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  • Springer  (70,803)
  • Oxford University Press  (5,963)
  • American Association for the Advancement of Science (AAAS)  (2,477)
  • 1995-1999  (79,243)
  • 1995  (79,243)
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  • 1995-1999  (79,243)
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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
    Electronic Resource
    Electronic Resource
    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
    Electronic Resource
    Electronic Resource
    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 
    Details
    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
    Electronic Resource
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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
    Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458317
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  • 6
    Electronic Resource
    Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458320
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  • 8
    Electronic Resource
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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.
    Type of Medium: Electronic Resource
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460615
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  • 11
    Electronic Resource
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460617
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  • 12
    Electronic Resource
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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.
    Type of Medium: Electronic Resource
    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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    A simple method for solving the LQG stochastic control problem using a polynomial approach (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 57-67 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The paper presents a simple method for solving the optimal (LQG) control problem on an infinite time horizon for linear plants described by proper rational transfer function matrices. Since the class of proper plants discussed in the paper is more general than the one commonly used, additional properties of solutions are presented. Two numerical examples illustrate the theoretical considerations. The examples have been performed on an IBM PC using the proposed algorithm. This algorithm is a part of a public ASMCS package developed by the author for analysis, synthesis, and simulations of multi-input, multi-output (MIMO) control systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183748
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  • 17
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    Behavior of Hilbert networks under perturbations of their elements (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 135-143 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We study the behavior of a Hilbert network (i.e., a finite or countably infinite network whose variables are in a Hilbert space and in which the associated total energy is finite) whose elements are affected by perturbations. More specifically, we will give estimates for a change of the current distribution caused by (a) perturbations of the elements of the nominal network when the voltage sources are fixed, and (b) a change of voltage sources in a network whose elements are perturbed. The conditions given in our theorems imply insensitivity and robust stability of the nominal network. The applications of the results are illustrated by an example of an infinite network.
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    URL: http://dx.doi.org/10.1007/BF01183831
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  • 18
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    Further improved 2-D lattice filter structure employing missing reflection coefficients (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 473-494 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new lattice filter structure to model two-dimensional (2-D) autoregressive (AR) fields is proposed. The proposed structure utilizes and extracts the information contained in the backward prediction error fields and their delayed versions. The main idea is to use two sets of reflection coefficients corresponding to two quadrant filters and to increase the number of reflection coefficients with the order of the lattice filter. Increasing the number of reflection coefficients at each stage produces a sufficient number of independent parameters to model AR fields up to order three, which is an improvement over the existing 2-D lattice filter structures. The improvement is confirmed by computer simulations. In addition, a relationship between the reflection coefficients and the AR coefficients is derived. It is also shown that the entropy contained in the backward prediction error field vector of the proposed structure is closer to the input entropy when compared to those contained in existing 2-D lattice filters.
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    URL: http://dx.doi.org/10.1007/BF01260333
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  • 19
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    A set of necessary stability conditions form-D nonlinear digital filters (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 555-561 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper addresses the problem of global asymptotic stability in recursive first hyperquadrant causalm-D digital filters. A set of simple-to-check 1-D conditions necessary for stability of them-D system is given. Generalizations tov-dimensional (v〈m) subsystems are also provided. These derived conditions are useful in determining asymptotic convergence ofm-D digital filters implemented in fixed or floating point arithmetic. The set of 1-D conditions can be considered the analogous result to practical bounded input bounded output (BIBO) stability for linearm-D systems.
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    URL: http://dx.doi.org/10.1007/BF01260337
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  • 20
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    Maximally linear FIR digital differentiators (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 633-637 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new efficient algorithm for calculating the weighting coefficients of maximally linear, FIR digital differentiators is presented. Simple closed-form explicit and recursive formulas are derived in a very straightforward manner. Moreover, a simple recursive equation is established, relating coefficients of two digital differentiators of adjacent ranks.
