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  • Springer  (197,312)
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  • American Meteorological Society
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  • 1940-1944  (5,473)
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  • 1995-1999  (74,455)
  • 1990-1994  (157,186)
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  • 1
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 137-144 
    ISSN: 1476-5535
    Keywords: Composting ; Explosives ; Propellants ; Thermophilic ; Mesophilic ; Bioremediation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Composting was investigated as a bioremediation technology for clean-up of sediments contaminated with explosives and propellants. Two field demonstrations were conducted, the first using 2,4,6-trinitrotoluene (TNT), octahydro-1,3,5,7-tetranitro-1,3,5,7-tetraazocine (HMX), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and N-methyl-N,2,4,6-tetranitroaniline (tetryl) contaminated sediment, and the second using nitrocellulose (NC) contaminated soil. Tests were conducted in thermophilic and mesophilic aerated static piles. Extractable TNT was reduced from 11840 mg/kg to 3 mg/kg, and NC from 13090 mg/kg to 16 mg/kg under thermophilic conditions. Under mesophilic conditions, TNT was reduced from 11 190 mg/kg to 50 mg/kg. The thermophilic and mesophilic half-lives were 11.9 and 21.9 days for TNT, 17.3 and 30.1 days for RDX, and 22.8 and 42.0 days for HMX, respectively. Known nitroaromatic transformation products increased in concentration over the first several weeks of the test period, but decreased to low concentrations thereafter.
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  • 2
    ISSN: 1476-5535
    Keywords: Fructo-oligosaccharide ; 1-Kestose ; Glycoprotein ; Fructosyl-transferring activity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Two extracellular β-fructofuranosidases (E-1 andE-2) fromAureobasidium sp. ATCC 20524, producing 1-kestose (1F-β-fructofuranosyl-sucrose) from sucrose, were purified to homogeneity. Molecular weights of the enzymes were estimated to be about 304000 (E-1) and 315000 (E-2) Da by gel filtration. The enzymes contained 33% (w/w) (E-1) and 27% (w/w) (E-2) carbohydrate. TheK m values for sucrose ofE-1 andE-2 andE-2 were 0.34 and 0.28 M, respectively. were 0.34 and 0.28 M, respectively. The enzymatic profiles of these enzymes were almost identical to intracellular enzymesP-1 andP-2 except for the differences in carbohydrate content andK m values ofE-2 andP-2.
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  • 3
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 149-161 
    ISSN: 1476-5535
    Keywords: Toxin ; Secondary plant metabolite ; Allelochemical ; Insecticide ; Mycotoxin ; Endocytobiont
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Many species of insects cultivate, inoculate, or contain symbiotic fungi. Insects feed on plant materials that contain plant-produced defensive toxins, or are exposed to insecticides or other pesticides when they become economically important pests. Therefore, it is likely that the symbiotic fungi are also exposed to these toxins and may actually contribute to detoxification of these compounds. Fungi associated with bark beetles, ambrosia beetles, termites, leaf-cutting ants, long-horned beetles, wood wasps, and drug store beetles can variously metabolize/detoxify tannins, lignins, terpenes, esters, chlorinated hydrocarbons, and other toxins. The fungi (Attamyces) cultivated by the ants and the yeast (Symbiotaphrina) contained in the cigarette beetle gut appear to have broad-spectrum detoxifying abilities. The present limiting factor for using many of these fungi for large scale detoxification of, for example, contaminated soils or agricultural commodities is their slow growth rate, but conventional strain selection techniques or biotechnological approaches should overcome this problem.
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  • 4
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 163-172 
    ISSN: 1476-5535
    Keywords: Biosensors ; Process control ; Enzyme thermistor ; Immunoassay ; Bio-field effect transistor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A short review about the biosensor research activities for bioprocess monitoring in the F.R.G. after its reunification is given. The principles of biosensor applications are presented. In situ sensors and sensors based on the principles of flow injection analysis are studied. Some applications of a four-channel enzyme thermistor, bio-field effect transistors, and immunoanalysis systems for real process monitoring are presented.
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  • 5
    ISSN: 1476-5535
    Keywords: Vibrio vulnificus ; Oyster ; Monoclonal antibody ; Most probable number ; Enzyme immunoassay
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Oysters, suspended particulate matter (SPM), sediment and seawater samples were collected from West Galveston Bay, Texas over a 16-month period and analyzed for the presence ofVibrio vulnificus, a naturally-occurring human marine pathogen. Detection and enumeration ofV. vulnificus was performed using a species-specific monoclonal antibody (mAb FRBT37) in an enzyme immunoassay (EIA)-most probable number (MPN) procedure capable of detecting as few as 2000 target organisms.V. vulnificus was not detected in seawater, oyster or SPM samples during the cold weather months, but was detected at low levels in several sediment samples during this time period. Increased levels of the organism were first observed in early spring in the sediment, and then in SPM and oysters. The major increase inV. vulnificus occurred only after the seawater temperature had increased above 20°C and the winter-spring rainfall had lowered the salinity below 16‰. The highestV. vulnificus levels at each site were associated with suspended particulate matter. These results are consistent with the hypothesis that (1)V. vulnificus over-winters in a floc zone present at the sediment-water interface, (2) is resuspended into the water column in early spring following changes in climatic conditions, (3) colonizes the surfaces of zooplankton which are also blooming during early spring and (4) are ingested by oysters during their normal feeding process.
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  • 6
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 235-238 
    ISSN: 1476-5535
    Keywords: Biodegradation ; Pseudomonas putida ; Immobilization ; Sodium cyanide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Pseudomonas putida, isolated from contaminated industrial wastewaters and soil sites, was found to utilize sodium cyanide (NaCN) as a sole source of carbon and nitrogen. Cells, immobilized in calcium alginate beads (1–2 mm diameter) were aerated in air-uplift-type fluidized batch bioreactor containing 100–400 ppm of NaCN. Degradation of NaCN was monitored for 168 h by analyzing gaseous and dissolved ammonia (NH3), CO2, pH and optical density. The results indicated that the alginate-immobilized cells ofP. putida were able to degrade NaCN into NH3 and CO2 in a time-dependent manner.
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  • 7
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 229-234 
    ISSN: 1476-5535
    Keywords: Heat shock protein (HSP) ; Yeast ; Saccharomyces ; Viability ; Thermotolerance ; Ethanol tolerance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Heat shock and ethanol stress of brewing yeast strains resulted in the induction of a set of proteins referred to as heat shock proteins (HSPs). At least six strongly induced HSPs were identified in a lager brewing strain and four HSPs in an ale brewing strain. Four of these HSPs with molecular masses of approximately 70, 38, 26 and 23 kDa were also identified in two laboratory strains ofSaccharomyces cerevisiae. The appearance of HSPs correlated with increased survival of strains at elevated temperatures and high concentrations of ethanol. These results suggest that HSPs may play a role in the ethanol and thermotolerance of yeasts. The properties of these proteins and membrane fatty acids in relation to heat and ethanol shock are being investigated.
