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  • Springer  (126,331)
  • American Geophysical Union  (7,236)
  • American Meteorological Society
  • 1995-1999
  • 1990-1994  (135,848)
  • 1993  (70,062)
  • 1991  (65,786)
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  • 1995-1999
  • 1990-1994  (135,848)
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  • 101
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    Circuits, systems and signal processing 12 (1993), S. 51-60 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we apply the technique of interval analysis to get bounds on the initial value response of a linearized single machine infinite bus problem when a parameter is varied. It is generally believed that responses for parameter variations in an interval should lie within the responses for the extremums of the parameter variations. This is not generally true and our example demonstrates this. The interval-analysis technique permits getting the overall bound on the response. Further experimentation also revealed that the method has some limitations particularly involving lightly damped long-term dynamics. The technique is useful in finding the robustness of a particular design such as the power system stabilizer for parameter variations.
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  • 102
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    Circuits, systems and signal processing 12 (1993), S. 105-117 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The high-order Yule-Walker (HOYW) method of sinusoidal frequency estimation based on a singular value decomposition (SVD) is known to have excellent statistical performance. Here, we show that the SVD-based step of the HOYW method can be replaced by a computationally more convenient QR decomposition (QRD)-based step, without affecting the asymptotic properties of the frequency estimates.
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  • 103
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    Circuits, systems and signal processing 12 (1993), S. 85-103 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract For the given observations set of the ARMA (autoregressive moving average) process, the likelihood function depends, not only on model parameters, but on the starting values of the input and output. Therefore, it is called theconditional likelihood function. Theunconditional likelihood function can be obtained in two ways. The first is to set the starting values to zero, as is often done, and the second is to set them to the properly estimated values. The difference between these two types of likelihood functions is significant when the given data sequence is short, and any of the zeros of the moving average part is close to the boundary of the unit circle. In this paper the direct method of starting value estimation and its application to two off-line ARMA estimation algorithms, the maximum likelihood (ML) algorithm and the iterative inverse filtering (ITIF) algorithm, is proposed. Experimental results prove both increased efficiency and stability of these algorithms. The importance of setting the starting values properly is also significant when the recursive algorithm, with previously estimated parameters, has to be restarted. The advantage of the proposed reinitialization method is shown on the recursive lattice algorithm working in the block mode.
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  • 104
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    Circuits, systems and signal processing 12 (1993), S. 151-151 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
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  • 105
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    Circuits, systems and signal processing 12 (1993), S. 133-149 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we consider nonlinear, infinite networks of purely resistive type where the voltage across a branch of the network is proportional to a fixed power of the current flowing in the branch. It is known that the study of currents in such networks amounts to studying the space of the functions on a network which have finite Dirichlet sums of orderp. Such a study was carried out in [7], [9], and [11]–[14] under the assumption that every node is connected to only finitely many different nodes of the network. In this paper we drop this assumption and work with general countable networks. We prove that most results of the locally finite case, and especially the classification theory, hold true in a more general context. Moreover, we give necessary and sufficient conditions for a network to have only constant Dirichlet finitep-harmonic functions. The relationship with discrete Markov processes is also pointed out.
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  • 106
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    Circuits, systems and signal processing 12 (1993), S. 155-175 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract One of the major drawbacks of the backpropagation algorithm is its slow rate of convergence. Researchers have tried several different approaches to speed up the convergence of backpropagation learning. In this paper, we present those rapid learning methods as three categories, and implement the representative methods of each category: (1) for the numerical method based approach, the Aitken's Δ2 process, (2) for the heuristics based approach, the dynamic adaptation of learning rate, and (3) for the learning strategy based approach, the selective presentation of learning samples. Based on these implementations, the performance is evaluated with experiments and the merits and demerits are briefly discussed.
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  • 107
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    Circuits, systems and signal processing 12 (1993), S. 177-210 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The area of artificial neural networks has recently seen an explosion of theoretical and practical results. In this paper, we present an artificial neural network that is algebraically distinct from the classical artificial neural networks, and several applications which are different from the typical ones. In fact, this new class of networks, calledmorphology neural networks, is a special case of a general theory of artificial neural nets, which includes the classical neural nets. The main difference between a classical neural net and a morphology neural net lies in the way each node algebraically combines the numerical information. Each node in a classical neural net combines information by multiplying output values and corresponding weights and summing, while in a morphology neural net, the combining operation consists of adding values and corresponding weights, and taking the maximum value. We lay a theoretical foundation for morphology neural nets, describe their roots, and give several applications in image processing. In addition, theoretical results on the convergence issues for two networks are presented.
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  • 108
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    Circuits, systems and signal processing 12 (1993), S. 309-329 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Higher order moment computations are generally necessary wherever the recognition task exceeds the confines of linearity. This paper provides an overview of recent progress on a specific neural network design, which explicitly uses higher order moment information. Attention is focused on the training algorithms used in the design and on network performance in prototype applications.
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  • 109
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    Circuits, systems and signal processing 12 (1993), S. 375-390 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In the present paper we study the problem of the existence and uniqueness of solutions of implicit systems considered on a finite interval of time. We consider two kinds of existence problems: input-acceptance and input-acceptance when the boundary conditions of a corresponding trajectory are set to zero, and two kinds of uniqueness problems: output uniqueness and output uniqueness when the boundary conditions of the corresponding trajectory are unknown. Geometric conditions for all of these notions are given, and the duality of these notions is studied.
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  • 110
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    The Geneva risk and insurance review 18 (1993), S. 103-105 
    ISSN: 1554-9658
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
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  • 111
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 137-139 
    ISSN: 1476-5535
    Keywords: Cellulomonas flavigena ; Protoplast ; Transformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Protoplasts ofCellulomonas flavigena (Cms) were transformed with plasmid pC194. Transformation frequency was 2.72×10−3 in MR-1 regeneration medium with 2 μg/ml chloramphenicol. Transformation conditions are described.
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  • 112
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 133-136 
    ISSN: 1476-5535
    Keywords: Biosurfactant production ; Pseudomonas aeruginosa ; Rhamnolipid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Biosurfactant accumulation occurred in the exponential and stationary phases. Production started when the nitrogen level was very low. Surfactant was produced with a diauxic pattern. Rhamnolipid concentration increased as nitrogen levels increased. Maximum product yield (Y p/x) 2.9 was detected when C/N ratio was 6.6 and specific rate of product formation (p q) was calculated. The examination of these kinetics parameters such as product yield and specific rate of product formation should be taken into account to develop a high efficient production process.
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  • 113
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 141-146 
    ISSN: 1476-5535
    Keywords: Soil venting ; Bioremediation ; Soil volatilization ; Jet fuel ; Diesel ; Hydrocarbons ; Petroleum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Bioventing combines the capabilities of soil venting and enhanced bioremediation to cost-effectively remove light and middle distillate hydrocarbons from vadose zone soils and the groundwater table. Soil venting removes the more volatile fuel components from unsaturated soil and promotes aerobic biodegradation by driving large volumes of air into the subsurface. In theory, air is several thousand times more effective than water in penetrating and aerating fuel-saturated and low permeability soil horizons. Aerobic microbial degradation can mitigate both residual and vapor phase hydrocarbon concentrations. Soil venting is being evaluated at a number of U.S. military sites contaminated with middle distillate fuels to determine its potential to stimulate in situ aerobic biodegradation and to develop techniques to promote in situ vapor phase degradation. In situ respirometric evaluations and field pilot studies at sites with varying soil conditions indicate that bioventing is a cost-effective method to treat soils contaminated with jet fuels and diesel.
