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  • 1984  (48,999)
  • 101
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    Circuits, systems and signal processing 3 (1984), S. 447-475 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The representation of functions in a basis function expansionz(t)= ∑k=1/∞=,a k〉 x k (t) is straightforward when the basis functionsx k (t) are orthogonal. There has been very little work up to this time in determining how to use nonorthogonal bases in signal representation. On the other hand, applications in data compression and signal synthesis often require using specific tailor-made bases. Presented here is a method for constructing very general nonorthogonal bases. Orthogonality has often been used to show that a basis spans the set of functions of interest and to calculate the coefficients of the representation. In this paper, both of these fundamental aspects are addressed for nonorthogonal bases. A new basis {y k (t)} is obtained by performing a linear transformation on a known existing basis {x k (t)}. This transformation is constructed such that the coefficients of signal representation on the new basis are readily found. Then, a useful and sufficient condition is placed upon the new basis such that representations converge. The fundamental methods are applied to the standard examples of signal representation. The complex sinusoids, the Rademacher functions, the orthogonal polynomials, and the decaying exponentials are used as the original basis {x k (t)} from which a new basis {y k (t)} is generated. Two examples are given to illustrate general applications: one in signal synthesis and one in signal analysis.
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  • 102
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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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  • 103
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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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  • 104
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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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  • 105
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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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  • 106
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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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  • 107
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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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  • 108
    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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  • 109
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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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  • 110
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    Bulletin of mathematical biology 53 (1991), S. 57-87 
    ISSN: 1522-9602
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  • 111
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    Bulletin of mathematical biology 53 (1991), S. 89-118 
    ISSN: 1522-9602
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  • 112
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    Bulletin of mathematical biology 53 (1991), S. 1-32 
    ISSN: 1522-9602
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    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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  • 113
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    Bulletin of mathematical biology 53 (1991), S. 119-134 
    ISSN: 1522-9602
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  • 114
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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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  • 115
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    Bulletin of mathematical biology 53 (1991), S. 215-229 
    ISSN: 1522-9602
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  • 116
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    Bulletin of mathematical biology 53 (1991), S. 135-165 
    ISSN: 1522-9602
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    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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  • 117
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    Bulletin of mathematical biology 53 (1991), S. 193-213 
    ISSN: 1522-9602
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    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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  • 118
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    Bulletin of mathematical biology 53 (1991), S. 231-252 
    ISSN: 1522-9602
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  • 119
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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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  • 120
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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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  • 121
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    Bulletin of mathematical biology 53 (1991), S. 383-401 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    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
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    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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  • 123
    ISSN: 1522-9602
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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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  • 124
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    Bulletin of mathematical biology 53 (1991), S. 457-467 
    ISSN: 1522-9602
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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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  • 125
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    Bulletin of mathematical biology 53 (1991), S. 469-485 
    ISSN: 1522-9602
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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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  • 126
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    Bulletin of mathematical biology 53 (1991), S. 487-503 
    ISSN: 1522-9602
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    Bulletin of mathematical biology 53 (1991), S. 525-536 
    ISSN: 1522-9602
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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 46 (1984), S. 81-102 
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    Notes: Abstract The temperature regulation in homothermic animals is an example of a negative feedback system. It shows sudden changes of parameter values, and therefore suggests the use of catastrophe theory for its description. This paper reports on work done on the human temperature regulation mechanism to shows that the five-dimensional dual butterfly catastrophe model is sufficient for its description. Nearly all experiments reported in the literature overlook the dynamic multiparametric nature of the process. Use of catastrophe theory, on the other hand, shows that one cannot find a model with fewer than five parameters for such a system. From work by Benzinger and Kitzinger, the exact shape of part of the corresponding bifurcation set is determined.
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    Bulletin of mathematical biology 46 (1984), S. 103-114 
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    Notes: Abstract This paper is an analytical study on the pulse wave velocities in the aorta. In conformity to a physiologic state of loading, the distensibility of the vessel wall has been accounted for. The wall material is treated by using the theory of large elastic deformations. The orthotropicity of wall tissues and the effect of the surrounding tissues have been incorporated in the analysis which is based on the use of the strain energy function suggested by Vaishnavet al. Numerical values of the wave velocities of the canine middle descending thoracic aorta are computed by using the derived analytical expressions.