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  • 8
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 239-245 
    ISSN: 1476-5535
    Keywords: Novel polysaccharide ; Bacillus licheniformis ; Raffia venifera ; d-Glucose ; d-Mannose ; d-Xylose
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A polysaccharide producing strain ofBacillus licheniformis was isolated from exudate of raffia palm,Raffia vinifera. The optimum conditions for growth and polysaccharide production have been investigated and established. No appreciable polysaccharide was formed on glucose. It grew best in Czapek-Dox media with sucrose as the carbon source. The polysaccharide has been characterized as a heteropolymer containingd-glucose,d-mannose andd-xylose.
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  • 9
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 269-269 
    ISSN: 1476-5535
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 10
    ISSN: 1476-5535
    Keywords: β-Fructofuranosidase ; Deglycosylation ; Aureobasidium ; Enzymatic stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Most of the carbohydrate moiety of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 was removed by endo-β-N-acetylglucosaminidase F. A subunit of 94000 Da was observed in SDS-PAGE after deglycosylation. TheK m value for sucrose was not changed by deglycosylation but the stability at pH 4–5 and 50°C was decreased. The deglycosylated enzyme was more sensitive to proteases such as pronase E and subtilisin than the native enzyme. It is considered that the carbohydrate moiety of β-fructofuranosidaseP-1 contributes to the stability of the enzyme but is not essential in its catalytic function.
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  • 11
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    Bulletin of mathematical biology 54 (1992), S. 1-20 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An organism persists only if it satisfies internal and external constraints. Within the organism networks of processes meet the constraints. In such networks a principle of matching often obtains: the pattern of coupling among processes matches the correlation among constraints. That is, a module—a cluster of coupled processes—meets a constraint. Dissociable modules meet dissociàble constraints. A hierarchy of modules meets a hierarchy of constraints. We have inquired whether such matching is predicted by an optimality criterion in a simple example. We find that in an ensemble of networks with unreliable processes, the networks that meet the constraints with highest reliability obey the principle of matching. The difference in reliability between modular and nonmodular networks that meet the same constraints is a function of the probability of success per process. Our results suggest that this difference is maximal at a probability of success that increases monotonically with the number of processes in the network.
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  • 12
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    Bulletin of mathematical biology 54 (1992), S. 59-75 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A method is described for estimating the distribution and hence testing the statistical significance of sequence similarity scores obtained during a data-bank search. Maximum-likelihood is used to fit a model to the scores, avoiding any costly simulation of random sequences. The method is applied in detail to the Smith-Waterman algorithm when gaps are allowed, and is shown to give results very similar to those obtained by simulation.
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  • 13
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    Bulletin of mathematical biology 54 (1992), S. 401-412 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We develop a theory for host seeking decisions in mosquitoes that explicitly considers the tradeoffs mosquitoes face in allocation to somatic and gametic function. Specifically, we consider conditions under which mosquitoes should seek out nectar and blood hosts upon encountering host odours. Results from development of a dynamic model that considers free and crop energy states suggest that mosquitoes should seek out blood hosts under a wide variety of conditions but that decisions to seek nectar depends upon crop volume, concentration and free energy. This pattern arises because mosquitoes carrying large crop loads are constrained in their ability to obtain large blood meals due to space limitations in the abdomen. The predicted patterns of behaviour are supported by published observations of mosquito behaviour.
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  • 14
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    Bulletin of mathematical biology 54 (1992), S. 413-422 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In behavioral ecology, diet selection is often predicted by using a theory in which it is assumed that behaviors have evolved to maximize the rate of intake of energy. In this theory, it is assumed that fitness is a monotonic function of energy intake. An alternative is to deal directly with fitness, measured in terms of expected reproduction, and thus connect short term behavior with reproduction. Following the usual assumptions of the theory of diet choice, fitness satisfies a partial differential-difference equation. Conditions under which rate maximizing and state variable theories of diet selection yield identical predictions are identified. When predation, as well as starvation, is a source of mortality, the identification is not as complete.
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  • 15
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    Bulletin of mathematical biology 54 (1992), S. 445-464 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Environmental uncertainty can be both a cause and consequence of chance variation in many of the phenotypic factors associated with the control of clutch size in birds. When such uncertainty inflates or otherwise influences the variance associated with expected reproductive success for any genotype, it will also influence the resulting phenotypic optima. Random variation that affects the evolution of clutch size optima explicitly may occur both within (intra-) and across (inter-) generations. Examples of intra-generational uncertainty could include chance variation in: (1) the quality and quantity of offspring, (2) parental quality, and (3) temporal resources like food. Inter-generational uncertainty would include chance variation in demographic and population characters. With respect to clutch (or litter) size, almost all forms of uncertainty tend to favor an optimum (genetic) strategy with a clutch that is smaller than the clutch associated with the apparent or actual maximal fitness of an individual parent. The overall effect of all the components of uncertainty can be evaluated through the integration of all this phenotypic variation: however each step of the integration is a conditional expectation of each component. Therefore, a single factor analysis may indicate a false optimum, and an integrated analysis of all components is necessary to evaluate the importance of their individual and joint effects on the adaptive evolution of clutch size.
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  • 16
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    Bulletin of mathematical biology 54 (1992), S. 503-519 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A difference equation model for the dynamics of a semelparous size-structured species consisting of juvenile and adult individuals is derived and studied. The adult population consists of two size classes, a smaller class and a larger more fertile class. Negative feedback occurs through slowed juvenile growth due to increased total population levels during the developmental period and consequently a smaller adult size at maturation. Intra-specific competition coefficients are size dependent and measure the strength of intra-specific competition between juveniles and adults. It is shown that equilibrium states in which adults and juveniles occur together at all times are in general destabilized by significantly increased juvenilevs adults competition with the result that stable periodic cycles appear, in which the generations alternate in time and hence avoid competition. This result supports the tenet that intra-specific competition between juveniles and adults is destabilizing. Exceptions to this destabilization principle are found, however, in which populations exhibiting non-equilibrium, aperiodic dynamics can be equilibrated by increase competition between juveniles and adults. This occurs, for example, when adult fertility and competition coefficients are significantly size class dependent.
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  • 17
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    Bulletin of mathematical biology 54 (1992), S. 537-561 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a previously developed model of the toad urinary bladder (Strieteret al., 1990,J. gen. Physiol. 96, 319–344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified model of the epithelium of the thick ascending limb of Henle.
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  • 18
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    Bulletin of mathematical biology 54 (1992), S. 687-694 
    ISSN: 1522-9602
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  • 19
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    Bulletin of mathematical biology 54 (1992), S. 649-672 
    ISSN: 1522-9602
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    Notes: Abstract Models of the dynamical interactions important in generating immune reactivity have generally assumed that the immune system is a single well-stirred compartment. Here we explicitly take into account the compartmentalized nature of the immune system and show that qualitative conclusions, such as the stability of the immune steady state, depend on architectural details. We examine a simple model idiotypic network involving only two types of B cells and antibody molecules. We show, for model parameters used by De Boeret al. (1990,Chem. Eng. Sci. 45, 2375–2382), that the immune steady state is unstable in a one compartmental model but stable in a two compartment model that contains both a lymphoid organ, such as the spleen, and the circulatory system.