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    URL: http://dx.doi.org/10.1007/BF01213959
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  • 21
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    Generating a PRSA with triangular symmetry (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 661-667 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a sequence of pseudorandom arrays with triangular symmetry. The sequence of arrays is also pseudorandom in nature, so it can be called a pseudorandom sequence of arrays, or PRSA. A circuit for the PRSA generator is given and some interesting properties of this type of PRSA are discussed. Also, some of the concepts presented in this paper are clarified with an example.
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    URL: http://dx.doi.org/10.1007/BF01213962
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  • 22
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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.
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    URL: http://dx.doi.org/10.1007/s00041-001-4021-8
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  • 23
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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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  • 24
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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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  • 25
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    Deterministic and statistical properties of two-dimensional FIR-median hybrid filters (1995)
    Springer
    Circuits, systems and signal processing 14 (1995), S. 1-16 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we present a new class of two-dimensional FIR-median hybrid (FMH) filters, which we call separable FMH filters, for image noise smoothing. In a separable FMH filter, a one-dimensional FMH filter is applied to the rows and the columns of an image successively. The deterministic properties of separable and cross window FMH filters are discussed. Under certain assumptions, it is proved that a root of a separable FMH filter is a root of the corresponding cross window FMH filter. The noise attenuating properties of a separable FMH filter are studied and compared with those of the separable median filter, the two-dimensional median filter with a square window, and the cross window FMH filter.
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    URL: http://dx.doi.org/10.1007/BF01183745
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    The AICE-CRT and digital signal processing algorithms: The complex case (1995)
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    Circuits, systems and signal processing 14 (1995), S. 69-85 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The Chinese remainder theorem is a fundamental technique widely employed in digital signal processing for designing fast algorithms for computing convolutions. Classically, it has two versions. One is over a ring of integers and the second is over a ring of polynomials with coefficients defined over a field. In our previous papers, we developed an extension to this well-known theorem for the case of a ring of polynomials with coefficients defined over a finite ring of integers. The objective was to generalize number-theoretictransforms, which turn out to be a special case of this extension. This paper focuses on the extension of the Chinese remainder theorem for processing complex-valued integer sequences. Once again, the present work generalizes the complex-number-theoretic transforms. The impetus for this work is provided by the occurrence of complex integer sequences in digital signal processing and the desire to process them using exact arithmetic.
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    URL: http://dx.doi.org/10.1007/BF01183749
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    Design considerations and stability of a digital filter with finite wordlength (1995)
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    Circuits, systems and signal processing 14 (1995), S. 145-166 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A method to improve the stability of the forced response of a recursive digital filter with nonlinearities due to finite wordlength is presented. An analysis of applying a stability criterion on the nonlinear filter is performed by transforming the problem into a mathematical problem of finding a zero set. As a result of the mathematical analysis, one can find a maximal sector size that bounds an equivalent nonlinearity, so that stability is ensured. This sector size is influenced by the choice of the desired nonlinearity characteristic appropriate to the problem, and the amount of the input scaling needed. Another improvement of the filter's stability is obtained by adding a feedback gain, the value of which is determined by using the zero set-finding method. Simulation results showing the improved stability properties of a filter designed by this method are presented.
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    URL: http://dx.doi.org/10.1007/BF01183832
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    Pipelining the unconstrained three-port wave filter adaptor at the bit level (1995)
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    Circuits, systems and signal processing 14 (1995), S. 285-298 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper a fully systolic, bit level, three-port unconstrained adaptor, which constitutes the main nontrivial building block of ladder wave digital filters, is generated. The one-dimensional binary convolution is used as the underlying algorithm for the implementation of a multiplication. The Isb-first input data organization approach is adopted and thecanonical mapping methodology is used to fully systolize the unconstrained parallel three-port adaptor at the bit level with piplining period a=1. The technique is based on a transformation of the adaptor's signal-flow graph, so that unidirectional data flow takes place. A ring-systolic scheme is proposed for implementing communications among adaptors.