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    Bulletin of mathematical biology 46 (1984), S. 41-80 
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    Notes: Abstract The theory of a symmetrical 3-barrier, 4-site, single-filing ionic channel is developed. The model goes beyond earlier models by including additional sites, as well as barriers which need not be symmetrical in the applied field, and contains the earlier models as special cases. It is itself a special case of the most general 4-site model, which has 5 barriers. By considering the barriers at the mouth and middle of the channel to be sufficiently larger than the barriers separating the sites in each channel half, these barriers can be neglected; thus this case reduces to a 3-barrier model where the sites in each channel half can then be assumed to be in equilibrium with each other. The alternative 3-barrier, 4-site case, where the barrier between the sites is considered to be larger than that at the mouth of the channel, is considered elsewhere. Pure cation permeation is considered and only single-salt properties of the system are analyzed, namely occupancy, conductance, flux ratio exponent and current-voltage relation. The concentration dependences of these properties are computed and interrelated and, where possible, also given in analytical form. The mathematical relations are obtained for a channel which is symmetrical around its middle, which is the appropriate assumption for the gramicidin channel. However, the barriers themselves are allowed to be asymmetric with respect to the potential dependence, which has been found to be essential for gramicidin. Mathematically, a straight-forward matrix formulation is used; but a general theoretical method is presented for reducing a complex model (with more than 2 sites) to a simpler cases when equilibrium exists across one or several barriers, as is often the cases. This method is a prototype which makes analytical solutions of complex barrier models possible in many cases.
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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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    Bulletin of mathematical biology 46 (1984), S. 219-227 
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    Notes: Abstract A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomach) are placedw o white balls andr black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, onlyr blacks are put in, with no whites. A sample of sizer is transferred from the 1st, 2nd and 3rd urns to the 2nd, 3rd and 4th (infinite universe) urns. From the random variable difference equations the first and second moments for the distribution of the number of radio atoms present in each urn are obtained. The variance of the contents of radioatoms in the excretion urn is
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    Bulletin of mathematical biology 46 (1984), S. 229-234 
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    Notes: Abstract A power series solution is presented which describes the steady-state concentration profiles for substrate and product molecules in immobilized enzyme systems. Diffusional effects and product inhibition are incorporated into this model. The kinetic consequences of diffusion limitation and product inhibition for immobilized enzymes are discussed and are compared to kinetic behavior characteristic of other types of effects, such as substrate inhibition and substrate activation.
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    Bulletin of mathematical biology 46 (1984), S. 205-217 
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    Notes: Abstract The use of spheroids as a tumor model has become commonplace since it was discovered that many cell lines can form spheroids when grown on a surface to which the cells cannot attach. This culture system complicates experiments which depend on oxygen supply because the oxygen concentration in the vicinity of a stationary spheroid has not been well defined. We present in this paper solutions to the oxygen diffusion equation for simple geometries: a spheroid in an infinite stationary medium and in a finite spherical stationary medium. Comparison of these solutions provides an estimate of the oxygen supply to a spheroid in a Petri dish. We show that typical spheroids can be expected to cause a substantial depletion of the oxygen in the nearby medium. Any disturbance of the medium or the spheroids will temporarily increase the oxygen supply. We provide a method for estimating the rate of return to equilibrium in the finite cases. These results indicate that the oxygen supply to stationary spheroids can be altered temporarily by small movements or changes in temperature which cause convection currents, or permanently by changes in the depth of the medium.
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    Bulletin of mathematical biology 46 (1984), S. 235-246 
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    Notes: Abstract Alternative sufficient conditions are derived that guarantee the stability of spatially heterogenous steady-state distributions of motile aerobic bacterial populations attracted chemotactically by oxygen, motile anaerobic populations repelled by oxygen, and the oxygen concentration itself through a stationary aqueous medium. In particular, it follows from the latter criteria that the heterogeneous steady-state distributions for cylindrical regions with arbitrary cross-sections, uniform depth and mixed Dirichlet-Neumann boundary conditions on the oxygen concentration (appropriate to certain still-water bodies in nature) are stable with respect to arbitrary perturbations in the bacteria cell and the oxygen distributions.