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  • 20
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    Bulletin of mathematical biology 54 (1992), S. 839-873 
    ISSN: 1522-9602
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    Notes: Abstract Using the chromium release assay and the single cell assay in agarose, we study the cytotoxic reaction of the MHC-restricted T lymphocyte clones P89:15 and P1:3, which recognize distinct but specific tumour antigens on the surface of syngeneic P815 mastocytoma cells. We propose a mathematical model which describes these experiments, accounts for the strongly non-Michaelian behaviour of the reaction and permits us to estimate the kinetic parameters characterizing effector-target conjugation and lethal hit delivery. The results show that the binding and lytic activity of effector cells is modulated by the number of targets bound to them. The binding of a second target by an effector having already a target bound is facilitated; on the other hand, an effector having bound two targets delivers a lethal hit more slowly than one with a single target bound. We investigate the role of these kinetic properties in the competition between the process of tumour progression due to cancer cell replication and the process of tumour regression due to T lymphocyte cytotoxic activity. For both clones, we estimate the effector-target ratio beyond which rejection prevails. This ratio is nine times larger for P1:3 than for P89:15. Furthermore, our analysis suggests that there exists an optimal specificity minimizing this ratio. Deviations from this optimum, be it in the sense of an increase or decrease of specificity, tendsto stabilize the tumoural state: a situation which in the broader context of the immune response evolution and regulation can be viewed as animmune response dilemma.
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  • 21
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    Bulletin of mathematical biology 54 (1992), S. 929-938 
    ISSN: 1522-9602
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    Notes: Abstract In this paper a stochastic model for a two-compartment system which incorporates Erlang residence time distributions (i.e. the residence times have the gamma distribution where the shape parameters assume integer values only) into each compartment is generalized to include random rate coefficients. Analytical forms of the model are derived for the case where the rate coefficients have gamma densities. A relationship is established between the new models and existing models that are in current practical usage.
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  • 22
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    Bulletin of mathematical biology 54 (1992), S. 939-955 
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    Notes: Abstract Oscillations and chaos can be modelled and observed in a realistic simulation model of interacting prey-predator populations based on Monte Carlo simulation methods. These nonlinear phenomena are linked with some biological and physical bifurcation parameters and mathematical tools from dynamical systems theory may be used in order to characterize this behaviour. Chaotic dynamics are therefore, in our simulation, more the rule than the exception, and are related to delays associated with spatial degrees of freedom.
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  • 23
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    Bulletin of mathematical biology 54 (1992), S. 1023-1038 
    ISSN: 1522-9602
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    Notes: Abstract Cells displaying the classic multidrug resistant (MDR) phenotype possess a transmembrane protein (p170 or P-glycoprotein) which can actively extrude cytotoxic agents from the cytoplasm. A mathematical model of this drug efflux pump has been developed. Outward transport is modeled as a facilitated diffusion process. Since energy-dependent efflux of cytotoxic agents requires that ATP also bind to p170, the model includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP. The final system consists of one partial differential equation (PDE) for the facilitated diffusion of substrate agents out of the cell a 2×2 ordinary differential equation (ODE) system for the dynamic calculation of the ATP-ADP pool, and a dynamic algebraic calculation of the efflux rate given substrate levels at the interior cell membrane interface and ATP levels in the cell. A stability analysis of the ATP-ADP pool distribution and a simplistic closed form solution of the linearized PDE are included. Numerical simulations are also provided.
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    Bulletin of mathematical biology 54 (1992), S. 1039-1056 
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    Notes: Abstract Reentry in the heart is the repeated excitation of the same tissue by a single excitation wave; it is responsible for several types of cardiac arrhythmia. The simplest model which permits the phenomenon of reentry is two laterally coupled excitable fibers; in this paper we examine such a model in order to establish a basis for the understanding of the fundamental physical processes underlying the process of reentry. Two versions of the FitzHugh-Nagumo equations are used to develop complementary numerical and analytical results for the coupled fiber model. On the basis of numerical studies, regions of qualitatively different behaviour are mapped in the parameter space of excitation threshold and coupling strength between the fibers, and the effect of the rate of recovery is explored. Some of these regions are also obtained analytically, in good agreement with the numerical results. Finally, the results are discussed in the light of recent work on the role of the anisotropy of cardiac tissue in the initiation of reentrant activity in the heart.
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    Bulletin of mathematical biology 54 (1992), S. 1069-1081 
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    Notes: Abstract A sigmoid curve with three fitting parameters is proposed as a descriptive model for the spatial velocity field in one-dimensional growth of plant organs. Analytic expressions are derived for the relative elemental growth (REG) rate, the position and value of the REG rate maximum, the length of the growth zone, the inverse of the growth trajectory and cell length in the “elongation only” zone. The expressions are fit to published data to characterize the effects of environmental variation on growth of monocotyledonous roots. The simple expressions for growth may prove useful in mechanistic models. The fitted curves summarize more than a decade of observations and thus provide a challenge to theorists.
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    Bulletin of mathematical biology 55 (1993), S. 1-13 
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    Notes: Abstract A simple one-dimensional model of single-species populations is studied by means of computer simulations. Although the model has a rich spectrum of dynamics including chaotic behavior, the introduction of survival thresholds makes the chaotic region so small that it can be hardly observed. Stochastic fluctuations further reduce the chaotic region because they accidentally lead populations to extinction. The model thus naturally explains the observation that the majority of natural populations do not show chaotic behavior but a monotonic return to a stable equilibrium point following a disturbance.
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    Notes: Abstract Current understanding of the pattern of proliferation within intestinal crypts involves the notion of a cutoff region introduced by Cairnieet al. (Exp. Cell. Res. 39, 539–553, 1965b). (Cells produced above the cutoff are non-cycling, whereas cells produced below the cutoff are cycling.) They contrasted the predicted distribution of proliferation in the extreme cases of a cutoff of width 0 (a sharp cutoff) with one eight cells wide (a slow cutoff) and concluded that the data were better explained by the latter. We have shown that crypt size variation artificially broadens the apparent distribution of proliferating cells in the crypt (Totafurnoet al., Biophys. J. 54, 845–858, 1988). Here we show that the measurement and analysis of crypts of a specified height reduces this artifact. This work introduces the use of distance from the crypt base (in microns) to specify the location of cells within the crypt as an improvement over the cell position ordering traditionally used in the determination of the distribution of proliferating cells. We also show how to explicitly correct for several artifacts in the measurement of the labelling index. We conclude that cell proliferation within the crypt is more localized than previously realized; in fact, a cutoff as slow as eight cells wide is rejected.