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    URL: http://dx.doi.org/10.1007/BF01189014
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    Stochastic adaptive control of nonminimum phase systems in the presence of unmodelled dynamics (1995)
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    Circuits, systems and signal processing 14 (1995), S. 317-349 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider the problem of robust stochastic adaptive control of not necessarily minimum phase systems in the presence of unmodelled dynamics. Stochastic gradient algorithms with parameter projection and modified gain sequence are used for the estimation of the unknown controller parameters. Global stability of the adaptive system is achieved without requiring the strictly positive real condition and the persistency exciting condition to be satisfied.
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    URL: http://dx.doi.org/10.1007/BF01189016
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    On the local qualitative behavior of differential-algebraic equations (1995)
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    Circuits, systems and signal processing 14 (1995), S. 427-443 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A theoretical framework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equilibrium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a given equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that these theorems are stated in terms of the given problem and not in terms of the corresponding vector field.
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    The prime and generalized nullspaces of right regular pencils (1995)
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    Circuits, systems and signal processing 14 (1995), S. 495-524 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The classical notion of the λ-generalized nullspace, defined on a matrixA εR n×n,where λ is an eigenvalue, is extended to the case of ordered pairs of matrices(F, G), F, G ε R m×nwhere the associated pencilsF − G is right regular. It is shown that for every α εC ∪ {∞} generalized eigenvalue of (F, G), an ascending nested sequence of spaces {P α i ,i=1, 2,...} and a descending nested sequence of spaces {ie495-02 i=1, 2,...} are defined from the α-Toeplitz matrices of (F, G); the first sequence has a maximal elementM α * , the α-generalized nullspace of (F, G), which is the element of the sequence corresponding to the index τα, the α-index of annihilation of (F, G), whereas the second sequence has the first elementP α * as its maximal element, the α-prime space of (F, G). The geometric properties of the {M α i ,i=1, 2,...,τα and {P α i ,i=1, 2,...sets, as well as their interrelations are investigated and are shown to be intimately related to the existence of nested basis matrices of the nullspaces of the α-Toeplitz matrices of (F, G). These nested basis matrices characterize completely the geometry ofM α * and provide a systematic procedure for the selection of maximal length linearly independent vector chains characterizing theα-Segre characteristic of (F, G).
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    URL: http://dx.doi.org/10.1007/BF01260334
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    On the robustness of stability for uncertain large-scale systems subjected to multiple time delays (1995)
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    Circuits, systems and signal processing 14 (1995), S. 563-586 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.
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    URL: http://dx.doi.org/10.1007/BF01213955
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    A new approach to speech segmentation based on the maximum likelihood (1995)
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    Circuits, systems and signal processing 14 (1995), S. 615-632 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Successful speech recognition is highly dependent on appropriate speech segmentation. The poor efficiency of the sequential detection of abrupt changes in the signals with relatively short stationary intervals, as is the case with speech signals, can be improved by the off-line maximum likelihood segmentation algorithm. In this paper the new segmentation algorithm is presented. For the a priori known number of segments, the algorithm determines such signal partitions for which the sum of segment distortion is minimal. The generalized maximum likelihood distortion measure has been introduced, and has proven to be particularly efficient on short signal segments. In the case of an unknown number of segments, its estimate is obtained comparing the reduction of the distortion. The asymptotic properties of the distortion sequence have been analyzed, which led to the definition of the presented segmentation algorithm. The introduced measure can be applied both to the AR and ARMA models. The segmentation algorithm is verified on test signals as well as on the natural speech signal, for which the pitch synchronous framing scheme is applied. The experimental results also include a comparison of the AR and ARMA model-based segmentations. The first results show that ARMA model-based segmentation gives somewhat better results than the AR model algorithm.
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    URL: http://dx.doi.org/10.1007/BF01213958
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    An efficient bit-serial FIR filter architecture (1995)
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    Circuits, systems and signal processing 14 (1995), S. 639-651 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new bit-serial architecture for implementation of high order FIR filters is introduced, as well as example FPGA and CMOS realizations. This structure exploits the simplicity of coefficients that consist of two power-of-two terms to yield efficient implementations. Quantization effects are discussed and a simple block scaling method for reducing rounding and truncation noise in high order filters is also presented.