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  • 114
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 165-169 
    ISSN: 1476-5535
    Keywords: Fermentation ; Complex medium ; RecombinantEscherichia coli ; Glyceraldehyde 3-phosphate dehydrogenase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary The influence of complex compounds on the growth of a recombinant strain ofEscherichia coli containing the gene encoding glyceraldehyde 3-phosphate dehydrogenase, as well as the production of this enzyme have been studied. Batchwise cultures led to an accumulation of acetate, which was not utilized in a yeast extract-free medium. After glucose exhaustion, growth stopped and enzyme activity decreased. Whereas yeast extract allowed acetate assimilation and growth, peptone stabilized the enzymatic activity. The addition of both compounds resulted in optimal performances for enzyme production.
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  • 115
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 259-264 
    ISSN: 1476-5535
    Keywords: Steroids ; Δ′-Dehydrogenation ; Immobilized cells ; Arthrobacter simplex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Arthrobacter simplex ATCC 6946 (viable cells) was immobilized in a calcium polygalacturonate gel. The trapped cells were used for repeated batchwise bioconversion of steroids. Reichstein's compound S and hydrocortisone were dehydrogenated introducing a double bond between C1 and C2 of ring A. The products 1-dehydro S and prednisolone, respectively, were identified by high pressure liquid chromatography. Steroid dehydrogenase activity increased in the system when an artificial electron acceptor, such as menadione (vitamin K3) was present in the reaction mixture. An airlift-type reactor was used to bioconvert up to 90% of substrate in 15 min, under optimal conditions. The gel entrapped cell preparations were used for repeated batch bioconversion during 30 days; 69 batch bioconversions for Reichstein's compound S were performed during 15 days of operation of the reactor. The operational stability of the process and the feasibility of repeated batch bioconversions was shown to be comparable to similar processes.
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  • 116
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    Journal of industrial microbiology and biotechnology 8 (1991), S. 281-283 
    ISSN: 1476-5535
    Keywords: Biofilm ; Contamination ; Biofouling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary With equal cell densities, surface film thickness did not influence the numbers ofSalmonella typhimurium andListeria monocytogenes cells which attached to glass. MotileL. monocytogenes cells had a greater cell surface charge and generally attached in higher numbers than non-motile cells.
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  • 117
    ISSN: 1476-5535
    Keywords: Cladosporium herbarum ; Cladosporium cladosporioides ; Biodeterioration of paint ; Airborne fungi
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Cladosporium cladosporioides andC. hebarum colonized painted metal surfaces of covering panels and register vents of heating, air conditioning and ventilation systems. Hyphae penetrated the paint film and developed characteristic conidiophores and conidia. The colonies were tightly appressed to the metal surface and conidia were not readily detectable via standard air sampling procedures.
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  • 118
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    Bulletin of mathematical biology 53 (1991), S. 33-55 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
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  • 119
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    Bulletin of mathematical biology 53 (1991), S. 57-87 
    ISSN: 1522-9602
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  • 120
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    Bulletin of mathematical biology 53 (1991), S. 89-118 
    ISSN: 1522-9602
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  • 121
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    Bulletin of mathematical biology 53 (1991), S. 1-32 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper reviews the work of Kermack and McKendrick on the development of simple mathematical models of the transmission dynamics of viral and bacterial infectious agents within population of hosts. The focus of attention is centred on the notion of a threshold density of susceptible hosts to trigger an epidemic and recent extensions of this idea as expressed in the definition of a basic or case reproductive rate of infection. The main body of the paper examines recent developments of the basic Kermack-McKendrick model with an emphasis on deterministic models that describe various types of heterogeneity in the processes that determine transmission between infected and susceptible persons. Particular attention is given to the role of behavioural heterogeneity within the framework of a contact or mixing matrix which defines “who acquires infection from whom”.
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  • 122
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    Bulletin of mathematical biology 53 (1991), S. 119-134 
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    Bulletin of mathematical biology 53 (1991), S. 167-191 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Recent progress in the study of aquatic food-cycle relationships invites a reappraisal of certain ecological tenets. Quantitative productivity data provide a basis for enunciating certain trophic principles, which, when applied to a series of successional stages, shed new light on the dynamics of ecological succession.
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    Bulletin of mathematical biology 53 (1991), S. 215-229 
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  • 125
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    Bulletin of mathematical biology 53 (1991), S. 135-165 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The random-walk problem is adopted as a starting point for the analytical study of dispersal in living organisms. The solution is used as a basis for the study of the expanson of a growing population, and illustrative examples are given. The law of diffusion is deduced and applied to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats on various assumptions as to the mode of population growth or decline. For the numerical solution of certain cases an iterative process is described and a short table of a new function is given. The equilibrium states of the various analytical models are considered in relation to the size of the habitat, and questions of stability are investigated. A mode of population growth resulting from the random scattering of the reproductive units in a population discrete in time, is deduced and used as a basis for study on interspecific competition. The extent to which the present analytical formulation is applicable to biological situations, and some of the more important biological implications are briefly considered.
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    Bulletin of mathematical biology 53 (1991), S. 193-213 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This concluding survey of the problems considered in the Symposium naturally falls into three sections. In the first brief section certain of the areas in which there is considerable difference in outlook are discussed with a view to ascertaining the nature of the differences in the points of view of workers in different parts of the field; no aspect of the Symposium has been more important than the reduction of areas of dispute. In the second section a rather detailed analysis of one particular problem is given, partly because the question, namely, the nature of the ecological niche and the validity of the principles of niche specificity has raised and continues to raise difficulties, and partly because discussion of this problem gives an opportunity to refer to new work of potential importance not otherwise considered in the Symposium. The third section deals with possible directions for future research.
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    Bulletin of mathematical biology 53 (1991), S. 231-252 
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    Bulletin of mathematical biology 53 (1991), S. 355-382 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract A simple model of a population of asexually reproducing individuals, evolving in a flat fitness landscape, is defined. It is shown that the model is equivalent to a dynamical system with stochastic dynamics, the Annealed Random Map Model. Thus, it is possible to solve exactly for the genealogy statistics and for the genetic variability of the population. Fluctuations of quantities, like the average relatedness and the variability, which also take place in the limit of an infinitely large population, are computed.
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    Bulletin of mathematical biology 53 (1991), S. 425-441 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The aerial visual field of aquatic animals living near the water surface is distorted by refraction. The imaging of aerial objects by one or two submerged eyes is studied. The aerial binocular image field is determined for pairs of submerged eyes in horizonal and vertical planes. These two image spaces have significantly different structures. Aquatic animals have to correct for refraction, adapting themselves to the former aerial image field in order to recognize aerial predators or to capture such prey. The other aerial image space is only of theoretical interest.
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    Bulletin of mathematical biology 53 (1991), S. 383-401 
    ISSN: 1522-9602
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    Notes: Abstract This paper concerns oscillations arising in a sequence of biochemical reactions whose end-product inhibits the rate of the first reaction. Except for the end-product inhibition, each reaction rate is assumed to be unaffected by S i other than its reactant. It is shown that with a constant concentration of S0 a necessary condition for instability at a critical point (steady state) is $$\frac{{\beta _1 \beta _2 ...\beta _{n - 1} \phi }}{{\alpha _1 \alpha _2 ...\alpha _n }} \geqslant (\sec \pi /n)^n $$ whereβ i is the order of reaction (with respect to the concentrationS i of S i ) of the formation of S i+1 from S i ;α i is the order of reaction (with respect toS i ) of the combined processes of metabolic conversion and all other processes removing S i ; and ϕ is the order of the negative feedback, i.e.—ϕ is the order of reaction (with respect toS n ) of the conversion of S0 to S1. The order of a chemical reaction with respect toS i is defined as ∂ logV/∂ logS i , whereV is the rate of reaction. So defined, order of reaction may be concentration-dependent; and in the above inequality any concentration-dependent reaction orders must be evaluated at the critical point. The above inequality, with strict inequality, is a sufficient condition for instability in the special case where all the diagonal elements of the Jacobian matrix are equal at the critical point. With a saturable final elimination process (α n 〉1), the above condition may be met even if ϕ≤1, i.e. feedback is not cooperative. Saturable elimination of an intermediate metabolite has a similar effect, but this effect is weak unless there is a relatively large loss of that metabolite from the reaction sequence. A 3-component model is constructed which has saturable final elimination and no feedback cooperativity and shows stable oscillations.