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    Bulletin of mathematical biology 46 (1984), S. 339-355 
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    Notes: Abstract Closed positive feedback loops of catalytic reactions between macromolecules, or hypercycles, provide a kinetic mechanism whereby each Species serves to catalyze selfreproduction of its successor in the loop. Hypercycles of five members or more evolve into limit cycles characteristic of a biochemical clock. Computer study of the coupled non-linear differential equations which describe these systems shows that the periodT n of then-species limit cycle is given byT n=nτn, where τn is an elemental repeat period reflecting translational time invariance. Analytic solutions of the equations are developed so that the time evolution of elementaryn-hypercycles can be traced in dynamical detail. It is shown that the magnitude of τn is, to good approximation, a linear function ofn. For a givenn, τn is a very sensitive function of the relative concentration a given member of the loop has at the time its predecessor dominates the state of the hypercycle. These concentrations decrease with increasingn. Aroundn=15 they become so small that elementary hypercycles become unstable against disruptive concentration fluctuations. Species concentrations for more realistic hypercycles tend not to be as small, so that the present estimate of a maximum number of components is a lower bound.
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    Bulletin of mathematical biology 46 (1984), S. 399-406 
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    Notes: Abstract The technique of the probability generating function is used to derive the stochastic differential equations for a nonlinear model based on Eigen and Schuster's theory of biomolecular selection and evolution. The stabilities of various steady states are analyzed by using the linear stability approximation. The instability of a small starting population is investigated numerically. The minimum starting populations required for steady-state survival are then estimated for a wide range of parameters.
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    Bulletin of mathematical biology 46 (1984), S. 389-398 
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    Notes: Abstract Some morphological features of the human bronchial tree were simulated by computergenerated trees. The trees were ordered by the methods of Horsfield and Strahler. Delta, the difference between the Horsfield orders of the two branches at a bifurcation, was determined by pseudorandom numbers generated according to a distribution of probabilities defined on input. By trial and error a distribution was found which resulted in trees being generated with average Strahler order branching ratios of 2.82, similar to a real bronchial tree. Branching angles and length ratio could also be defined on input. By varying these input parameters it was found that the form of the tree was quite sensitive to them, and that by a suitable choice the intrasegmental part of the bronchial tree could be simulated. It is concluded that branching ratio, length ratio, mean branching angles and distribution of delta are controlled within tight limits in the bronchial tree, and this may support the concept of optimal design.
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    Bulletin of mathematical biology 46 (1984), S. 407-422 
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    Notes: Abstract In this paper perturbation methods are used for the mathematical analysis of coupled relaxation oscillators. This study covers entrainment by an external periodic stimulus as well as mutual entrainment of coupled oscillators with different limit cycles. The oscillators are of a type one meets in the modeling of biological oscillators by chemical reactions and electronic circuits. Special attention is given to entrainment different from 1∶1. The results relate to phenomena occurring in physiological experiments, such as the periodic stimulation of neural and cardiac cells, and in the non-regular functioning of organs and organisms, such as the AV-block in the heart.
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    Bulletin of mathematical biology 46 (1984), S. 423-446 
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    Notes: Abstract A new, more realistic model of the action of ionizing radiation on mammalian cells growingin vitro is presented. Although this model requires a large number of parameters, these are linked to biologically observable quantities rather than being abstract sensitivities, as had previously been the case. Three different stochastic processes are required: {X(t);t ∈ [0, τ]}, representing damage alterations during irradiation; {(X(t), S(t));t ∈ [τ, τ+T D]}, representing changes in both damageX(t) and cell cycle positionS(t) during the post-irradiation cell cycle; and {N x(t);t ∈ [0,T G]}, representing the subsequent colony growth process conditioned on the value ofX(τ+T D). The assumptions used to define these processes extend a previous model of short term DNA damage formation and repair (Nelson S. J. 1982,Radiat. Res. 92, 120–145) to include the influence of cell cycle progression on damage in the irradiated cell and the effect of permanent inherited damage on the daughter cells' colony growth pattern. Expressions corresponding to commonly measured radiation effects are derived from the model and compared with predictions from previous models. It is found that these previous models oversimplified the mechanism of radiation action because they did not adequately represent repair during irradiation, the influence of radiation-induced cycle delays and damage inheritance by any daughter cells. Suggestions are then made for ways in which the new model can be used to test the importance of these effects.
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    Bulletin of mathematical biology 46 (1984), S. 461-465 
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    Bulletin of mathematical biology 46 (1984), S. 467-472 
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    Bulletin of mathematical biology 46 (1984), S. 447-460 
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    Notes: Abstract A stochastic approach is utilized to develop a model equation capable of describing the time course of germination in a sample of bacterial spores. The time required by a spore to complete the change characteristic of germination consists of an initial interval of no change followed immediately by the duration of the change itself. The experimental basis of the proposed model is the observation that each of these time intervals is distributed over a range of values in a spore sample. Mixed continuous and discrete probabilities are employed in arriving at an average single-spore germination curve which, to a different scale, describes the sample in time.