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    Implementation of matrix decomposition structures of 2-D digital filters via VLSI array processors (1995)
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    Circuits, systems and signal processing 14 (1995), S. 39-55 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper describes an implementation of 2-D FIR and IIR linear digital filters via VLSI array processors. The underlying realization structures are based on the matrix decomposition approach. The 2-D concurrent processing is used in order to implement the row and column delays within the cycle time. A high degree of concurrency is achieved by exploiting the pipelining of the array processors with the inherent parallelism of the matrix decomposition structure. The resulting structures are modular, and regular, use only local communication and internal local feedback loops, and achieve high throughput and sampling rates.
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    Equilibrium Equivalence Theorem and its applications to control and stability analysis (1995)
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    Circuits, systems and signal processing 14 (1995), S. 111-134 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This article studies dynamical systems under perturbations. We prove an Equilibrium Equivalence Theorem that guarantees that the dynamics of the system remains unchanged under perturbations with certain fairly general assumptions. We also prove that a power system is robust with respect to parameter changes in generic situations. Concepts of equilibrium equivalence and equilibrium equivalence structural stability are developed and are applied to studies of bifurcations of vector fields on noncompact manifolds. A constructive approach to equilibrium equivalence structural stability verification is emphasized. General results on structural stability of vector fields on differential manifolds are established and important applications of this theory to stability analysis are considered.
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    On the design of feedback controllers to achieve prescribed initial value constraints (1995)
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    Circuits, systems and signal processing 14 (1995), S. 167-185 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The problem of designing a stabilizing compensator for a control system to achieve prescribed initial value constraintsυ (i)(0+)=yi is considered. Indeed, modulo certain technical conditions, such a compensator exists if and only if yi=0;i= 0,1,...,r〈p〉 +r〈t〉 −2; wherer〈p〉 is the relative degree of the plant andr〈t〉 is the relative degree of the system input. This theorem is derived and a complete parameterization of the set of compensators that achieve the prescribed design constraints is formulated.
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    AR models for wideband source location (1995)
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    Circuits, systems and signal processing 14 (1995), S. 255-278 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Wideband source location in array signal processing has received much attention in the literature lately. Methods such as the Coherent Signal Subspace (CSS) method proposed by Wang and Kaveh [12], and the signal subspace method used by Cadzow [3], are typical of the approaches used to tackle the multiple wideband source location problem. Most of these methods are variations of the narrowband high-resolution methods. Grenier [5], on the other hand, has applied the idea of time-dependent Auto-Regressive (AR) modeling [7] for a nonstationary process to the frequency domain AR modeling of the sensor outputs in a linear array and has been able to produce good results for a wideband signal. The AR coefficients in the model are expanded in a set of frequency-dependent basis functions. The choice of the basis functions was deemed immaterial and the method works even when only one snapshot of the array output is available. In this paper, we re-examine this method and present an extension of the frequency-dependent AR modeling approach to a planar array. It is shown that the use of a set of sinc functions for representing the frequency-dependent AR coefficients accurately tracks their evolution in the frequency domain, and gives superior performance compared to that when power or Legendre functions are used. We also propose two methods for smoothing the spatial spectra, from which the source locations are determined. Comparison with the CSS method are also presented.
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    Decentralized array processing using the MODE algorithm (1995)
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    Circuits, systems and signal processing 14 (1995), S. 17-38 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Centralized methods for source location using sensor arrays have computational and communication burdens that increase significantly with the number of sensors in the array. Therefore, these methods may not be usable in the applications involving very large arrays. In such applications, the data processing may need to be decentralized. This paper introduces two methods for decentralized array processing, based on the recently proposed MODE algorithm. For prescribed nonoverlapping subarrays, both methods are shown to be statistically optimal in the sense that asymptotically they provide the most accurate decentralized estimates of source location parameters. The problem of subarray selection to further optimize the estimation accuracy is only briefly addressed. The two methods are intended for different types of applications: the first should be preferred when there exist significant possibilities for local processing or for parallel computation in the central processor; otherwise the second method should be preferred. The accuracy of the two decentralized methods is compared to the centralized Cramér-Rao bound, both analytically and numerically, in order to provide indications about the loss of accuracy associated with decentralized processing.