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    Bulletin of mathematical biology 53 (1991), S. 403-424 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider ann-component biochemical system whose Jacobian matrixJ is of upper Hessenberg form, with principal subdiagonal elementsb 1,b 2, ...,b n−1 and upper right-hand corner element −f. The open-loop Jacobian matrixJ 0 is formed fromJ by settingf=0. It is shown that if the characteristic roots of −J 0 are real and non-negative then a necessary condition for instability at a critical point (steady state) is $$\frac{{b_1 b_2 ...b_{n - 1} f}}{{\left| { - J_0 } \right|}} \geqslant (\sec \pi /n)^n $$ This condition is analyzed in terms of reaction orders. For a metabolic sequence with some reversible steps, no loss of intermediate metabolites, and competitive inhibition of the first enzyme by the last metabolite, the above necessary condition becomes $$\frac{{\beta _{N - 1} X_{n + 1} }}{{\xi _{N - 1} E_{0T} }} \geqslant (\sec \pi /N)^N $$ whereN is the number of components (metabolites, enzyme-substrate complexes, and enzyme-inhibitor complex),β N-1 the order of the enzyme-inhibitor reaction (with respect to the inhibitor),ξ N-1 the order of reaction for the removal of the last metabolite, andX n+1 /E 0T the fraction of first enzyme blocked by inhibitor. It is shown that, under certain assumptions, a critical point is always stable in a single two-step enzymatic process (formation of enzyme-substrate complex, followed by conversion to product, then loss of product) with slow negative feedback by competitive product inhibition. A model is constructed showing that stable oscillations can occur in a feedback system with only two metabolic steps and negative feedback by competitive inhibition with no cooperativity. The instability is due to a slow feedback reaction and saturable removal of the second metabolite.
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  • 132
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    Notes: Abstract Many biochemical reactions consist of the spontaneous fluctuation between two states: A⇌B. For example these two states could be a ligand bound to an enzyme and the ligand and the enzyme separated from each other. A typical case would be the unbinding of CO from myoglobin (Mb), namely, MbCO⇌Mb+CO. Another example is the fluctuation in the ion channel protein in the cell membrane between conformations that are closed to the passage of ions and those that are open to the passage of ions, namely, closed⇌open. Such chemical reactions can be described as two energy levels corresponding to the two states, separated by a distribution of activation energy barriers. Since a kinetic rate can be associated with each energy barrier, this is also equivalent to a distribution of kinetic rate constants. We derive the distribution of the kinetic rates that produces the stretched exponential probability distribution, exp(−at b ) where 0〈b≤1, which has been observed for such reactions. We also derive the form of the cumulative probability distribution when the pathways connecting the states have minimum or maximum rate constants.
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    Bulletin of mathematical biology 53 (1991), S. 457-467 
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    Notes: Abstract A mathematical model has been developed which collapses a dendritic neuron of complex geometry into a single electrotonically tapering equivalent cable. The modified cable equation governing the transient distribution of subthreshold membrane potential in a branching tree is transformed, becoming amenable to analytic solution. This transformation results in a Riccati differential equation whose six solutions (expressed in terms of elementary functions) control the amount and degree of taper found in the equivalent cable model. To illustrate the theory, an analytic solution (in series form) of the modified cable equation is obtained for a voltage-clamp present at the soma of a quadratically tapering equivalent cable whose distal end is sealed.
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    Bulletin of mathematical biology 53 (1991), S. 469-485 
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    Notes: Abstract The classification of the dynamical behaviour of first order replicator equations is extended to models with monotonical growth rates. It is shown that for two species there is a general classification independent of the particular form of the growth function. For three species a common dynamical behaviour for all power laws can be found and the existence of limit cycles is disproved. For more general growth functions, however, limit cycles may occur.
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    Bulletin of mathematical biology 53 (1991), S. 487-503 
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    Bulletin of mathematical biology 53 (1991), S. 525-536 
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    Notes: Abstract Several investigations have been made for the heat flow problems in skin and subdermal tissues under normal physiological and atmospheric conditions. This paper considers the existence of a malignant tumour in the underlying tissues of epidermis of a human body. The surrounding tissues are assumed to have normal physiological functions, namely self-controlled metabolic activity, variable blood flow and perspiration. For the malignant portion the metabolic activity is taken to be continuous and uncontrolled. The effect of this factor is studied on the temperature profiles of the skin.
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    Bulletin of mathematical biology 53 (1991), S. 505-523 
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    Notes: Abstract The experimental literature has dealt intensively with the cortical contribution to epilepsy. Possibly because of the direction of technological advance, much less attention has been paid to the role of other structures. A model which emphasizes the role of some of those non-cortical structures, specifically that of thalamocortical modulation of cortical excitability, is developed. Some aspects of the petit mal seizure, a seizure type considered by some investigators to involve thalamocortical mechanisms, are predicted by the model. Although the thalamocortical mechanisms under study are not the only mechanism underlying seizures, a full understanding of the phenomenology of epilepsy needs to take into account the role of subcortical modification of cortical activities in addition to other mechanisms. Gloor has described two types of epileptogenesis: type I characteristic of non-convulsive seizure and type II characteristic of convulsions. There is disagreement as to whether or not the two mechanisms represent qualitatively different phenomena. Utilizing the thalamocortical model, it can be shown that the two types of epileptogenesis are qualitatively different. Furthermore, the thalamocortical model leads to a possible explanation of clinically different profiles of antipileptic efficacy of medications.
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    Bulletin of mathematical biology 53 (1991), S. 537-555 
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    Notes: Abstract A method for obtaining delay histograms for the time course of neurotransmitter release is presented. The delay histogram is derived from the measured psc (or the sum of several psc's) and the mpsc (obtained experimentally or otherwise) by means of a simple, quick, mathematical procedure. The procedure may be automated for the greater part. No approximation of the mpsc shape is performed, and the method is applicable to all quantal contents. For low and medium quantal contents, the delay histograms obtained by the method are compared to those obtained by direct analysis. A reasonable agreement is achieved. An experiment of high quantal content, for which direct analysis is impossible, is then analysed using the new method. Difficulties which may arise when applying the procedure and methods to overcome them are discussed at length. Other methods are set forth in the Discussion.
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    Bulletin of mathematical biology 53 (1991), S. 557-577 
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    Notes: Abstract The invasion success of a diffusing predator which changes its diffusion coefficient depending on whether the prey exists or not is investigated. The prey is assumed to be immobile and distributed in an isolated patch. The isolated patch consists of two kinds of region: prey-existing zone and prey-vacant zone. We discuss what relation a heterogeneity of prey distribution has with the predator's invasion success into the patch. Its spatial heterogeneity appears to affect significantly the predator's invasion. In an Appendix we briefly treat an analogous problem involving two competing species.
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    Bulletin of mathematical biology 53 (1991), S. 639-656 
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    Notes: Abstract A mathematical model of tumor growth including autocrine and paracrine control has been developed. The model starts with the logistic equation of Verhulst: dV/dt=rV(1−V/K). Autocrine controls are described as modifiers of the Malthusian growth rate (r), while paracrine controls modify the carrying capacity (K) of the system. The control mechanisms are expressed in terms of “candidate” functions, which are based upon the dynamic distribution of TGF-alpha and TGF-beta in the local tumor environment. Three paradigms of tissue growth have been modeled: normal tissue wound repair, unrestricted, unperturbed tumor growth, and tumor growth in a (radiation) damaged environment (the Tumor Bed Effect, TBE). These scenarios were used to test the dynamics of the system against known phenomena. Computer simulations are presented for each case. The model is being extended to include the description of heterogeneous tumors, within which subpopulations can express differential degrees of growth activity. Heterogeneous tumor models, with and without emergent subpopulations, and models of terminal differentiation are also discussed.