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    Bulletin of mathematical biology 46 (1984), S. 473-500 
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    Notes: Abstract Mathematical methods for comparison of nucleic acid sequences are reviewed. There are two major methods of sequence comparison: dynamic programming and a method referred to here as the regions method. The problem types discussed are comparison of two sequences, location of long matching segments, efficient database searches and comparison of several sequences.
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    Bulletin of mathematical biology 46 (1984), S. 579-590 
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    Notes: Abstract An algorithm for nucleic acid and protein sequence alignment is presented. It is a non-metric local similarity minimal-difference algorithm and in the current implementation, assembles the matching regions found into a pseudo-global format. Its strengths are its speed of execution and the especially convenient presentation of its output. The algorithm is intended for use in sequence melding and local (small-region) similarity searching. It is not designed to replace a metric Needleman-Wunsch-Sellers-type similarity algorithm. The program is written in FORTRAN and is designed to be easily transportable to a variety of computer systems.
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    Bulletin of mathematical biology 46 (1984), S. 591-621 
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    Notes: Abstract This is a review of past and present attempts to predict the secondary structure of ribonucleic acids (RNAs) through mathematical and computer methods. Related areas covering classification, enumeration and graphical representations of structures are also covered. Various general prediction techniques are discussed, especially the use of thermodynamic criteria to construct an optimal structure. The emphasis in this approach is on the use of dynamic programming algorithms to minimize free energy. One such algorithm is introduced which comprises existing ones as special cases.
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    Bulletin of mathematical biology 46 (1984), S. 641-659 
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    Notes: Abstract It is shown that the concepts of grammar complexity and syntactic structure provide a useful mathematical framework for the investigation of some current problems in protein structure. Grammar complexity gives a measure of the degree of aperiodicity of a sequence and also an optimization criterion for evaluating amino acid categorizations. Three systems of amino acid categorization are compared in relation to their value for describing molecular architecture.
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    Bulletin of mathematical biology 46 (1984), S. 623-639 
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    Notes: Abstract A scheme for representing amino acids as vectors in the plane is presented and justified. The two dimensions of the plane are size and hydrophobicity. The vector representation is then applied to generate a consensus sequence for some sets of homologous proteins. A figure of merit for the degree of homology of a set of sequences results from the analysis. Some other applications of the scheme are considered also. This work grew from ideaseeds planted by Margaret Dayhoff's work in theAtlas of Protein Structure and Sequence. It is with gratitude that I dedicate this paper to her memory.
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    Bulletin of mathematical biology 46 (1984), S. I 
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    Bulletin of mathematical biology 46 (1984), S. 699-744 
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    Notes: Abstract An annotated bibliography of mathematical and computer analyses of protein and nucleic acid sequences is presented. The major subject areas represented are the determination of sequences, restriction mapping, similarity searching, sequence alignment, codon utilization, statistical analysis, information theoretic analysis, the construction of secondary and tertiary structure and DNA topology.
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    Notes: Abstract DISGEO is a new implementation of a distance geometry algorithm which has been specialized for the calculation of macromolecular conformation from distance measurements obtained by two-dimensional nuclear Overhauser enhancement spectroscopy. The improvements include (1) a decomposition of the complete embedding process into two successive, more tractable calculations by the use of “substructures”, (2) a compact data structure for storing incomplete distance information on a structure, (3) a more efficient shortest-path algorithm for computing the triangle inequality limits on all distances from this information, (4) a new algorithm for selecting random metric spaces from within these limits, (5) the use of chirality constraints to obtain good covalent geometry without the use ofad hoc weights or excessive optimization. The utility of the resultant program with nuclear magnetic resonance data is demonstrated by embedding complete spatial structures for the protein basic pancreatic trypsin inhibitor vs all 508 intramolecular, interresidue proton-proton contacts shorter than 4.0 Å that were present in its crystal structure. The crystal structure could be reproduced from this data set to within 1.3 Å minimum root mean square coordinate difference between the backbone atoms. We conclude that the information potentially available from nuclear magnetic resonance experiments in solution is sufficient to define the spatial structure of small proteins.