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    Bulletin of mathematical biology 55 (1993), S. 141-154 
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    Notes: Abstract Multiple string (sequence) alignment is a difficult and important problem in computational biology, where it is central in two related tasks: finding highly conserved subregions or embedded patterns of a set of biological sequences (strings of DNA, RNA or amino acids), and inferring the evolutionary history of a set of taxa from their associated biological sequences. Several precise measures have been proposed for evaluating the goodness of a multiple alignment, but no efficient methods are known which compute the optimal alignment for any of these measures in any but small cases. In this paper, we consider two previously proposed measures, and given two computationaly efficient multiple alignment methods (one for each measure) whose deviation from the optimal value isguaranteed to be less than a factor of two. This is the novel feature of these methods, but the methods have additional virtues as well. For both methods, the guaranteed bounds are much smaller than two when the number of strings is small (1.33 for three strings of any length); for one of the methods we give a related randomized method which is much faster and which gives, with high probability, multiple alignments with fairly small error bounds; and for the other measure, the method given yields a non-obviouslower bound on the value of the optimal alignment.
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    Bulletin of mathematical biology 55 (1993), S. 197-212 
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    Notes: Abstract The kinematics of helical motion are descirbed for an organism treated as a rigid body with six degrees of freedom relative to the organism's frame of reference, i.e. the organism can translate in the direction of, or rotate around any of, three orthogonal axes fixed to its body. Equations are derived that express the unit vectors of the Frenet trihedron and the torsion and curvature of the trajectory in terms of the organism's translational and rotational velocities. These equations permit description of the radius, pitch, angular velocity and axis of a helical trajectory in terms of the translational and rotational velocities of the organism swimming along that trajectory. The results of this analysis are then used in two later papers that describe how organisms can orient to an external stimulus.
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    Bulletin of mathematical biology 55 (1993), S. 257-257 
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    Bulletin of mathematical biology 55 (1993), S. 231-255 
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    Notes: Abstract Organisms that move along helical trajectories change their net direction of motion largely by changing the direction, with respect to the body of the organism, of their rotational velocity (Crenshaw and Edelstein-Keshet, 1993,Bull. math. Biol. 55, 213–230). This paper demonstrates that an organism orients to a stimulus field, such as a chemical concentration gradient or a ray of light, if the components of its rotational velocity, with respect to the, body of the organism, are simple functions of the stimulus intensity encountered by the organism. For example, an organism can orient to a chemical concentration gradient if the rate at which it rotates around its anterior-posterior axis is proportional to the chemical concentration it encounters. Such an orientation can be either positive or negative. Furthermore, it is true taxis—orientation of the axis of helical motion is direct. It is neither a kinesis nor a phobic response—there is no random component to this mechanism of orientation.
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    Bulletin of mathematical biology 55 (1993), S. 277-294 
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    Notes: Abstract A basic but neglected property of neuronal trees is their finite length. This finite length restricts the length of a segment to a certain maximum. The implications of the finite length of the tree with respect to the segment length distributions of terminal and intermediate segments are shown by means of a stochastic model. In the model it is assumed that branching is governed by a Poisson process. The model shows that terminal segments are expected to be longer than intermediate segments. Terminal and intermediate segments are expected to decrease in length with incrasing centrifugal order. The results are compared with data fromin vivo pyramidal cells from rat brain and tissue cultured ganglion cells from chicken. A good agreement between data and model was found.
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    Bulletin of mathematical biology 55 (1993), S. 345-364 
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    Notes: Abstract Shape and size of elongating cells were examined in three plant tissues: the adaxial epidermis of the petiole ofZebrina pendula L., the abaxial epidermis ofAnacharis densa L. leaves and the abaxial epidermis of the scale leaf ofAllium cepa L. Based on a few simple assumptions, the expected probability distribution frequencies (pdf) for cell length and number of adjacent walls were calculated. Actual data of cell lengths closely approximated those expected with the pdfs being asymmetrical since there are more younger, shorter cells than older, longer cells. Data for number of lateral walls of real cells were similar to that expected and these walls increase in compensating mechanism exists to maintain a constant range of cell lengths through many cell generations. It is expressed by longer than average new daughter cells dividing relatively soon while shorter than average new daughter cells divide after a relatively long cycle.
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    Bulletin of mathematical biology 55 (1993), S. 365-384 
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    Notes: Abstract Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism for pattern formation in numerous embryological and ecological contexts. However, the possible effects of environmental inhomogeneities has received relatively little attention. We consider a general two species reaction-diffusion model in one space dimension, with one diffusion coefficient a step function of the spatial coordinate. We derive the dispersion relation and the solution of the linearized system. We apply our results to Turing-type models for both embryogenesis and predator-prey interactions. In the former case we derive conditions for pattern to be isolated in one part of the domain, and in the latter we introduce the concept of “environmental instability”. Our results suggest that environmental inhomogeneity could be an important regulator of biological pattern formation.
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    Notes: Abstract The particular dynamics of the previously proposed model of a catalytic network formed byn error-prone self-replicative species without and with superimposed competition is analysed. In the first case, two situations are studied in detail: a uniform network in which all the species are inter-coordinated in the same way, and a network with a species differentiated in its catalytic relation with the remaining elements. In the second case, the superimposed competition is introduced at two levels: first, as an asymmetry in one of the network species amplification factor considering a null self-catalytic vector, and secondly, as a non-null self-catalytic vector with no asymmetry in the other propertics of the species. This kind of system does not present complex behaviour and can be adequately deseribed by performing a standard linear analysis, which gives direct information on the asymptotic behaviour of the sytem. Finally, the biological implications of this analysis within the framework of biological evolution are discussed.
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    Bulletin of mathematical biology 55 (1993), S. 451-464 
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    Notes: Abstract A theoretical model is proposed for the formation of cell distribution patterns in the slug stage of the cellular slime moldDictyostelium discoideum. The equilibrium distribution of two types of cells, prestalk and prespore, is obtained by minimizing the free energy, which is defined in terms of differential chemotaxis, differential cell adhesion and randomness of cell movement. Resulting distributions show various segregation patterns of cell types. The condition for cell sorting is obtained from stability analysis of the set of diffusion equations governing the evolution of cell type distribution and the concentration of chemoattractant. The intensities of differential chemotaxis and random cell movement are quantitatively evaluated from experimental data to show that two cell types can sort themselves completely by these forces.
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    Bulletin of mathematical biology 55 (1993), S. 655-674 
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    Notes: Abstract Multicell spheroids, small spherical clusters of cancer cells, have become an importantin vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.
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    Bulletin of mathematical biology 55 (1993), S. 675-691 
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    Bulletin of mathematical biology 55 (1993), S. 693-693 
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    Bulletin of mathematical biology 55 (1993), S. 695-713 
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    Notes: Abstract In recent years, methods of consensus, developed for the solution of problems in the social sciences, have become widely used in molecular biology. Westudy a method of consensus originally due to Watermanet al. (Waterman, Galas and Arratia. 1984. Pattern recognition in several sequences: consensus and alignment.Bull. math. Biol. 46, 515–527) which is used to identify patterns or features in a molecular sequence where a pattern can vary in position within a given window. We show that some well-known consensus methods of the social sciences, the median and the mean, are special cases of this method for certain choices of the parameters used in it and give a precise account of the parameters for which these special cases arise. We also show that the specific parameters used in the method of Watermanet al. make their method equivalent to the median procedure which is widely used in the social sciences.