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    Bulletin of mathematical biology 53 (1991), S. 623-638 
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    Notes: Abstract A generalization of the “constant overall organization” constraint of Eigen's quasispecies and hypercycle models, called herein “global population regulation”, is shown to lead to mathematically tractable spatial generalizations of these two models. The spatially uniform steady state of Eigen's quasispecies model is shown to be stable and globally attracting for all possible values of the mutation and replication rates. In contrast, the spatially and temporally uniform solutions to the hypercycle with fewer than five members, the only ones insensitive to stochastic perturbations, are shown to be unstable, and a lower bound to the spatial inhomogeneities is obtained. The prospect that the spatially localized hypercycle might be immune to various instabilities cited in the literature is then briefly considered. Although spatial localization makes possible a much richer dynamical repertoire than previously considered, it is also more difficult to understand how Darwinian selection of hypercycles could result in a unique genetic code.
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    Bulletin of mathematical biology 53 (1991), S. 679-684 
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    Notes: Abstract An axiomatic characterization is presented for consensus functions defined on weak hierarchies. These functions are generalizations of the majority rule consensus.
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    Bulletin of mathematical biology 53 (1991), S. 701-719 
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    Notes: Abstract We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.
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    Bulletin of mathematical biology 53 (1991), S. 751-768 
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    Notes: Abstract Two series expressions were obtained that give the first and second order rates of change in population fitness during competitive replication at elevated mutation rates. At their zeroerror limit, the respective power series reduces to the second (Fisher’s theorem) and third moments of the fitness distribution. The first series maximized the variation in mean polymer fitness, for a given amount of population covariance. From experimental results reported by Spiegelman’s group on evolutionin vitro among Qβ RNA variants, it was demonstrated: (i) terms in the (second) series fall-off at a rate broadly equal to the replicase error (ε≅10−4); (ii) the rate of change in mean RNA fitness (polymer formation rate constant) corresponds to the variance in fitness; and (iii) agreement exists between second order rate changes in fitness and the third moment (skewness) regression line, extending over 20 successive replication reactions. The impact of these findings on the standard model of evolution has been discussed.
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    Bulletin of mathematical biology 53 (1991), S. 769-796 
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    Notes: Abstract A fundamental problem in molecular biology is the determination of the conformation of macromolecules from NMR data. Several successful distance geometry programs have been developed for this purpose, for example DISGEO. A particularly difficult facet of these programs is the embedding problem, that is the problem of determining those conformations whose distances between atoms are nearest those measured by the NMR techniques. The embedding problem is the distance geometry equivalent of the multiple minima problem, which arises in energy minimization approaches to conformation determination. We show that the distance geometry approach has some nice geometry not associated with other methods that allows one to prove detailed results with regard to the location of local minima. We exploit this geometry to develop some algorithms which are faster and find more minima than the algorithms presently used.
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    Bulletin of mathematical biology 53 (1991), S. 805-823 
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    Notes: Abstract Several critical issues associated with the processing of olfactory stimuli in animals (but focusing on insects) are discussed with a view to designing a neural network which can process olfactory stimuli. This leads to the construction of a neural network that can learn and identify the quality (direction cosines) of an input vector or extract information from a sequence of correlated input vectors, where the latter corresponds to sampling a time varying olfactory stimulus (or other generically similar pattern recognition problems). The network is constructed around a discrete time content-addressable memory (CAM) module which basically satisfies the Hopfield equations with the addition of a unit time delay feedback. This modification improves the convergence properties of the network and is used to control a switch which activates the learning or template formation process when the input is “unknown”. The network dynamics are embedded within a sniff cycle which includes a larger time delay (i.e. an integert s 〈1) that is also used to control the template formation switch. In addition, this time delay is used to modify the input into the CAM module so that the more dominant of two mingling odors or an odor increasing against a background of odors is more readily identified. The performance of the network is evaluated using Monte Carlo simulations and numerical results are presented.
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    Bulletin of mathematical biology 53 (1991), S. 853-879 
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    Notes: Abstract A statistical framework is proposed for analysing DNA fingerprint data from experiments aimed at constructing ordered clone physical maps of chromosomes. The fingerprint data consists of the lengths and hybridization states of restriction digest fragments and the paper develops a solution to the fundamental problem of deciding whether or not two randomly selected clones overlap. Overlap probabilities are calculated using Bayes’ rule together with appropriate statistical descriptions of the chromosome and experimental procedure. The analysis is flexible, allowing a variety of assumptions to account for experimental errors and difficulties, such as unobserved fragments. The approach described here provides a basis for predicting the rate of progress of an experimental protocol and hence for comparing alternate protocols. It is readily generalized to related problems with a wide range of possible data. Results are presented for the clone mapping protocol currently being employed at Los Alamos National Laboratory on human chromosome 16
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    Notes: Abstract Based on experimental work on the ontogeny of the electroretinogram circadian rhythm in crayfish, we present a mathematical model simulating changes in both frequency and amplitude of the electroretinogram oscillation during several developmental stages until shortly before the adult age. Simultaneously, we propose a hypothetical oscillation in the hormonal release whose frequency is imposed on the electroretinogram oscillation. The model consists of two coupled nonlinear oscillators in which a dynamical response is obtained mainly through an Andronov-Hopf bifurcation. Through the construction of the model, a biological hypothesis about the essential elements underlying the ERG circadian rhythm and their interrelations is formulated and discussed.
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    Bulletin of mathematical biology 55 (1993), S. 111-129 
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    Notes: Abstract Several of the known scaling laws in the animal kingdom are based on a so-called allometric correlation in which some physical quantity is presumed to scale as some power of the mass of the animal. Such a simple correlation, when deduced purely as an empirical result, often hides the physical balances that fix the relevant scaling law. In particular, the emphasis on a simple allometric scaling has often masked the fundamental role played by time scales associated with the physical balances being struck. In this paper I have concentrated on three different attributes to which the use of dimensional analysis, scaling arguments and some judicious guesswork have led to new results and an understanding of some balances that occur in the animal kingdom. The running speed of animals is examined and a rationale deduced for the resolution of a conundrum first posed by A.V. Hill of why it is that many animals appear to have approximately the same maximum speed. A complete dimensional analysis for scaling the basal metabolic rate for a class of animals suggests that a detailed understanding of the physical balances that fix the metabolic rate could be quite subtle. However, the use of such an analysis has led to the discovery of a new correlation for mammals, relating the metabolic rate to the mass and the pulse rate of the animal. At the heart of many scaling laws for animal motion is the provision of an estimate of how the skeletal structure depends on the mass of the animal. It has been known for some time that the assumption of isometry between the builds of animals is too constrictive to describe the observed scaling laws. It is shown here how to relax the isometric assumption and deduce scaling laws in good agreement with observation. Thus, it appears that the skeletal dimensions of many animals with exoskeletons are fixed by the need to support static rather than dynamical loads. The scaling laws associated with endoskeletons are more complex, apparently, though the analysis does suggest that it is dynamical loading which is decisive for the skeletal design of land mammals.
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    Bulletin of mathematical biology 55 (1993), S. 465-486 
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    Notes: Abstract This article presents a new method for the comparison of multiple macromolecular sequences. It is based on a hierarchical sequence synthesis procedure that does not require anya priori knowledge of the molecular structure of the sequences or the phylogenetic relations among the sequences. It differs from the existing methods as it has the capability of: (i) generating a statistical-structural model of the sequences through a synthesis process that detects homologous groups of the sequences, and (ii) aligning the sequences while the taxonomic tree of the sequences is being constructed in one single phase. It produces superior results when compared with some existing methods.
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    Bulletin of mathematical biology 55 (1993), S. 503-524 
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    Notes: Abstract This paper presents a dynamic programming algorithm for aligning two sequeces when the alignment is constrained to lie between two arbitrary boundary lines in the dynamic programming matrix. For affine gap penalties, the algorithm requires onlyO(F) computation time andO(M+N) space, whereF is the area of the feasible region andM andN are the sequence lengths. The result extends to concave gap penalties, with somewhat increased time and space bounds.