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    Recursive-in-order least-squares parameter estimation algorithm for 2-D noncausal Gaussian Markov random field model (1995)
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    Circuits, systems and signal processing 14 (1995), S. 87-110 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We present in this paper a recursive-in-order least-squares (LS) algorithm to compute efficiently the parameters of a 2-D Gaussian Markov random field (GMRF) model. The algorithm is based on the fact that the least-squares estimation of the parameters of a 2-D noncausal GMRF model is consistent and the coefficient matrix in the normal equation has near-to-block-Toeplitz structure. Hence, it has a Levinson-like form for the updating of model parameters by introducing auxiliary variables. Moreover, this paper proposes the concept ofrecursive path for 2-D recursive-in-order algorithms, and points out that there exists a tradeoff between fast computation of the parameters and accurate choice of model support; a compromise recursive path is then suggested where the orders change alternately in two directions. The computational complexity of the developed algorithm is analyzed, and the results show that the algorithm is more efficient when either the image size or the model support is larger. It is found that the total number of multiplications (mps) involved in the new algorithm is only about 14% of that in the conventional LS method when the image size is 512 × 512 and the neighbor set of the model is a 17 × 17 window. Computer simulation results using the recursive-in-order algorithm developed in this paper and the conventional LS method are given to verify the correctness of the new algorithm.
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    New Time-Frequency Distribution (1995)
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    Circuits, systems and signal processing 14 (1995), S. 539-553 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Cross terms are an inherent consequence of the second order nature of Cohen's class TFDs (Time-Frequency Distributions) [5], [6]. They are manifest in a TFD of multicomponent signals as spurious artifacts arising from interactions between the various signal components, and they can often appear at times and/or frequencies inconsistent with the underlying physical nature of the signal, causing misinterpretation [2], [3], [4]. There are many time frequency distributions that avoid the cross term effect; the best are the Choi-Williams ED (Exponential Distribution) [1] and Levin's IPS (Instantaneous Power Spectrum) [9]. In this paper we combine the cross term reducing philosophy of the ED and IPS to obtain a new TFD that most effectively reduces the cross term effect. Surprisingly, the new TFD also satisfies most desired TFD properties.
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    Neuronal growth via hybrid system of self-growing and diffusion based grammar rules: I (1995)
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    Bulletin of mathematical biology 57 (1995), S. 205-227 
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    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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    Interlocking triads of growth control in tumors (1995)
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    Bulletin of mathematical biology 57 (1995), S. 345-366 
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    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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    Optimal population stabilization and control using the Leslie matrix model (1995)
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    Bulletin of mathematical biology 57 (1995), S. 381-399 
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    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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    A data assimilation technique applied to a predator-prey model (1995)
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    Bulletin of mathematical biology 57 (1995), S. 593-617 
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    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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    Building activity and longevity of queenless groups of the Oriental hornet,Vespa orientalis (1995)
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    Bulletin of mathematical biology 57 (1995), S. 441-460 
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    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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    Topics: Biology , Mathematics
    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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    Topics: Biology , Mathematics
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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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    Topics: Mathematics
    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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    Topics: Mathematics
    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 concentrated stochastic likelihood function in array signal processing (1995)
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    Circuits, systems and signal processing 14 (1995), S. 669-674 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The stochastic likelihood function [(STO)LF] associated with the narrowband signal processing problem can be concentrated with respect to the signal covariance matrix elements and the noise power. Although this is a known fact, no clear-cut derivation of the concentrated (STO)LF appears to be available in the literature. In this short paper we provide a simple, complete proof of the concentrated (STO)LF formula.