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    Bulletin of mathematical biology 46 (1984), S. 765-783 
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    Notes: Abstract Recent evidence suggests that the cyclic nucleotides play a central role in the intracellular processing of neural signals. The dynamics of this system may be seen as a realization of the enzymatic neuron model. Enzymatic neurons are formal neurons which map binary afferent signals into patterns of excitation across an abstract membrane. The distribution of enzyme-like elements called excitases enables a set of local threshold functions to determine the firing activity of the neuron. This paper analyzes the basic properties of enzymatic neurons in a simple continuous-time framework, and shows how they may be presented as reaction-diffusion networks which model the cyclic nucleotide system. We present the results of computer simulations of this neuron and discuss its implications for selectional learning and its relation to conventional two-factor systems. One fundamental property of the reaction-diffusion neuron is its so-called “double-dynamics” property; examination of this property and its contribution to the computing power of the neuron provides some insight into the obscure relation between microscopic and macroscopic models of computation.
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    Bulletin of mathematical biology 46 (1984), S. 745-764 
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    Notes: Abstract A model for enzymic catalysis is presented using the mathematical theories of differential geometry and Stieltjes integration. The Stieltjesintegrator is a complex-valued function of bounded variation which represents the curvature and torsion, hence the conformation, of the backbone of an enzyme molecule. Theintegrand is a complex-valued continuous function which describes the shape of the surface of a substrate molecule. We postulate that enzyme-substrate interactions correspond to evaluations of Stieltjes integrals, and that observables of enzymic catalysis correspond to projections. Results from the mathematical theory of the Stieltjes integral are discussed together with their biological interpretations. We contrast the difference between structural and functional proteins, and construct analogues of enzyme cofactors, modifications, and regulation. Various techniques of locating the active site on enzymes are also given. We construct a total variation metric, which is particularly useful for detecting similarities among proteins. An examination on the many different modes of convergence of mathematical functions representing biological molecules leads to a mathematical statement of the fundamental dogma of molecular biology, that ‘structure implies function’. Similar arguments also result in the converse statement ‘function dictates structure’, which is a basic premise of relational biology. Stepped-helical approximations of the backbone space curves of enzymes provide a concrete computational tool with which to calculate the Stieltjes integrals that model enzymic catalysis, by replacing the integral with a finite series. The duality between enzymes and substrates (that they aremeters ‘observing’ one another) is shown to be a consequence of the mathematical duality of Banach spaces. The Stieltjes integrals of enzyme-substrate interactions are hence shown to be bounded bilinear functionals. The mechanism of enzymic catalysis, the transformation from substrate to product, is also formulated in the Stieltjes integration context via the mathematical theory of adjoints. The paper closes with suggestions for generalizations, prospects for future studies, and a review of the correspondence between mathematical and biological concepts.
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    Bulletin of mathematical biology 46 (1984), S. 785-825 
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    Notes: Abstract An earlier theory of cell differentiation and morphogenesis (Wassermann, 1972, 1973, 1978) is combined with the genetic control model of Davidson and Britten (e.g. 1979). The resulting new theory suggests how, bysystematic process algorithms, specifically enumerated combinations of batteries of structural genes can become switched on in particularly enumerated cells, via battery-specific enumerable regulator genes. The systematization is idealized. Up to a certain stage of development in each mitotically arising cell a unique cell-specific combination of structural genes called ‘marker genes’ is active. Marker genes are assumed to code for cell-specifying marker proteins (CSMPs) which permit cells carrying related markers to recognize each other, thus permitting specific cell sorting.Batteries of marker genes could ensure great developmental precision and can safeguard—via redundancies of CSMP types—against accidental loss or detrimental mutational modification of CSMPs or marker genes, respectively. This paper is much concerned with cell lineage in relation to ‘microdifferentiation’, where ‘microdifferentiation’ of a cell refers to a cell's active marker genes and its syntheses of CSMPs. A drastic distinction is made between ‘microdifferentiation’ and ‘gross’ differentiation of a cell, where the same ‘gross’ differentiation may be shared by a large number of cells that could each be uniquely ‘microdifferentiated’. Typical ‘gross’ differentiation could manifest itself in tissue specificity, whereas, up to certain stages of development, all cells of the same gross differentiation type (say tissue specificity) could each be uniquely ‘microdifferentiated’. The theory also assumes that at certain stages of the developmental process some (or in some organisms all) of the previously uniquely specified cells could give rise to small (or occasionally large) clones of equispecified cells, some of which might form clusters that represent complete ‘morphogenetic fields’ Tentative implementation mechanisms are proposed which suggest how the theory could operate in molecular biological terms. In particular, CSMPs could endow cell surface membranes with a highly specific protein network, and an associated equally specific cell surface coat. It is suggested how these highly specified cell surface coats and other systems could provide an ‘extracellular guidance network’ which could help to direct cells to attain energetically optimal locations relative to each other based on the matching of their surface specificities. In numerous experimental situations, where normally present optimal matching of cells is excluded, ‘alternative matching’ based on experiment-specific suboptimal matching could explain many data, notably in experimental development neurobiology (Wassermann, 1978).