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    Bulletin of mathematical biology 55 (1993), S. 561-583 
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    Notes: Abstract A general model of zymogen activation is proposed and explicit kinetic equations for the time courses of the various species and products involved are given. These equations are valid for the whole course of the reaction and therefore for both the transient phase and the steady state. This model is sufficiently general to include mechanisms possessing one or more steps of zymogen activation besides possible steps of inhibition (reversible or irreversible) or inactivation.
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    Bulletin of mathematical biology 55 (1993), S. 585-608 
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    Notes: Abstract Cell migration can be characterized by two independent variables: the speed,v, and the migration angle, ϕ. Each variable can be described by a stochastic differential equation—a Langevin equation. The migration behaviour of an ensemble of cells can be predicted due to the stochastic processes involved in the signal transduction/response system of each cell. Distribution functions, correlation functions, etc. are determined by using the corresponding Fokker-Planck equation. The model assumptions are verified by experimental results. The theoretical predictions are mainly compared with the galvanotactic response of human granulocytes. The coefficient characterizing the mean effect of the signal transduction/response system of the cell is experimentally determined to 0.08 mm/V sec (galvanotaxis) or 0.7 mm/sec (chemotaxis) and the characteristic time characterizing stochastic effects in the signal transduction/response system is experimentally determined as 30 sec. The temporal directed response induced by electric field pulses is investigated: the experimental cells react slower but are more sensitive than predicted by theory.
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    Bulletin of mathematical biology 53 (1991), S. 825-843 
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    Notes: Abstract Modelling studies have played an important role in research on the mechanism of urine concentration and dilution by the medulla of the kidney ever since Hargitay and Kuhn (1951,Z. Elektrochem. 55, 539–558) first proposed that the parallel tubular structures in the kidney medulla must function as a “countercurrent multiplication” system. Present-day models, in keeping with our considerably improved understanding of most aspects of medullary structure-function relationships, have evolved into rather sophisticated systems of parallel tubes. In spite of this increasing complexity, it has remained the case that “model medullas” do not concentrate as well as the real kidney, especially in the inner medulla where only passive, diffusional transport occurs. Inasmuch as these models take into account the majority of contemporary ideas making up our global hypothesis about the functioning of this system, their failure to behave physiologically indicates that our understanding remains incomplete. The purpose of the present modelling study was to evaluate the implications of some recent measurements showing that permeabilities of NaCl (P s ) and urea (P u ) vary along the length of the descending thin limbs of Henle (Imaiet al., 1988,Am. J. Physiol. 254, F323–F328), rather than being constant throughout this segment as had been assumed earlier. It was hoped that these newly measured values might explain, by a passive, diffusional process, the net solute addition at the bend of Henle’s loop observed under some circumstances and heretofore attributed (though without any supporting experimental evidence) to active transport into the descending limb. The results of the present study show that whereas incorporation of the new values forP s andP u in the descending limbs of short nephrons does indeed improve the concentrating power of the model, these new values are nonetheless not sufficient to allow the model to build an osmolarity gradient that increases all the way through the inner medulla. This failing, which is common to virtually all modelling studies to date using measured values from rat kidneys, probably points to a key role for preferential exchange supposed by some to exist among certain tubule segments within vascular bundles in species whose kidneys have the highest concentrating power.
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    Bulletin of mathematical biology 53 (1991), S. 901-909 
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    Notes: Abstract A kinetic analysis is performed for the description of the germination of fungal spores. The present stochastic model assumes that the germination process under consideration can be simulated by a series of random events. The transition of a fungal spore from one state to another is governed by probabilistic laws. The present analysis yields a differential equation describing the evolution of the probability distribution of the number of spores in each state. The variations of the mean and the variance of the number of germinated spores as a function of time are derived. The applicability of the present stochastic model is examined by analysing the germination ofRhizopus oligosporus spores.
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    Bulletin of mathematical biology 53 (1991), S. 941-951 
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    Bulletin of mathematical biology 53 (1991), S. 953-953 
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    Bulletin of mathematical biology 55 (1993), S. 15-35 
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    Notes: Abstract A classical predator-prey model is considered in this paper with reference to the case of periodically varying parameters. Six elementary seasonality mechanisms are identified and analysed in detail by means of a continuation technique producing complete bifurcation diagrams. The results show that each elementary mechanism can give rise to multiple attractors and that catastrophic transitions can occur when suitable parameters are slightly changed. Moreover, the two classical routes to chaos, namely, torus destruction and cascade of period doublings, are numerically detected. Since in the case of constant parameters the model cannot have multiple attractors, catastrophes and chaos, the results support the conjecture that seasons can very easily give rise to complex populations dynamics.
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    Bulletin of mathematical biology 55 (1993), S. 75-96 
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    Notes: Abstract We briefly review the literature on the division of labour in ant colonies with monomorphic worker populations, and show that there are anomalies in current theories and in the interpretation of existing data sets. Most ant colonies are likely to be in unstable situations and therefore we doubt if an age-based division of labour can be sufficiently flexible. We present data for a type of small ant colony in a highly seasonal environment, concentrating on individually marked older workers. We show that contrary to expectation such workers undertake a wide variety of tasks and can even retain their ability to reproduce, even whilst younger workers are actively foraging. Our analysis shows that old workers occupy four distinct spatial stations within the nest and that these are related to the tasks they perform. We suggest that correlations between age and task in many ant colonies might simply be based on ants foraging for work, i.e. actively seeking tasks to perform and remaining faithful to these as long as they are profitably employed. For this reason, employed older workers effectively displace unemployed younger workers into other tasks. In a companion paper, Tofts 1993,Bull. math. Biol. develops an algorithm that shows how foraging for work can be an efficient and flexible mechanism for the division of labour in social insects. The algorithm creates a correlation between age and task purely as a by-product of itsmodus operandi.
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    Bulletin of mathematical biology 55 (1993), S. 131-140 
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    Notes: Abstract A class of deformations of polyhedra which preserve both the combinatorial type and the location of all but one vertex are examined, leading to the concepts of unconditional and conditional vertex mobility. A simple criterion for vertex mobility is given, and equimobility classes of polyhedra are introduced. The polyhedral mobility characterization is suggested for applications in dynamic molecular modeling, shape analysis of protein folding, and the study of rearrangements of atomic clusters.
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    Bulletin of mathematical biology 55 (1993), S. 155-174 
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    Notes: Abstract The optimal shape of the front profile of the thick lens in the eye of the scallop,Pecten is theoretically, geometric optically investigated as a function of the refractive index of the lens and the retina, as well as of the geometrical parameters of the eye. The shape of the theoretical front surfaces is compared with that of the real, experimentally determined front face of the lens. The degree of correction of the lens for spherical aberration of the reflecting spherical mirror in thePecten eye is examined. The optimal shape of the front profile of the lens depends strongly on a set of parameters, such that a certain fine tuning is required among them to assure a full correction for spherical aberration. The extreme variability of the eye parameters and the shape of the front face of the lens in the scallop is inconsistent with this fine tuning requirement. The degree of correction of thePecten lens for spherical aberration might not be as good as it could be, a possible biooptical reason for which is discussed.
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    Bulletin of mathematical biology 55 (1993), S. 175-195 
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    Notes: Abstract A population of cells suspended in a liquid nutrient medium is considered. The process of growth, division and death of a cell is interpreted mathematically as the Bellman-Harris stochastic process governed by random meetings between the cell and nutrient particles. Growth of a cell is considered to be a result of two processes: mass inflow into and mass outflow from the cell. It is found that, in the absence of food limitations and inhibitors, population growth is not exponential. However, the exponential increase is approached asymptotically over time. Population net growth rate is a variable rather than a constant, but tends over time to a constant value which is the rate of exponential growth. The rate of exponential growth, the probabilities of cell division and death, and the life expectancy of a cell are expressed analytically via average rate of meetings between a cell and nutrient particles. The paper presents an independent phase in calculating mathematical relations between the rate of exponential growth and the concentration of food in a substrate.