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    A study of bounds on limit cycles in digital filters (1995)
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    Circuits, systems and signal processing 14 (1995), S. 725-734 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We give bounds on the self-sustained limit cycles in fixed-poin implementations of state-variable-form digital filters having general stable system matrices. These bounds, which are period independent and which concern limit cycles due to quantization errors in physical realizations of digital filters, are given in closed form for second-order sections. A numerical comparison shows that the bounds are smaller than corresponding ones reported in the literature. This is due to our use of real similarity transformations.
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    Reachability of Polynomial Matrix Descriptions (PMDs) (1995)
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    Circuits, systems and signal processing 14 (1995), S. 787-815 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We consider the concept reachability for Polynomial Matrix Descriptions (PMDs); i.e., systems of the form ∑: A(ρ)β(t)=B(ρ)u(t),y(t)=C(ρ)β(t), whereρ:=d/dt the differential operator,A(ρ)=A0+A1 ρ+...+ Av ρ v εR r×r[ρ], AiεR r×r,i=0, 1,..., ν ≥ 1 with rank R A v ≤r B(ρ) =B 0+B 1ρ+...+B σρσ εR r×m[ρ], Bi εR r×m,i=0,1,...,σ ≥ 0 C(ρ)=C0+C1 ρ+...+Cσ1 ρ σ1 εR m1×r[ρ],C i εR m1×r ,i=0, 1,..., σ1 ≥ 0, β(t): (0−, ∞) →R r is the pseudostate of (∑),u(t): [0, ∞) →R m is the control input to (∑), and y(t) is the output of the system (∑). Starting from the fact that generalized state space systems, i.e., systems of the form ∑1: Ex(t)=Ax(t)+ Bu(t), y(t)=Cx(t), whereE εR r×r, rank R E 〈r, A εR r×r,B εR r×m,C εR m1×r represent a particular case of PMDs, we generalize various known results regarding the smooth and impulsive solutions of the homogeneous and the nonhomogeneous system (∑1) to the more general case of PMDs (∑). Relying on the above generalizations we develop a theory regarding the reachability of PMDs using time-domain analysis, which takes into account finite and infinite zeros of the matrix A(s)=L.[A(ρ)]. The present analysis extends in a general way many results previously known only for regular and generalized state space systems.
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    Model conversions of uncertain linear systems using a scaling and squaring geometric series method (1995)
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    Circuits, systems and signal processing 14 (1995), S. 445-463 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper proposes a scaling and squaring geometric series method along with the inverse-geometric series method for finding discrete-time (continuous-time) structured uncertain linear models from continuous-time (discrete-time) structured uncertain linear systems. The above methods allow the use of well-developed theorems and algorithms in the discrete-time (continuous-time) domain to indirectly solve the continuous-time (discretetime) domain problems. Moreover, these methods enhance the flexibility in modeling and control of a hybrid composite system. It has been shown that the commonly used bilinear approximation model is a specific class of the proposed geometric series model.
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    Impulse stress wave propagation in elongated bodies: Apparent deviations from circuit realizability principles (1995)
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    Circuits, systems and signal processing 14 (1995), S. 525-538 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Of concern is the undistorted propagation of pulse stress waves in long thin bodies. The primary signals are arbitrarily sharp pulses projected along thex-axis. It will be seen that these pulses travel close to the speed of sound in unbounded media. Secondary pulses follow representing interactive disturbances traveling along they-axis. But the process brings out certain anomalies in circuit realizability requirements. These issues, transmission parameters, and coupling between the various signals are studied in detail. The results are supported by experiments.
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    Circuit duality for recurrent Markov processes (1995)
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    Circuits, systems and signal processing 14 (1995), S. 187-211 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper investigates circuit Markov processes under the standpoint of duality principle.