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    Bulletin of mathematical biology 55 (1993), S. 745-780 
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    Notes: Abstract We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.
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    Bulletin of mathematical biology 55 (1993), S. 781-816 
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    Notes: Abstract Two types of behavior have been previously reported in models of immune networks. The typical behavior of simple models, which involve B cells only, is stationary behavior involving several steady states. Finite amplitude perturbations may cause the model to switch between different equilibria. The typical behavior of more realistic models, which involve both B cells and antibody, consists of autonomous oscillations and/or chaos. While stationary behavior leads to easy interpretations in terms of idiotypic memory, oscillatory behavior seems to be in better agreement with experimental data obtained in unimmunized animals. Here we study a series of models of the idiotypic interaction between two B cell clones. The models differ with respect to the incorporation of antibodies, B cell maturation and compartmentalization. The most complicated model in the series has two realistic parameter regimes in which the behavior is respectively stationary and chaotic. The stability of the equilibrium states and the structure and interactions of the stable and unstable manifolds of the saddle-type equilibria turn out to be factors influencing the model's behavior. Whether or not the model is able to attain any form of sustained oscillatory behavior, i.e. limit cycles or chaos, seems to be determined by (global) bifurcations involving the stable and unstable manifolds of the equilibrium states. We attempt to determine whether such behavior should be expected to be attained from reasonable initial conditions by incorporating an immune response to an antigen in the model. A comparison of the behavior of the model with experimental data from the literature provides suggestions for the parameter regime in which the immune system is operating.
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    Bulletin of mathematical biology 55 (1993), S. 865-867 
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    Bulletin of mathematical biology 55 (1993), S. 869-889 
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    Notes: Abstract We show that the existence of diffusional resistance due to the presence of a solid phase can have a positive effect on the metabolic reactions of plant cells. In this case the efficiency of metabolic reactions, defined as the ratio of rate of production of biomass of aggregated cells/rate of production of biomass of dispersed cells, can be greater than unity for a certain range of aggregate sizes for both solid spheres (common plant cell aggregates) and hollow spheres (e.g.Volvox aggregates). This means that, under appropriate conditions, plant cells tend to stay in the aggregated form to improve the efficiency of their metabolic reactions. The result of the present analysis provides an explanation as to why aggregates of plant cells are observed under typical culture conditions.
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    Bulletin of mathematical biology 55 (1993), S. 937-952 
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    Notes: Abstract The Hodgkin and Huxley equations model action potentials in squid giant axons. Variants of these equations are used in most models for electrial activity of excitable membranes. Computational tools based upon the theory of nonlinear dynamical systems are used here to illustrate how the dynamical behavior of the Hodgkin Huxley model changes as functions of two of the system parameters.
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    Bulletin of mathematical biology 55 (1993), S. 919-936 
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    Notes: Abstract The description of the “microbial loop” has led to some major changes in our understanding of nutrient cycling within aquatic ecosystems. It now appears that in many settings it is not uncommon for some 50% of phytoplankton production to be diverted into microbial pathways rather than passing up to higher trophic levels. As a result the microbial loop is responsible for enhanced and rapid nutrient cycling at the very base of the food web. Since tight recycling is often associated with unstable positive feedback, we use a model to examine the possible repercussions in more detail. The model simulates the dynamics of the microbial loop and finds it to greatly affect the way in which aquatic primary production responds to nutrient pulses.
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    Bulletin of mathematical biology 55 (1993), S. 953-971 
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    Notes: Abstract The maintenance activity of plants is investigated in terms of a simple model. Maximization of a certain biomass fraction we refer to asnonactive biomass is postulated. Optimal behaviour of plants according to this principle is explicitly derived and expressed depending on environmental conditions. Several interesting hypotheses result, e.g. a quadratic law relating specific growth rate and gross rate of photosynthesis. A qualitative comparison with data from the literature is performed, with a special emphasis on the question whether plants stressed by air pollutants repair optimally. Regarding long-term constant environmental conditions, no data were found that contradict optimal behaviour. Exact quantitative testing of the theory is desirable, appropriate experiments are suggested.
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    Bulletin of mathematical biology 55 (1993), S. 993-1011 
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    Notes: Abstract In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth.Bull. math. Biol. 53, 639–656). The target population, a generic tumor, was modeled as a single, homogeneous population using the standard Verhulst equation of logistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represented by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumor growth, and (3) tumor growth in a radiation damaged environment, a phenomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a “triad” of growth factor controls (autocrine, paracrine and endocrine) and heterogeneity of the target population. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiating tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication between differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the differentiated compartment; and (3) the development of hypoxia in a spherical tumor. The signal processing within the triad is discussed for each model and biologically reasonable constraints are defined for limits on growth control.
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    Bulletin of mathematical biology 55 (1993), S. 1039-1061 
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    Notes: Abstract A transient multispecies model for quantifying microbial space competition in biofilm is derived from existing models, introducing a new approach to biomass detachment modelling. This model includes inert biomass, substrate diffusion and utilization rate within the biofilm and diffusional layers. It predicts the evolution of biofilm thickness, bulk substrate concentration, species distribution and substrate concentration within the biofilm. A zero-dimensional transient model is described. Its steady-state solution is used to set up initial conditions of the one-dimensional model and case computation towards steady-state solution. Some numerical tools have been developed, enabling fast computation on microcomputers. Simulations show the validity of a zero-dimensional model and perturbated systems are also simulated. Simulations with experimental data give acceptable results.
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    Bulletin of mathematical biology 55 (1993), S. 1025-1038 
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    Notes: Abstract Recently, we proposed a new model of DNA sequence evolution (Arquès and Michel. 1990b.Bull. math. Biol. 52, 741–772) according to which actual genes on the purine/pyrimidine (R/Y) alphabet (R=purine=adenine or guanine, Y=pyrimidine=cytosine or thymine) are the result of two successive evolutionary genetic processes: (i) a mixing (independent) process of non-random oligonucleotides (words of base length less than 10: YRY(N)6, YRYRYR and YRYYRY are so far identified; N=R or Y) leading to primitive genes (words of several hundreds of base length) and followed by (ii) a random mutation process, i.e. transformations of a base R (respectively Y) into the base Y (respectively R) at random sites in these primitive genes. Following this model the problem investigated here is the study of the variation of the 8 R/Y codon probabilities RRR,..., YYY under random mutations. Two analytical expressions solved here allow analysis of this variation in the classical evolutionary sense (from the past to the present, i.e. after random mutations), but also in the inverted evolutionary sense (from the present to the past, i.e. before random mutations). Different properties are also derived from these formulae. Finally, a few applications of these formulae are presented. They prove the proposition in Arquès and Michel (1990b.Bull. math. Biol. 52, 741–772), Section 3.3.2, with the existence of a miximal mean number of random mutations per base of the order 0.3 in the protein coding genes. They also confirm the mixing process of oligonucleotides by excluding the purine/pyrimidine contiguous and alternating tracts from the formation process of primitive genes.