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    Bulletin of mathematical biology 46 (1984), S. 859-868 
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    Notes: Abstract Two equations describing one-dimensional food chains are known to possess soliton solutions. It is demonstrated that both equations are embraced within another equation, which arises in the theory of chains of enzymic reactions. We find an elliptic function solution to this equation. We obtain a one-soliton solution from it and re-derive the elliptic function solutions of the two ecological equations.
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    Bulletin of mathematical biology 46 (1984), S. 879-889 
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    Topics: Biology , Mathematics
    Notes: Abstract The temperature distribution in a perfused biological tissue is calculated for an instaneous point source. An approximate solution, which is simple enough to be evaluated by means of a hand calculator, is derived from the exact solution. It is expressed in terms of the deviation from an average temperature distribution. In an example, using realistic parameters for blood flow and thermal properties of tissue, the approximate solution differs at most 2% from the exact one.
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    Bulletin of mathematical biology 46 (1984), S. 891-901 
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    Notes: Abstract A simple model for the introduction of a cannibalistic mutant into a noncannibalistic population (or vice versa) is developed for the case where the offspring of an adult are clumped. It is assumed that there is no difference between the cannibals and noncannibals except for eating habits. Conditions on the parameters specifying the population are derived such that noncannibalism is favored over cannibalism when these conditions are satisfied. Specifically, it is shown that noncannibalism is favored in a diffuse, highly clumped population if the probability of encountering one cannibal after another is greater than twice the probability of encountering a cannibal after encountering a noncannibal.
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    Bulletin of mathematical biology 46 (1984), S. 923-935 
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    Notes: Abstract In the field of numerical taxonomy it is often desirable to determine a tree which is the consensus (common part) of severaln-trees, each of which represents a classification of the same set of objects. In this note, ans-consensus tree and corresponding consensus index for a collection ofn-trees are defined. The choice of a value for the parameters will determine the number of nodes in thes-consensus tree and its tendency to resemble the strict or Adams-consensus tree.
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    Bulletin of mathematical biology 46 (1984), S. 903-922 
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    Notes: Abstract The convulsant pentylenetetrazol (PTZ) was used to trigger spike bursts and paroxysmal discharges inAplysia neurons. Voltage clamp experiments showed that PTZ induced a slow voltage-dependent potassium current and a persistent inward current. These currents are incorporated into a membrane model together with modified spike-generating Hodgkin-Huxley equations. From these data a metaphoric model is constructed and represented by a slow-fast dynamical system defined inR 4. With some values of the main physiological parameters, the system might have limit cycles for the fast dynamic. A qualitative study of the system shows that it satisfactorily reproduces the various observed patterns produced by PTZ.
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    Bulletin of mathematical biology 46 (1984), S. 951-961 
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    Notes: Abstract Monte Carlo data on the comparison of a short sequence with a long one are developed in a manner to quantify the occurrence of gaps.
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    Bulletin of mathematical biology 46 (1984), S. 937-949 
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    Notes: Abstract The present study deals with the effect of a single cycle of body accelerations on blood flow in arteries. Such body accelerations are usually caused unintentionally, for example during travel in road vehicles, aircraft or spacecraft. A mathematical model of flow in single arteries subject to a pulsating pressure gradient due to the normal heart action as well as body acceleration expressible in terms of unit functions is presented. The body acceleration is such that it builds up from zero to a maximum value at a uniform rate, remains constant at the maximum value for some time, and thereafter reduces to zero at a uniform rate. The resulting equations are solved by using the technique of Laplace transforms. Computational results are presented for the effects of body accelerations on flow variables namely flow rate, velocity of flow, acceleration and shear stress corresponding to blood flow in the human aorta.
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    Bulletin of mathematical biology 46 (1984), S. 963-965 
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    Notes: Abstract It is shown that a biological population or subpopulation composed ofN individuals can be governed by a generalized Verhulst logistic equation with time-dependent rate functions if and only if certain characterizing conditions are satisfied by ∂N/∂N 0 whereN 0 is the value ofN att=0.