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    URL: http://dx.doi.org/10.1007/BF01183834
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    Estimation of direction-of-arrivals based on the array manifold space (1995)
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    Circuits, systems and signal processing 14 (1995), S. 237-254 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, a high resolution technique for estimating DOAs of spatially close source signals is presented. It is observed that the array manifold over a sector of interest is rank deficient and the dimension of the array manifold space, which is the range space of the array manifold, is less than the number of sensors in the array. The true signal subspace is a subspace in the array manifold space. A novel technique is provided that searches for the signal subspace in this array manifold space. The resulting estimated signal subspace has minimum principal angles with the data signal subspace generated by eigen-decomposing the covariance matrix of the array data vector. It is proved that the proposed estimator is asymptotically consistent and the estimated signal subspace is closer to the true signal subspace than the data signal subspace formed by MUSIC. The proposed novel technique has better performance than the MUSIC algorithm. Its performance is comparable to MLE and MD-MUSIC yet it requires only one-dimensional searches and is computationally much less intense. Simulation results are presented to show the effectiveness of the proposed technique, and comparisons with MUSIC, MLE, and MD-MUSIC algorithms are also included.
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    High-level synthesis: current status and future prospects (1995)
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    Circuits, systems and signal processing 14 (1995), S. 351-400 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract High-level synthesis is becoming increasingly important in the area of VLSI CAD. During the last decade, much research has been carried out in this area and some results have been achieved. This paper presents a survey on the state-of-the-art of current high-level synthesis research and applications. Besides basic knowledge, a comprehensive overview has been conducted among the various theories, methods, algorithms, and applications of the existing systems. Their advantages, limitations, and feasibilities are also described. Finally, some points on current status and future directions of high-level synthesis are addressed.
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    URL: http://dx.doi.org/10.1007/BF01189017
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    The running time-frequency distributions (1995)
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    Circuits, systems and signal processing 14 (1995), S. 401-414 
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    ISSN: 1531-5878
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper introduces the running kernels that yield recursive structures for time-frequency distributions (TFDs). The running kernels offer important properties not possessed by the commonly used block distribution kernels. The introduced kernels allow an invariance in computations with respect to the extent of the kernel in the time or the lag variable. However, contrary to the wide class of block kernels that satisfy the desired timefrequency (t-f) properties, most recursive (running) time-frequency distributions (RTFDs) violate the marginal and the support properties. This paper considers both the direct and the indirect types of recursion and presents examples for illustration.
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    URL: http://dx.doi.org/10.1007/BF01189018
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    Robust estimation and signal detection with dependent nonstationary data (1995)
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    Circuits, systems and signal processing 14 (1995), S. 465-472 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper the dual topics of robust signal detection and robust estimation of a random variable are considered, where the data may be both dependent and nonstationary. We note that classical saddlepoint techniques for robustness do not readily apply in the dependent and/or nonstationary situation, and thus our results have application in a larger domain than what was feasible heretofore. In addition, our methods make possible the quantitative measurement of robustness and admit essentially arbitrary perturbations in an underlying joint statistical distribution away from the nominal. In particular, our methods show that the presence of dependency can result in a reduction of the robustness of the linear detector by approximately 50% and that appropriate censoring can improve this situation. We also show that, somewhat surprisingly, a weak amount of censoring can actually reduce robustness rather than increase it, even with dependent data that is “almost” independent. This calls into question the common practice, inspired by classical saddlepoint results for independent data, of employing censoring in cases where residual dependency is conceded. When applied to estimation, our work shows that for nominally Gaussian data, the conditional expectation estimator is optimal not only in terms of performance but also robustness (under appropriate performance measures), thus reinforcing the appeal of this estimator. On the other hand, for other performance measures, we also note that the conditional expectation estimator can be completely unrobust, regardless of whether the data is nominally Gaussian or not. Finally, our results establish a bound on estimator robustness.