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    Bulletin of mathematical biology 55 (1993), S. 1199-1210 
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    Notes: Abstract It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two-and three-dimensional mathematical model describing the folding process as a free energy minimization problems is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard (“conditionally intractable”). Some of the possible ramifications of this results are speculated upon.
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    Bulletin of mathematical biology 55 (1993), S. 1133-1182 
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    Notes: Abstract A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, which contains the total impact of proliferation and differentiation at the fixed points, is defined in order to enable an exact analysis. The analysis of the memory states is restricted in this paper to a two-species system. The conditions for the existence of locally stable steady states with expanded B cell and antibody populations are established for various combinations of different field-response functions (e.g. linear, saturation, log-bell functions). The stable fixed points are interpreted as memory states in terms of immunity and tolerance. It is proven that a combination of linear response functions for both proliferation and differentiation does not give rise to stable fixed points. However, due to competition between proliferation and differentiation saturation response functions are sufficient to obtain two memory states, provided proliferation preceeds differentiation and also saturates earlier. The use of log-bell-shaped response functions for both proliferation and differentiation gives rise to a “mexican-hat” effective response function and allows for multiple (four to six) memory states. Both a primary response and a much more pronounced secondary response are observed. The stability of the memory states is studied as a function of the parameters of the model. The attractors lose their stability when the mean residence time of antibodies in the system is much longer than the B cells' lifetime. Neither the stability results nor the dynamics are qualitatively chanbed by the existence of non-proliferating B cells: memory states can exist and be stable without non-proliferating B cells. Nevertheless, the activation of non-proliferating B cells and the competition between proliferation and differentiation enlarge the parameter regime for which stable attractors are found. In addition, it is shown that a separate activation step from virgin to active B cells renders the virgin state stable for any choice of biologically reasonable parameters.
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    Bulletin of mathematical biology 60 (1998), S. 195-196 
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    Bulletin of mathematical biology 60 (1998), S. 101-129 
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    Notes: Abstract Due to the increasing importance of the extracellular matrix in many biological problems, in this paper we develop a model for fibroblast and collagen orientation with the ultimate objective of understanding how fibroblasts form and remodel the extracellular matrix, in particular its collagen component. The model uses integrodifferential equations to describe the interaction between the cells and fibers at a point in space with various orientations. The equations are studied both analytically and numerically to discover different types of solutions and their behavior. In particular we examine solutions where all the fibroblasts and collagen have discrete orientations, a localized continuum of orientations and a continuous distribution of orientations with several maxima. The effect of altering the parameters in the system is explored, including the angular diffusion coefficient for the fibroblasts, as well as the strength and range of the interaction between fibroblasts and collagen. We find the initial conditions and the range of influence between the collagen and the fibroblasts are the two factors which determine the behavior of the solutions. The implications of this for wound healing and cancer are discussed including the conclusion that the major factor in determining the degree of scarring is the initial deposition of collagen.
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    Bulletin of mathematical biology 60 (1998), S. 215-230 
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    Notes: Abstract This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous rigorous results can be heuristically explained in terms of the more transparent dynamics of an approximating deterministic system. The model is then extended to include a host population structured into patches, with weak nearest-neighbour mixing of infection. It is shown, by considering the approximating deterministic system, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N 〉 N c where N c is a critical patch size below which transits are unlikely to occur. This corresponds to the simple decomposition of the time of an epidemic into the time it takes to spread through one patch plus the time it takes to transit to each of n successive patches. Expressions for this threshold and the coefficients of the time to extinction are given in terms of the transmission parameters of infection and the coupling strength between patches. These expressions are compared with numerical results using parameters relevant to a study of phocine distemper virus in North Sea seals, and the agreement is found to be good for large and small N. In the region when N ≈ N c , where transits may or may not occur, interesting transitional behaviour is seen, leading to a non-monotonicity of the extinction time as a function of N.
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    Bulletin of mathematical biology 60 (1998), S. 409-415 
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    Bulletin of mathematical biology 60 (1998), S. 355-372 
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    Notes: Abstract When directly transmitted infectious diseases are modeled assuming an everlasting induced immunity (and constant contact rate), there are well-established formulas to deal with, which is not true if we include the loss of induced immunity. In general, the immunity induced by the disease is everlasting. We propose a model considering the loss of immunity and present methods for the estimation of two epidemiological parameters: the force of infection and the basic reproduction ratio. We also analyze the effects of the loss of immunity on these parameters. Based on these results, we conclude that reinfection can play an important role in highly vaccinated populations.
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    Bulletin of mathematical biology 60 (1998), S. 449-475 
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    Notes: Abstract We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.
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    Bulletin of mathematical biology 60 (1998), S. 197-213 
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    Notes: Abstract A possible experimental design for combination experiments is to compare the doseresponse curve of a single agent with the corresponding curve of the same agent using either a fixed amount of a second one or a fixed dose ratio. No interaction is then often defined by a parallel shift of these curves. We have performed a systematic study for various types of doseresponse relations both for the dose-additivity (Loewe additivity) and for the independence (Bliss independence) criteria for defining zero interaction. Parallelism between doseresponse curves of a single agent and those of the same agent in the presence of a fixed amount of another one is found for the Loewe-additivity criterion for linear doseresponse relations. For nonlinear relations, one has to differentiate between effect parallelism (parallel shift on the effect scale) and dose parallelism (parallel shift on the dose scale). In the case of Loewe additivity, zero-interaction dose parallelism is found for power, Weibull, median-effect and logistic doseresponse relations, given that special parameter relationships are fulfilled. The mechanistic model of competitive interaction exhibits dose parallelism but not effect parallelism for Loewe additivity. Bliss independence and Loewe additivity lead to identical results for exponential doseresponse curves. This is the only case for which dose parallelism was found for Bliss independence. Parallelism between single-agent doseresponse relations and Loewe additivity mixture relations is found for examples with a fixed doseratio design. However, this is again not a general property of the design adopted but holds only if special conditions are fulfilled. The comparison of combination doseresponse curves with single-agent relations has to be performed taking into account both potency and shape parameters. The results of this analysis lead to the conclusion that parallelism between zero interaction combination and single-agent doseresponse relations is found only for special cases and cannot be used as a general criterion for defining zero-interaction in combined-action assessment even if the correct potency shift is taken into account.
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    Bulletin of mathematical biology 60 (1998), S. 1-26 
    ISSN: 1522-9602
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    Notes: Abstract Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.
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    Bulletin of mathematical biology 60 (1998), S. 79-100 
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    Notes: Abstract A model, based on the principles of continuum mechanics, is presented for the analysis of cell-velocity fields within wool follicles. The model requires specification of three follicle characteristics in the form of spatially varying fields: viscosity, cell density and cell production rate. The viscosity is introduced as an attempt to model both complex intercellular interactions and individual cell deformation as the cells move. It is demonstrated that the distribution of cell production is more important than axial variation in viscosity in determining the overall flow pattern.