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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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    Circuits, systems and signal processing 3 (1984), S. 373-383 
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    Notes: Abstract The definitions and properties of various ideals of a nest algebra are reviewed. These correspond to strengthenings of the concept of causality. The interrelationships between these concepts are examined. An open question concerning these ideals is settled, namely that the strongly strictly causal operators form the largest of the classes commonly considered.
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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 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 3 (1984), S. 3-20 
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    Notes: Abstract A class of efficient filter structures is proposed which uses a recursive realization of an FIR filter. The structures are in some sense a generalization of the frequency sampling structure, but they are more versatile and arise from a time-domain rather than frequency-domain argument. The new structure has a tap out of every block delay, and the length of the block delay is the length of each piecewise section of the time-domain approximation. The number of taps, filter coefficients, and the amount of arithmetic are proportional to the number of piecewise sections, not to the actual filter length or order. This filter is particularly efficient when a long-length filter can be approximated by a few piecewise sections, which is the case for many practical filters.
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    Circuits, systems and signal processing 3 (1984), S. 127-127 
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    Circuits, systems and signal processing 3 (1984), S. 139-160 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper introduces a new iterative image restoration method which is capable of restoring noisy blurred images by incorporatinga priori knowledge about the image and noise statistics into the iterative procedure. The iteration equation consists of a prediction part which is based on a noncausal image model description and an innovation part which is weighted by a gain factor. The gain is computed using a linear MSE optimization procedure and is updated at each step of the iteration. The convergence of the algorithm, the resolution of some convergence difficulties by using “reblurring,” and methods for the introduction of physical constraints will be discussed. This image restoration scheme can be interpreted as an iterative procedure with a statistical constraint on the image data. Results of several experiments with noisy blurred data are presented to demonstrate the feasibility of this approach.
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    Circuits, systems and signal processing 3 (1984), S. 361-371 
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    Circuits, systems and signal processing 3 (1984), S. 387-408 
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    Notes: Abstract Fast decimation-in-time (DIT) algorithms for the various discrete cosine transforms (DCT) and discrete sine transforms (DST) are systematically developed, based on a radix-2 factorization of the transformation matrix. The results indicate these to be attractive alternatives to existing algorithms in terms of computational complexity and structural simplicity.
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    Circuits, systems and signal processing 3 (1984), S. 435-445 
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    Notes: Abstract The circuit-simulator program SPICE has been used worldwide by industry and academia to simulate wide varieties of IC designs. With the advance of technology have come many new devices that cannot be simulated by SPICE in its current form. We present methods for implementing classes of new DC device models directly into the source code of SPICE. The techniques described are illustrated for the case of the El-Mansy MOSFET model.
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    Circuits, systems and signal processing 3 (1984), S. 493-503 
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    Notes: Abstract We consider the discrete-time detection of a known time-varying deterministic signal in white noise, where the univariate noise density is known perfectly only on an interval about the origin. We present a method to enhance the asymptotic performance of the detector by exploiting this knowledge, and at the same time preserve robustness properties of the detector to the remaining inexact knowledge of the univariate noise density. We then provide examples to show that improved performance is indeed obtained.
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    Circuits, systems and signal processing 3 (1984), S. 79-104 
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    Notes: Abstract This paper reviews and compares different special transfer functions, of nonminimum order, characterized by low poleQ's and high selectivity. These functions extend the use of the cascade configuration, employing standard low-order sections implemented by active devices, to selective filters.
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    Circuits, systems and signal processing 3 (1984), S. 21-57 
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    Notes: Abstract Recursive filter structures have been found for FIR filters with piecewisepolynomial or piecewise-(polynomial · sinusoid) impulse responses. The amount of arithmetic required for these filters is proportional to the number of piecewise sections in their impulse responses rather than the actual filter lengths. In this paper, it is shown that these impulse response expressions are quite good approximations to many practical filters. Low-pass filters, high-pass filters, narrowband, band-pass, and band-stop filters, Hilbert transformers, and differentiators all have impulse responses which can be approximated by these forms, and a long filter impulse response consists of only a few piecewise sections with greatly reduced arithmetic requirements. Though this technique is based on time-domain approximation, a frequency-domain optimization to select filter parameters is presented with excellent results.