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    Bulletin of mathematical biology 55 (1993), S. 213-230 
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    Notes: Abstract We analyse the helical motion of organisms, concentrating on the means by which organisms change the direction in space of the axis of the helical trajectory, which is the net direction of motion. We demonstrate that the direction of the axis is determined largely by the direction of the organism's rotational velocity. Changes in direction of the rotational velocity, with respect to the organism's body, change the direction in space of the axis of the helical trajectory. Conversely, changes in direction of the translational velocity, with respect to the body of the organism, have little effect on the direction in space of the axis of the trajectory. Because the axis of helical motion is the net direction of motion, it is likely that organisms that move in helices change direction by pointing their rotational velocity, not their translational velocity, in a new direction.
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    Bulletin of mathematical biology 55 (1993), S. 259-275 
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    Notes: Abstract The mechanistic model of the phytoplankton photosynthesis-light intensity relationship by Eilers and Peeters (1988.Ecol. Modelling 42, 199–215) is investigated mathematically. The model is based on the physiological idealization of transition probabilities between states of the photosynthetic factories,PSF. The model was found to have under constant light condition a globally stable unique positive equilibrium, while under periodically varying light (e.g. daily periodicity) there exists a unique globally asymptotically stable periodic solution. Based on this, the adaptation to a change of light intensity is defined as a process by which the state ofPSF converges to an equilibrium. Assuming that phytoplankton regulates its photosynthetic production rate with a certain strategy which maximizes production, two such possible strategies were examined. Both the instantaneous and the integral maximal photosynthetic production were shown to have the same result. With realistic qualitative assumptions of the shape of the dependence of the four model parameters on the light intensity to which phytoplankton is adapted, the numerical values of parameters under both constant and periodically varying conditions are determined by applying Pontryagin's maximum principle.
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    Bulletin of mathematical biology 55 (1993), S. 295-313 
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    Notes: Abstract Although the isobologram is presently the most widely used method of analysis for combined effects of agents, there are several different interpretations of the linear isobole isobole in regard to its use as a criterion of interaction. An investigation of the differential aspects of the linear isobole relation may cast some light in this regard. By conceptual extension of the present single effect level (i.e. effect-point) relation of the linear isobole to an effect-neighbourhood relation in which the linear isobole holds over a small continuous range of effect levels, the mathematical differential of the linear isobole can be developed and investigated. This differential aspect provides some useful insights into the implication and interpretation of the linear isobole relation when used as a general criterion in agent interaction studies. it can also serve as the mathematical basis for the formulation of analytic schemes in which the linear isobole relation is applicable over a continuous range of effect levels.
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    Bulletin of mathematical biology 55 (1993), S. 315-344 
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    Notes: Abstract We discuss in detail the behaviour of a model, proposed by Goldbeteret al. (1990.Proc. natn. Acad. Sci. 87, 1461–1465), for intracellular calcium wave propagation by calcium-induced calcium release, focusing our attention on excitability and the propagation of waves in one spatial dimension. The model with no diffusion behaves like a generic excitable system, and threshold behaviour, excitability and oscillations can be understood within this general framework. However, when diffusion is included, the model no longer behaves like a generic excitable system; the fast and slow variables are not distinct and previous results on excitable systems do not necessarily apply. We consider a piecewise linear simplification of the model, and construct travelling pulse and periodic plane wave solutions to the simplified model. The analogous behaviour in the full model is studied numerically. Goldbeter's model for calciuminduced calcium release is an excitable system of a type not previously studied in detail.
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    Bulletin of mathematical biology 55 (1993), S. 385-415 
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    Notes: Abstract A generalized model ofn catalytically-coupled self-replicative molecules witherror-prone replication is presented. A generalized mathematical formulation of this model and the outline of its asymptotic behaviour have been developed. Due to the complexity of the model, only in simple situations is it possible to draw general conclusions from the standard analysis. Some complex situations are illustrated by means of numerical integration of particular examples.
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    Bulletin of mathematical biology 55 (1993), S. 487-489 
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    Bulletin of mathematical biology 55 (1993), S. 491-502 
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    Bulletin of mathematical biology 55 (1993), S. 543-560 
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    Notes: Abstract We investigated the structural correlates of stability and resilience in strong hierarchies, that is, systems that can be represented by a rooted tree. A simple exponential model that incorporates three variables (the total number of nodesN; the number of basal nodesn B; and the number of single links among nodesN 1) accounts for 95% of the observed variability in stability among trees in our sample population. For resilience the situation is even simpler, with about 89% of the population variation being accounted for by tree size (N). For strong hierarchies, size and shape are the principal correlates of stability, while size alone explains the major proportion of the variability in resilience among stable trees. These results suggest that reasonably accurate statistical predictions about the stability and resilience of strong hierarchies can be made from a small set of (relatively) easily measured variables, without detailed knowledge of system topology.
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    Bulletin of mathematical biology 55 (1993), S. 525-541 
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    Notes: Abstract Numerous regulatory mechanisms in motor control involve the presence of time delays in the controlled behavior of the system. Experimentally, we have shown that an increase of the time delay in visual feedback induces different oscillations in control subjects and in patients with neurological diseases during the performance of a simple compensatory tracking task. A preliminary model is proposed to describe the oscillations observed in control subjects and in patients with neurological diseases. The influence of delays in two feedback loops are the main components of the motor control circuitry involved in this task and are studied from an analytical and physiological perspective. We analytically determine the influence in the model of each of these delays on the stability of the finger position. In addition, the influence of stochastic elements (“noise”) in the modeling equation is seen to contribute qualitatively to a more accurate reproduction of experimental traces in patients with Parkinson's disease but not in patients with cerebellar disease.
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    Bulletin of mathematical biology 55 (1993), S. 609-635 
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    Notes: Abstract A model of embryo energetics was fitted to data from the literature for species as different as snails and mammals. The model is based on assumptions about energy uptake, storage and utilization. It describes the animal by two state variables: volume and energy storage. Embryo weight is taken to be proportional to volume, yolk weight to energy storage, and respiration rate to storage utilization rate. The fits were good, with minor deviations occurring only in the early phases of development. For altricial birds, good model fits were obtained, but the parameter values markedly differed from those of other species. We hypothesized that, due to an increase in energy utilization towards hatching, the temperature of the embryo increases. As a result, metabolic processes are accelerated. When this was taken into account, parameter values were obtained that correspond better with those of other animals.
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    Bulletin of mathematical biology 55 (1993), S. 637-654 
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    Notes: Abstract Experimental evidence suggests that anisotropic stress induces alignment of intracellular actin filaments. We develop a model for this phenomenon, which includes a parameter reflecting the sensitivity of the microfilament network to changes in the stress field. When applied to a uniform cell sheet at rest, the model predicts that for sufficiently large values of the sensitivity parameter, all the actin filaments will spontaneously align in a single direction. Stress alignment can also be caused by a change in external conditions, and as an example of this we apply our model to the initial response of embryonic epidermis to wounding. Our solutions in this case are able to reflect the actin cable that has been found at the wound edge in recent experiments; the cable consists of microfilaments aligned with stress at the wound boundary of the epithelium. These applications suggest that stress-induced alignment of actin filaments could play a key role in some biological systems. This is the first attempt to include the alignment phenomenon in a mechanical model of cytogel.
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    Bulletin of mathematical biology 55 (1993), S. 715-730 
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    Notes: Abstract The problem of optimal dosage is studied for the administration of ddCyd using erythrocytes as carriers and bioreactors. The volume of erythrocytes and the initial amount of drug to be loaded have to be determined in such a way that the duration of the therapeutic effect is maximized without exceeding the toxic threshold. It is found that the optimal control is unique and it is at the upper vertex of the set of the admissible controls. A more general case is also briefly discussed.