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    Bulletin of mathematical biology 60 (1998), S. 131-150 
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    Notes: Abstract A microbial trichome extracts nutrients from its immediate surroundings. It may also oxidize electron donors, reduce electron acceptors, and exude the ‘waste’ products of endogenous redox metabolism. Finally, it may effect light harvesting. These exchange fluxes are summed up in a generic model, which covers photoautotrophs as well as chemoheterotrophs. The focus is on endogenous metabolism and the cellular homeostasis of both reducing and phosphorylating equivalents. A novel result is the formulation of four ‘rules’, akin to the Pasteur effect, which govern the compatibility of endogenous metabolism with various assimilatory processes.
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    Bulletin of mathematical biology 60 (1998), S. 49-65 
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    Notes: Abstract In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey subpopulations and more (or less) efficient predator subpopulations.
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    Bulletin of mathematical biology 60 (1998), S. 919-935 
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    Notes: Abstract To analyze signals measured from human blood flow in the time-frequency domain, we used the wavelet transform which gives good time resolution for high-frequency components and good frequency resolution for low-frequency components. Five characteristic frequency peaks, corresponding to five almost periodic rhythmic activities, were found on the time scale of minutes. These oscillations were characterized by time and spatial invariant measures. The potential of this approach in studying the blood-flow dynamics was illustrated by revealing differences between the groups of control subjects and athletes.
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    Bulletin of mathematical biology 60 (1998), S. 997-998 
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    Bulletin of mathematical biology 60 (1998), S. 1167-1200 
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    Notes: Abstract The interaction of a pair of weakly coupled biological bursters is examined. Bursting refers to oscillations in which an observable slowly alternates between phases of relative quiescence and rapid oscillatory behavior. The motivation for this work is to understand the role of electrical coupling in promoting the synchronization of bursting electrical activity (BEA) observed in the β-cells of the islet of Langerhans, which secrete insulin in response to glucose. By studying the coupled fast subsystem of a model of BEA, we focus on the interaction that occurs during the rapid oscillatory phase. Coupling is weak, diffusive and non-scalar. In addition, non-identical oscillators are permitted. Using perturbation methods with the assumption that the uncoupled oscillators are near a Hopf bifurcation, a reduced system of equations is obtained. A detailed bifurcation study of this reduced system reveals a variety of patterns but suggests that asymmetrically phase-locked solutions are the most typical. Finally, the results are applied to the unreduced full bursting system and used to predict the burst pattern for a pair of cells with a given coupling strength and degree of heterogeneity.
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    Bulletin of mathematical biology 60 (1998), S. 1017-1037 
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    Notes: Abstract Hemodynamic forces affect endothelial cell morphology and function. In particular, circumferential cyclic stretch of blood vessels, due to pressure changes during the cardiac cycle, is known to affect the endothelial cell shape, mediating the alignment of the cells in the direction perpendicular to stretch. This change in cell shape proceeds a drastic reorganization at the internal level. The cellular scaffolding, mainly composed of actin filaments, reorganize in the direction which later becomes the cell’s long axis. How this external mechanical stimulus is ’sensed’ and transduced into the cell is still unknown. Here, we develop a mathematical model depicting the dynamics of actin filaments, and the influence of the cyclic stretch of the substratum based on the experimental evidence that external stimuli may be transduced inside the cell via transmembrane proteins which are coupled with actin filaments on the cytoplasmic side. Based on this view, we investigate two approaches describing the formulation of the transduction mechanisms involving the coupling between filaments and the membrane proteins. As a result, we find that the mechanical stimulus could cause the experimentally observed reorganization of the entire cytoskeleton simply by altering the dynamics of the filaments connected with the integral membrane proteins, as described in our model. Comparison of our results with previous studies of cytoskeletal dynamics reveals that the cytoskeleton, which, in the absence of the effect of stretch would maintain its isotropic distribution, slowly aligns with the precise direction set by the external stimulus. It is found that even a feeble stimulus, coupled with a strong internal dynamics, is sufficient to align actin filaments perpendicular to the direction of stretch.
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    Bulletin of mathematical biology 60 (1998), S. 1149-1166 
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    Notes: Abstract We study a general predator—prey system in a spatially heterogeneous environment. The predation process, which occurs on a behavioural time-scale, is much faster than the other processes (reproduction, natural mortality and migrations) occurring on the population dynamics time-scale. We show that, taking account of this difference in time-scales, and assuming that the prey have a refuge, the dynamics of the system on a slow time-scale become donor-controlled. Even though predators may control the prey density locally and on a behavioural fast time-scale, nevertheless, both globally and on a slow time-scale, the prey dynamics are independent of predator density: the presence of predators generates a constant prey mortality. In other words, in heterogeneous environments, the prey population dynamics depend in a switch-like manner on the presence or absence of predators, not on their actual density.
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    Circuits, systems and signal processing 12 (1993), S. 153-154 
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    Notes: Abstract Once designed, implementation of an optimal mean-square binary morphological filter is extremely fast, especially when the erosions are implemented on a suitable parallel processor. On the other hand, optimal filter design involes a computationally burdensome search procedure that can, in practice, be intractable. The present paper provides an algorithm for filter design that is based on the relationship between the optimal morphological filter and the conditional expectation. The algorithm proceeds by changing the conditional expectation into a morphological filter while at the same time increasing the mean-square error by a minimal amount. It does so by switching observations between the 1-set and the 0-set of the conditional expectation. The switching algorithm is extremely efficient in many noise environments, and therefore provides a filter design that can be useful for online structuring-element updating. Owing to the relationship between stack and morphological filters, the algorithm is at once useful for finding optimal binary stack filters.
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    The journal of Fourier analysis and applications 4 (1998), S. 283-297 
    ISSN: 1531-5851
    Keywords: Primary 42B25 ; 30D10 ; Secondary 26A16 ; 46B45 ; 47B10 ; 47B35 ; Mean oscillation ; Paley-Wiener space ; Besov spaces ; wavelets ; commutators ; Hankel operators ; Schatten-von Neumann ideals
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    Notes: Abstract The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown.
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    The journal of Fourier analysis and applications 4 (1998), S. 329-340 
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    Keywords: 42C15 ; 46E35 ; Wavelets ; function spaces ; fractals
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    Notes: Abstract Wavelets on self-similar fractals are introduced. It is shown that for certain totally disconnected fractals, function spaces may be characterized by means of the magnitude of the wavelet coefficients of the functions.
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    The journal of Fourier analysis and applications 4 (1998), S. 357-375 
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    Keywords: 42C15 ; 94A12 ; wavelets ; interpolation ; orthogonal expansions
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    Notes: Abstract Gibbs' phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in such a series, it can be avoided. However, some series that exhibit Gibbs' phenomenon for orthogonal series do not for the associated sampling series.
