dual method. In each of the methods discussed, convergence is demonstrated without the need for a nondegeneracy assumption or a transformation that makes the provision of a feasible point trivial. In particular, convergence is established for a primal—dual algorithm that allows a different step in the primal and dual variables and does not require primal and dual feasibility. Finally, a new method for treating free variables is proposed.
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    The fleet assignment problem: Solving a large-scale integer program (1995)
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    Mathematical programming 70 (1995), S. 211-232 
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    ISSN: 1436-4646
    Keywords: Linear programming ; Mixed-integer programming ; Large-scale optimization ; Airline fleet assignment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a flight schedule and set of aircraft, the fleet assignment problem is to determine which type of aircraft should fly each flight segment. This paper describes a basic daily, domestic fleet assignment problem and then presents chronologically the steps taken to solve it efficiently. Our model of the fleet assignment problem is a large multi-commodity flow problem with side constraints defined on a time-expanded network. These problems are often severely degenerate, which leads to poor performance of standard linear programming techniques. Also, the large number of integer variables can make finding optimal integer solutions difficult and time-consuming. The methods used to attack this problem include an interior-point algorithm, dual steepest edge simplex, cost perturbation, model aggregation, branching on set-partitioning constraints and prioritizing the order of branching. The computational results show that the algorithm finds solutions with a maximum optimality gap of 0.02% and is more than two orders of magnitude faster than using default options of a standard LP-based branch-and-bound code.
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    An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities (1995)
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    Mathematical programming 71 (1995), S. 77-100 
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    ISSN: 1436-4646
    Keywords: Convex linearly constrained problems ; Variational inequalities ; Interior methods ; Entropy-like proximal method ; Maximal monotone operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, an entropy-like proximal method for the minimization of a convex function subject to positivity constraints is extended to an interior algorithm in two directions. First, to general linearly constrained convex minimization problems and second, to variational inequalities on polyhedra. For linear programming, numerical results are presented and quadratic convergence is established.
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    One-third-integrality in the max-cut problem (1995)
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    Mathematical programming 71 (1995), S. 29-50 
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    ISSN: 1436-4646
    Keywords: Max-cut ; Cut polytope ; Metric polytope ; Linear relaxation ; One-third-integrality ; Box one-third-integrality ; Forbidden minor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a graphG = (V, E), the metric polytopeS (G) is defined by the inequalitiesx(F) − x(C∖F) ⩽ |F| − 1 for $$F \subseteq C$$ , |F| odd,C cycle ofG, and 0 ⩽x e ⩽ 1 fore ∈ E. Optimization overS (G) provides an approximation for the max-cut problem. The graphG is called 1/d-integral if all the vertices ofS(G) have their coordinates in{i/d ∣ 0 ⩽ i ⩽ d}. We prove that the class of 1/d-integral graphs is closed under minors, and we present several minimal forbidden minors for 1/3-integrality. In particular, we characterize the 1/3-integral graphs on seven nodes. We study several operations preserving 1/d-integrality, in particular, thek-sum operation for 0 ⩽k ⩽ 3. We prove that series parallel graphs are characterized by the following stronger property. All vertices of the polytopeS (G) ∩ {x ∣ ℓ ⩽ x ⩽ u} are 1/3-integral for every choice of 1/3-integral boundsℓ, u on the edges ofG.
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    On minquantile and maxcovering optimisation (1995)
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    Mathematical programming 71 (1995), S. 101-112 
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    ISSN: 1436-4646
    Keywords: Minmax ; Maximal covering problems ; Multi criteria decision-making
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we introduce the parametric minquantile problem, a weighted generalisation ofkth maximum minimisation. It is shown that, under suitable quasiconvexity assumptions, its resolution can be reduced to solving a polynomial number of minmax problems. It is also shown how this simultaneously solves (parametric) maximal covering problems. It follows that bicriteria problems, where the aim is to both maximize the covering and minimize the cover-level, are reducible to a discrete problem, on which any multiple criteria method may be applied.
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    The Fermat—Weber location problem revisited (1995)
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    Mathematical programming 71 (1995), S. 71-76 
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    ISSN: 1436-4646
    Keywords: Location theory ; Fermat—Weber problem ; Weiszfeld's iterative algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Fermat—Weber location problem requires finding a point in ℝ N that minimizes the sum of weighted Euclidean distances tom given points. A one-point iterative method was first introduced by Weiszfeld in 1937 to solve this problem. Since then several research articles have been published on the method and generalizations thereof. Global convergence of Weiszfeld's algorithm was proven in a seminal paper by Kuhn in 1973. However, since them given points are singular points of the iteration functions, convergence is conditional on none of the iterates coinciding with one of the given points. In addressing this problem, Kuhn concluded that whenever them given points are not collinear, Weiszfeld's algorithm will converge to the unique optimal solution except for a denumerable set of starting points. As late as 1989, Chandrasekaran and Tamir demonstrated with counter-examples that convergence may not occur for continuous sets of starting points when the given points are contained in an affine subspace of ℝ N . We resolve this open question by proving that Weiszfeld's algorithm converges to the unique optimal solution for all but a denumerable set of starting points if, and only if, the convex hull of the given points is of dimensionN.
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    An efficient cost scaling algorithm for the assignment problem (1995)
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    Mathematical programming 71 (1995), S. 153-177 
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    ISSN: 1436-4646
    Keywords: Network optimization ; Assignment problem ; Algorithms ; Experimental evaluation ; Cost scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The cost scaling push-relabel method has been shown to be efficient for solving minimum-cost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.
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    Superfluous matrices in linear complementarity (1995)
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    Mathematical programming 71 (1995), S. 195-206 
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    ISSN: 1436-4646
    Keywords: Superfluous matrix ; Linear complementarity problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Superfluous matrices were introduced by Howe (1983) in linear complementarity. In general, producing examples of this class is tedious (a few examples can be found in Chapter 6 of Cottle, Pang and Stone (1992)). To overcome this problem, we define a new class of matrices $$\bar Z$$ and establish that in $$\bar Z$$ superfluous matrices of any ordern ⩾ 4 can easily be constructed. For every integerk, an example of a superfluous matrix of degreek is exhibited in the end.
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    Balanced 0, ±1-matrices, bicoloring and total dual integrality (1995)
    Springer
    Mathematical programming 71 (1995), S. 249-258 
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    ISSN: 1436-4646
    Keywords: Combinatorial optimization ; Integrality of polyhedra ; Generalized set packing ; Covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A 0, ±1-matrixA is balanced if, in every submatrix with two nonzero entries per row and column, the sum of the entries is a multiple of four. This definition was introduced by Truemper (1978) and generalizes the notion of a balanced 0, 1-matrix introduced by Berge (1970). In this paper, we extend a bicoloring theorem of Berge (1970) and total dual integrality results of Fulkerson, Hoffman and Oppenheim (1974) to balanced 0, ±1-matrices.
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