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    Fast algorithms for selection of test nodes of an analog circuit using a generalized fault dictionary approach (1995)
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    Circuits, systems and signal processing 14 (1995), S. 707-724 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Selection of test nodes is an important phase of the fault dictionary approach. It is demonstrated in this paper that the techniques used for this purpose in other approaches of analog fault diagnosis like fault analysis and fault verification are not in general suitable for the fault dictionary approach. The ambiguity set is a simple and effective concept for choosing test nodes in the context of dictionaries. These sets are formed such that each faulty condition lies in only one ambiguity set. Deviating from this thinking, overlapping ambiguity sets are proposed in this paper, giving rise to a generalized fault dictionary. These sets use information more fully and hence reduce the number of test nodes. The concept of hashing is applied in this paper for selecting test nodes. This gives a linear time algorithm (linear in the number of fault voltage specificationsf′) and it isf′ times faster than the existing methods. It is not possible to select test nodes faster than this. This technique can also be used to select test nodes by the process of elimination of nodes. This is also linear inf′ per node elimination. Even a group of nodes can be eliminated or selected within the same computation. This freedom is not possible with the existing methods.
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    Nonlinear AR modeling (1995)
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    Circuits, systems and signal processing 14 (1995), S. 689-705 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A major reason for the success of linear autoregressive (AR) modeling is that Kolmogrorov proved that every linear system could be represented by a linear AR model of infinite order. The computation of a finite order AR approximation is, of course, the practical goal. In this paper, we prove that every nonlinear system with a Volterra series expansion can be represented as a nonlinear AR model of infinite order. Our method shows how an approximation to any desired order and degree can be achieved.
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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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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    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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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    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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    An improved scheme for direct adaptive control of dynamical systems using backpropagation neural networks (1995)
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    Circuits, systems and signal processing 14 (1995), S. 213-236 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents an improved direct control architecture for the on-line learning control of dynamical systems using backpropagation neural networks. The proposed architecture is compared with the other direct control schemes. In this scheme the neural network interconnection strengths are updated based on the output error of the dynamical system directly, rather than using a transformed version of the error employed in other schemes. The ill effects of the controlled dynamics on the on-line updating of the network weights are moderated by including a compensating gain layer. An error feedback is introduced to improve the dynamic response of the control system. Simulation studies are performed using the nonlinear dynamics of an underwater vehicle and the promising results support the effectiveness of the proposed scheme.
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    Stabilization of spectral methods for the analysis of singular systems using piecewise constant basis functions (1995)
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    Circuits, systems and signal processing 14 (1995), S. 299-316 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The analysis of initial value problems associated with singular linear dynamic systems using spectral methods is discussed. These methods, though extensively studied in the literature, can be very sensitive to numerical errors and to the presence of noisy input data. Moreover, using piecewise constant functions, like Walsh or Block-Pulse, spectral methods have been shown to be unstable with respect to incorrect initial conditions. In this paper regularization techniques are used to reduce arbitrarily the sensitivity of the spectral methods, and at the same time to stabilize them. Although the regularized spectral methods maintain the structure of the original algorithm, they can also be rewritten in recursive form, leading to the definition of a class of discrete time filters. Finally, some applicative numerical examples are discussed in order to show the effectiveness of the proposed algorithms.
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    Iterative minimization of quadratic functional (1995)
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    Circuits, systems and signal processing 14 (1995), S. 415-425 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A complete solution is given to the problem of determining when a certain iteration will converge to the minimum of an important type of quadratic functional. It is shown that convergence occurs whenever the minimum exists, and that the iterates produced by the iteration will be unbounded for every starting point if the minimum does not exist. Applications are given concerning an adaptive filtering algorithm and nonharmonic series expansions.
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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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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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    Topics: Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s00041-001-4043-2
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    Electronic Resource
    Functions with Time and Frequency Gaps (1995)
    Springer
    The journal of Fourier analysis and applications 2 (1995), S. 611-614 
    Details
    ISSN: 1531-5851
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present an explicit, straightforward construction of smooth integrable functions with prescribed gaps around the origin in both time and frequency domain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s00041-001-4046-z
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