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    Circuits, systems and signal processing 3 (1984), S. 193-206 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The factorization of two-dimensional spectral functions is a problem of interest in the digital processing of signals because of the nonexistence of a fundamental theorem of algebra for bivariate polynomials. In this paper we consider the special case of rational spectral functions, which are quotients of polynomials or pseudo-polynomials of finite order. We first characterize the general use of asymmetric halfplane factors, and then propose recursive procedures to obtain the factors. In the case of strictly positive spectral functions, we use the homomorphic transform to characterize the causal factor by its first-order data and then apply the modified leastsquares approximation to obtain the rational factors. For those cases of partially characterized spectral functions, we propose extensions of one-dimensional procedures. These alternative procedures are based on the modified least-squares approximation as well as on the two-dimensional Levinson algorithm. All the procedures presented are recursive, thus computationally efficient, and guarantee the stability of the factors in most cases.
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    Circuits, systems and signal processing 3 (1984), S. 225-242 
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    Notes: Abstract Tests for the discrete scattering Hurwitz property of two-dimensional (2-D) polynomials are suggested. Results belonging to two different categories are presented. The first procedure uses a finite number of rational operations and relies on the so-called polynomial resultant algebra. Alternative methods of testing, which are computationally less complex to implement are also developed.
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    Circuits, systems and signal processing 3 (1984), S. 207-223 
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    Notes: Abstract This paper investigates the properties of the two-variable polynomialu (λ, z) built on the first column of the adjoint matrix ofλI -C, whereC is a given Hermitian Toeplitz matrix. In particular, the stability properties ofu (λ,z) are discussed and are shown to depend essentially on the location of X with respect to the eigenvalues ofC. The eigenvectors ofC, which have recently found some applications in signal processing and estimation theory, are obtained from the polynomialu(λ,z) whenλ tends to the eigenvalues ofC. This allows one to derive several results concerning the eigenpolynomials, including those for the case of multiple eigenvalues.
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    Circuits, systems and signal processing 3 (1984), S. 243-264 
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    Notes: Abstract A general-purpose interactive computer program for the design of linear causal shift-invariant two-dimensional recursive filters is presented in terms of its organization and operation. Narrow-band fan filters and circularly symmetric low-pass and high-pass filters for many useful image-processing applications can be designed using this program. The design is by numerical optimization of a guaranteedstable analog transfer function which is derived from a general two-dimensional passive prototype network. Corresponding discrete transfer functions are obtained by the double bilinear transformation. In using the program, selection of one code from a menu of predefined design codes provides the designer with various design features; these include the use of a doubly-terminated network to eliminate erroneous gain spikes, the use of a network particularly suited to circularly symmetric functions, and a facility for designing filters potentially useful for high-speed parallel processing. Design examples of a low-order highly selective fan filter and a circularly symmetric low-pass filter are included.
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    Circuits, systems and signal processing 3 (1984), S. 327-346 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The implementation of the Lin model for the non pinchoff depletion mode MOSFETs directly into the source code of the SPICE 2G.5 circuit simulation program is described. The computational advantages of our implementation over Lin's subcircuit approach are pointed out, and, more significantly, certain previously undiscovered limitations of both methods are discussed. The encoding of the model into SPICE is described in sufficient detail so as to be duplicable by other interested researchers. Our results compare favorably to experiment and to the more comprehensive El-Mansy model. Finally, a new method of parameter extraction is described for the El-Mansy model, which makes it possible to derive the parameters of the Lin and El-Mansy models simultaneously.
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    Circuits, systems and signal processing 3 (1984), S. 419-434 
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    Notes: Abstract The roundoff noise problem for multirate digital filters is difficult because rate changing inside the filter makes both scaling and roundoff noise calculation complicated. With a new multirate filter analysis technique, the transfer function between any two points inside a multirate filter can be easily found, thus, simplifies the scaling and noise calculation. This paper finds theL P scaling and derives the roundoff noise expressions for fixed point implementations of the multistage decimator, interpolator, and multirate narrow-band low-pass filter. It is shown that the noise source at a low sampling rate stage is more important than that at a higher sampling rate stage. Methods to reduce output roundoff noise are discussed.
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    Circuits, systems and signal processing 3 (1984), S. 477-491 
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    Notes: Abstract A relation between the types of symmetries that exist in signal and Fourier transform domain representations is derived for continuous as well as discrete domain signals. The symmetry is expressed by a set of parameters, and the relations derived in this paper will help to find the parameters of a symmetry in the signal or transform domain resulting from a given symmetry in the transform or signal domain respectively. A duality among the relations governing the conversion of the parameters of symmetry in the two domains is also brought to light. The application of the relations is illustrated by a number of two-dimensional examples.
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