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    Notes: Abstract To explore the biological similarities and differences between the HIV-1 and HIV-2 viruses, we model the probability of male-to-female transmission of either HIV virus as a function of the number of sexual partners, the prevalence of the viruses and the infectivity per contact. Using maximum likelihood estimation theory and data from a prospective study of registered female prostitutes in Dakar, Senegal, we estimate and compare the infectivities of HIV-1 and HIV-2. Graphical goodness-of-fit methods are used to show that our model fits the data well. We find that in male-to-female transmission HIV-1 is significantly more infectious than HIV-2. This findings is consistent with other data from laboratory and epidemiologic studies comparing the biology of HIV-1 and HIV-2.
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    Bulletin of mathematical biology 55 (1993), S. 817-827 
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    Notes: Abstract Predator-prey models where one or more terms involve ratios of the predator and prey populations may not be valid mathematically unless it can be shown that solutions with positive initial conditions never get arbitrarily close to the axis in question, i.e. that persistence holds. By means of a transformation of variables, criteria for persistence are derived for two classes of such models, thereby leading to their validity. Although local extinction certainly is a common occurrence in nature, it cannot be modeled by systems which are ratio-dependent near the axes.
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    Bulletin of mathematical biology 55 (1993), S. 847-864 
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    Notes: Abstract The apple twig borer (Amphicerus bicaudatus) is an insect pest of the grape vine, causing considerable damage to the grape vine in early spring. A simple difference equation model is formulated and analysed for this plant-herbivore system based on two control strategies, cane removal and pesticide application. The system has two equilibria, one where the pest is present and one where the pest is absent. Regions are found in parameter space for global stability of the equilibria and in the absence of global stability it is shown that there exist periodic or quasiperiodic solutions.
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    Bulletin of mathematical biology 55 (1993), S. 829-845 
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    Notes: Abstract A relative phase model of four coupled oscillators is used to interpret experiments on the coordination between rhythmically moving human limbs. The pairwise coupling functions in the model are motivated by experiments on two-limb coordination. Stable patterns of coordination between the limbs are represented by fixed points in relative phase coordinates. Four invariant circles exist in the model, each containing two patterns of coordination seen experimentally. The direction of switches between two four-limb patterns on the same circle can be understood in terms of two-limb coordination. Transitions between patterns in the human four-limb system are theoretically interpreted as bifurcations in a nonlinear dynamical system.
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    Bulletin of mathematical biology 55 (1993), S. 1063-1090 
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    Notes: Abstract A population dynamics approach based on a system of differential equations allows us to establish conditions for the emergence of mutualism for cases such as coelenterates-algae symbionts. A central assumption of the model is that a host organism is able to discriminate, via some molecular recognition mechanisms, among different invading organisms and preferentially rejectparasites rather thanbona fide symbionts. Large differential rejection rates allow the emergence of mutualism. Different attractors of the population dynamics correspond to the emergence of mutualism, predominance of “selfish” species, or coexistence of many species.
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    Bulletin of mathematical biology 55 (1993), S. 1091-1131 
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    Notes: Abstract A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments by Lundkvistet al. (1989.Proc. natn. Acad. Sci. U.S.A. 86, 5074–5078), injection ofAb 1 antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations ofAb 1 andAb 2 antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by Lundkvistet al. but not accounted for previously.
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    Bulletin of mathematical biology 55 (1993), S. 1183-1198 
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    Notes: Abstract The protein folding problem and the notion of NP-completeness and NP-hardness are discussed. A lattice model is suggested to capture the essece of protein folding. For this model we present a proof that finding the lowest free energy conformation belongs to the class of NP-hard problems. The implications of the proof are discussed and we suggest that the natural folding process cannot be considered as a search for the global free energy minimum. However, we suggest an explanation as to why, for many proteins, the native functional conformation maycoincide with the lowest free energy conformation.
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    Circuits, systems and signal processing 12 (1993), S. 3-35 
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    Notes: Abstract In this paper we study the performance of direction-finding systems which attempt to estimate unknown array parameters (such as sensor gains and phases) in addition to the estimation of the directions of arrival (DOA), as a way of performing array self-calibration. We develop compact closed form expressions for the Cramér-Rao bound associated with the joint estimation of DOAs, gains, phases, and the signal covariance matrix. By evaluating the Cramér-Rao bound for selected cases we gain some insight into the performance of direction-finding systems in the presence of gain and phase uncertainties.
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    Circuits, systems and signal processing 12 (1993), S. 61-83 
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    Notes: Abstract We consider input-output systems (not necessarily of feedback type) on the time domain [0, ∞) which are governed by nonlinear vector integral or differential equations that relate the input and the output. Assuming that these equations depend on a parameterA, describing perturbations, which is allowed to vary in a vicinity of a nominal valueA 0 in a linear space, we study how strongly the output is affected by changes of (a)A 0 when the input is fixed (insensitivity), and (b) the input whenA is fixed withA A 0 being not too large (robust stability). The results are based on the theory of input-output systems over abstract extended spaces given in Parts I and II of [3]. We discuss nominal systems described by nonlinear Volterra and differential equations, and consider two types of possible perturbations. We also prove a simple result on systems governed by singular differential equations whose perturbations can change the order of the system.
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    Circuits, systems and signal processing 12 (1993), S. 119-131 
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    Notes: Abstract A new family of RC-active biquadratic building blocks are proposed in this communication. These biquads are especially designed for MOSFET-C applications, since they achieve a complete MOS nonlinearity cancellation. The proposed circuits can realize all the generic transfer functions such as lowpass, highpass, bandpass, band-rejection, and allpass. They also enjoy low passband sensitivities with respect to passive elements. The gain-bandwidth product-sensitivity is investigated too. An example of a high Q-bandpass filter is given with its Monte-Carlo simulation to verify its sensitivity performance.
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    Circuits, systems and signal processing 12 (1993), S. 247-261 
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    Notes: Abstract A neural network for the traffic control problem applied to reverse baseline networks has been proposed in this paper. This problem has been first represented by an energy function. A neural network is applied for maximizing the energy of the function under the constraints of the reverse baseline network. The number of iteration steps in our neural network is limited by a performed upper bound O(n), wheren is the size of ann ×n network. The throughputs of our neural network have been shown by the empirical results to be better than the conventional algorithm (modified Bipartite Matching Algorithm) when the packet densities rise higher than 50%.
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    Circuits, systems and signal processing 12 (1993), S. 331-374 
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    Notes: Abstract There are currently several types of constructive, (or growth), algorithms available for training a feed-forward neural network. This paper describes and explains the main ones, using a fundamental approach to the multi-layer perceptron problem-solving mechanisms. The claimed convergence properties of the algorithms are verified using just two mapping theorems, which consequently enables all the algorithms to be unified under a basic mechanism. The algorithms are compared and contrasted and the deficiencies of some highlighted. The fundamental reasons for the actual success of these algorithms are extracted, and used to suggest where they might most fruitfully be applied. A suspicion that they are not a panacea for all current neural network difficulties, and that one must somewhere along the line pay for the learning efficiency they promise, is developed into an argument that their generalization abilities will lie on average below that of back-propagation.
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    Circuits, systems and signal processing 10 (1991), S. 15-30 
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    Notes: Abstract In the study of robust stability, the largest coefficient region of a given stable polynomial that guarantees stability preservation under perturbation of coefficients is to be determined. A general consideration including both Hurwitz and Schur polynomials is treated in this paper. For this purpose, the notion ofperturbation constant is introduced. As a consequence of our results, we also introduce a general Kharitonov-type stability test which is based on testing the stability and perturbation constant of a single polynomial.
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    Circuits, systems and signal processing 10 (1991), S. 163-173 
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    Notes: Abstract A few applications of a separable Hartley-like (CAS-CAS) transform in two-dimensional (2-D) signal processing is presented. The applications discussed include (i) the interpolation of signals, (ii) the computation of Hilbert transform, and (iii) the complex cepstrum computation. The computational advantage of the proposed methods over the algorithms using 2-D FFT are discussed.
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    Circuits, systems and signal processing 10 (1991), S. 221-232 
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    Notes: Abstract We introduce an efficient method for computing matrix products of the formY=AXB, whereA andB are sparse and constant. We analyze the complexity of the method, develop quantitative criteria for determining when it can be used effectively, and demonstrate its use in a Kalman filter.
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    Circuits, systems and signal processing 12 (1993), S. 223-246 
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    Notes: Abstract A forward-backward training algorithm for parallel, self-organizing hierarchical neural networks (PSHNNs) is described. Using linear algebra, it is shown that the forward-backward training of ann-stage PSHNN until convergence is equivalent to the pseudo-inverse solution for a single, total network designed in the least-squares sense with the total input vector consisting of the actual input vector and its additional nonlinear transformations. These results are also valid when a single long input vector is partitioned into smaller length vectors. A number of advantages achieved are: small modules for easy and fast learning, parallel implementation of small modules during testing, faster convergence rate, better numerical error-reduction, and suitability for learning input nonlinear transformations by other neural networks. The backpropagation (BP) algorithm is proposed for learning input nonlinearitics. Better performance in terms of deeper minimum of the error function and faster convergence rate is achieved when a single BP network is replaced by a PSHNN of equal complexity in which each stage is a BP network of smaller complexity than the single BP network.
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    Circuits, systems and signal processing 12 (1993), S. 279-307 
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    Notes: Abstract A fading-memory system is defined as a system whose response map has unique asymptotic properties over some set of inputs. It is shown that any discrete-time fading-memory system can be uniformly approximated arbitrarily closely over a compact set of input sequences by uniformly approximating either its external or internal representation sufficiently closely. In other words, the problem of uniformly approximating a fading-memory system reduces to the problem of uniformly approximating continuous real-valued functions on compact sets. The perceptron is shown to realize a set of continuous real-valued functions that is uniformly dense on compacta in the set of all continuous functions. Using the perceptron to uniformly approximate the external and internal representations of a fading-memory system results, respectively, in simple nonlinear finite-memory and infinite-memory system models.
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    Circuits, systems and signal processing 12 (1993), S. 431-440 
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    Notes: Abstract A new statistical test for selecting the order of a nonstationary AR modelyk is presented based on the predictive least-squares principle. This test is of the same order as the accumulated cost function Γ n =∑ k=1 n (∈ k * −∈ k )2;i.e., ∈* wherey k * is the predictive least-square estimate. It is constructed to show how many times the integrated AR processy k is differenced in order to obtain a stationary AR process given that the exact order of the process is unknown.
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    Circuits, systems and signal processing 12 (1993), S. 465-488 
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    Notes: Abstract New properties useful in connection with 1-D and 2-D lattice realizations are developed. These properties enable one to represent given, complicated 2-D separable-denominator digital filters in terms of simpler, more elemental building blocks which consist of two 1-D lattice realizations having dynamics in different directions and connected in a cascade form. The matrix-relationship between a 2-D discrete Schwarz form and a controller-observer canonical form is also derived. A notable property of the proposed 2-D lattice realization is that the impulse response energy of a 2-D separable-denominator digital filter can be readily obtained from the reflection coefficients and input/output tapped coefficients of the realization.
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    Circuits, systems and signal processing 12 (1993), S. 533-555 
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    Notes: Abstract This paper investigates the robustness of the saddle-node bifurcation for nonlinear systems under the addition of slow unmodeled dynamics. The robustness is examined in terms of existence and system behavior after bifurcation. Under fairly general conditions, it is shown that if the reduced model of a physical system encounters a saddle-node bifurcation due to a varying parameter, then the original model which includes small unmodeled dynamics will also encounter a saddle-node bifurcation. An error bound is derived between the bifurcation values and the bifurcation points of the reduced model and that of the original model. Furthermore, it is shown that the dynamics after the saddle-node bifurcation of the reduced model and that of the original model are approximately the same. The persistence and non-persistence of saddle-node bifurcations are illustrated by several examples.
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    Circuits, systems and signal processing 12 (1993), S. 603-612 
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    Notes: Abstract We prove that the current generated by finitely many current sources in an infinite nonlinear resistive network with no shorts at infinity can be approximated in norm by currents in finite open subnetworks.
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    Circuits, systems and signal processing 10 (1991), S. 433-441 
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    Notes: Abstract In this paper we firstly define two new formulations, the symmetric sine structure (SSS) and the symmetric cosine structure (SCS). Then we propose a simple algorithm to realize one-dimensional SCS and SSS with sequence lengths equal to 2 m . We show that a 2m-length discrete Hartley transform can be realized through a 2 m−1-length SCS and a 2 m−1-length SSS, which achieves the same multiplicative complexity as the minimum number of multiplications reported in the literature. However, our approach gives the advantage of requiring less additions compared with conventional approaches. Furthermore, this approach can also be applied to realize a 2m-length real-valued discrete Fourier transform, which requires the lowest number of multiplications compared with conventional real-valued algorithms and needs no complex number operations as found in other real-valued algorithms.
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    Circuits, systems and signal processing 10 (1991), S. 393-431 
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    Notes: Abstract In blind equalization a communication channel is adaptively equalized without resorting to the usual training sequence. In this paper we have introduced two new algorithms for blind equalization, which hard limit the equalizer input or the error at the output of the equalizer. These new algorithms are simple to implement and reduce the number of multiplications by approximately one-half. We show by way of simulations that the performance of the algorithm resulting from hardlimiting the error is comparable with the performance of the corresponding algorithm in which the error is not hardlimited. We formulate the new sign-error algorithm as a stochastic minimization of an error functional and demonstrate that the case of zero intersymbol interference corresponds to local minima of this error functional. We also present convergence analysis to predict the output mean square error in both these sign algorithms. Since the algorithms are highly nonlinear we incorporate several simplifying approximations and provide heuristic justifications for the validity of these approximations when the algorithms are operated in a typical practical environment. Computer simulations demonstrate the accuracy of the predicted convergence behavior.
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    Circuits, systems and signal processing 10 (1991), S. 443-454 
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    Notes: Abstract This paper is the second part of [6] which is concerned with the sensitivity of general input-output systems over extended spaces. It is assumed that such systems, which need not be of feedback type, are governed by nonlinear operator equations relating the input, the state, and the output. These equations depend on a parameterA that can vary in a neighborhood of a nominal valueA 0. Essentially, a system is called insensitive if any truncation of its output depends continuously onA provided the input is fixed. The theorems derived provide sufficient conditions for insensitivity. A control system of a feedback-feedforward type and a dynamical system described by a linear vector differential equation on [0, ∞) are discussed as examples.
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    Circuits, systems and signal processing 10 (1991), S. 471-483 
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    Notes: Abstract The problem of interpolating a given set of points by means of a squared magnitude rational function of minimal degree is considered. In this way, the resulting interpolating function can be factorized to yield a stable and minimum-phase transference. It is shown that in the polynomial case a nonnegative solution is easily obtained by adding to the standard Hermite interpolation polynomial a suitable term of immediately higher degree. Concerning the general rational case, a computationally efficient procedure, based on a Hermite-type parametrization, is suggested. The positivity requirement may again be met by inserting suitable terms in the numerator and denominator polynomials. An example is worked out to show the practicality of the method.
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    Circuits, systems and signal processing 12 (1993), S. 441-452 
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    Notes: Abstract For direct form digital filters with integer arithmetic, a characterization of the initial condition vector and state vectorX(ρ), for a fixedρ,ρ 〉 1, is established without the intermediate state vectors. This is used to determine initial conditions for stability and initial conditions for convergence to a limit cycle. Also, several properties of limit cycles are proven.
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