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    Circuits, systems and signal processing 11 (1992), S. 115-136 
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    Notes: Abstract By considering all orderings of the input samples, which are discrete-time continuous-valued, it is shown here that a weighted median (WM) filter of spanN can be specified unambiguously by 2N−1 consistent linear inequalities relating the weights. This specification is identical to that of a self-dual threshold function with the same weights. It is also shown that WM filters with symmetric weights can be specified by ternary threshold functions. Based on these inequalities, properties of WM filters which can be used to check equivalence of some WM filters are derived.
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    Circuits, systems and signal processing 11 (1992), S. 137-151 
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    Notes: Abstract Because binary mathematical morphology permits fast local neighborhood operations by flash conversion, it is used extensively in high-speed pattern-recognition computer systems. Further, since anyN-dimensional integer function may be represented by an (N + 1)-dimensional binary (bilevel) function, ordinary two-dimensional graylevel images become three-dimensional binary images. Thus these images may be processed by high-speed flash-conversion computers assuming that a sufficiently compact three-dimensional kernel can be devised. The tetradekahedron of the face-centered-cubic tessellation forms a perfect kernel in three-dimensions. Its neighborhood is compact. It has total symmetry with all 12 neighbors equidistant from the central element. Using this kernel a variety of useful three-dimensional morphological operations may be performed for target track detection, shaded graphics, data clustering, automated focusing, and spatial filtering.
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    Circuits, systems and signal processing 11 (1992), S. 153-169 
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    Notes: Abstract Two techniques for image restoration are compared in this paper. One is a technique based on the theory of optimal adaptive stack filtering; the other is a recently developed vector detection approach to image restoration. The primary difference between these two techniques is that the optimal detection technique exploits multilevela priori information, while the stack filter uses only single level zero crossing information. The design constraints for stack filters and vector detection are similar. Both approaches rely on the existence of a training sequence for the image source in order to obtain optimal processing. Adaptive stack filters do, however, require a training set of the noise while the optimal detection approach only needs a multivariate parametric representation. The image-restoration performance of these two methods is compared in a signal dependent noise environment characterizing imaging systems with speckle, film-grain, and Poisson shot noise. Comparisons are made using the mean absolute error measure as well as a subjective measure.
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    Circuits, systems and signal processing 11 (1992), S. 325-352 
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    Notes: Abstract The stability of digital ladder filters close in form, via the lossless discrete integrator (LDI) transformation, to doubly terminatedLC Cauer ladder low-pass filters is studied. The LDI transformation does not necessarily map stable analogue into stable digital filters. Necessary and sufficient conditions for these digital filter to be lossless and for a corresponding doubly terminated filter to be stable are given. LDIs are often used in the design of switched capacitor (SC) filters. For this case we provide a threshold sampling rate above which the SC LDI filter retains the stability of the analogue filter. In spite of the stability problem with the LDI mapping, it has been observed that when applied to simulate analogue filters the resulting filter is stable. It can now be argued that, in these cases, other factors in the determination of the sampling rate leads typically to a choice that is also sufficiently above the threshold rate for stability. The theory described is also useful to derive more general digital filters and to perform the design of stable LDI filters exclusively in the Z-plane without reference to analogue prototypes.
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    Circuits, systems and signal processing 11 (1992), S. 285-307 
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    Notes: Abstract In this paper we describe a family of operators for constructing nontrivial left and right coprime factorizations under rather weak conditions for a large class of nonlinear feedback control systems that has a stabilizable or unstabilizable plant, using a common criterion of input-output stability. The proposed sufficiency and construction method are based on a generalization of the nonlinear Lipschitz operator theory formulated by us for such systems. This class of generalized nonlinear Lipschitz operators constitutes a very large family (an infinite-dimensional Banach space) of bounded nonlinear operators that describe (part of) the underlying systems. One of the main difficulties in constructing coprine factorizations for nonlinear feedback systems has been in taking care of the nonlinear composite and inverse operators that appear in the closed-loop configuration such that the overall feedback system is well defined in the sense of stability, causality, and uniqueness of the internal signals and such that the coprime factorizations can be achieved. In this paper we show how these difficult issues can be handled nicely under our framework of generalized nonlinear Lipschitz operator theory, at least for a very large class of nonlinear control systems. We give a simple illustrative example to show how these coprime factorizations can actually be characterized and constructed to yield explicit closed-form solutions.
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    Circuits, systems and signal processing 11 (1992), S. 387-398 
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    Notes: Abstract In this paper we study the problem of designing a neural network that gives the correct binary representation of a given real number. Previously this problem has been studied by Tank and Hopfield. The network proposed by them exhibits “hysteresis” in the sense that the current vector of the network sometimes converges towards a binary vector that isnot the correct binary representation of the input current. The reason for this is that the network proposed by them has multiple asymptotically stable equilibria. In the present paper, we propose another neural network which has the property that it hasa single, globally attractive equilibrium for almost all values of the input current. Hence, irrespective of the initial conditions of the network, the current vector converges towards the correct binary representation of the input current.
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    Circuits, systems and signal processing 11 (1992), S. 421-430 
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    Notes: Abstract Concepts of observability and strong observability for singular systems are introduced and characterized geometrically in terms of the system matrices without using the Weierstrass decomposition. Duality relations between observability and controllability and that between reachability and strong observability are established. A canonical form for the action of the output injection group on the set of observable systems is presented.
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    Circuits, systems and signal processing 11 (1992), S. 455-492 
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    Notes: Abstract Mathematical morphology is becoming increasingly important in industrial vision applications for object recognition and defect inspection. In this paper we define a new function based on mathematical morphology, which we named the Rotationally Invariant Pecstrum (RIP). The RIP is proven to be invariant under rotation regardless of the shape of the structuring element. This paper also discusses how to use the RIP as an object descriptor and studies the effect of using different structuring elements on recognizing objects of different shapes.
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    Circuits, systems and signal processing 11 (1992), S. 493-508 
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    Notes: Abstract This work presents close-form formulas for typical two-dimensional bandselect linear-phase FIR filters (e.g., band-pass, high-pass, and band-stop filters) optimal in the least-squares sense. Cases of both circular and elliptical symmetry are considered. The formulas refer to the coefficients of the frequency sampling form of the frequency response. Therefore they can either be directly used for filter implementation, if the frequency sampling structure is adopted, or used to obtain the impulse response coefficients via an inverse FFT.
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    Circuits, systems and signal processing 12 (1993), S. 263-278 
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    Notes: Abstract New characteristics of feedback neural networks are studied. We discuss in detail the question of updating of neurons given incomplete information about the state of the neural network. We show how the mechanism of self-indexing for such updating provides better results than assigning ‘don't know’ values to the missing parts of the state vector. Issues related to the choice of the neural model for a feedback network are also considered. Properties of a new complex valued neuron model that generalizes McCulloch-Pitts neurons are examined.
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    Circuits, systems and signal processing 12 (1993), S. 391-407 
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    Notes: Abstract This paper deals with chained eigenstructure assignment for strongly controllable singular systems of the form Êx (t)=Â x(t)+B u(t) with state feedback control of the formu(t)=Kx(t)+w(t). The development of our method depends crucially on the properties of standard form singular systems. The closed-loop system will satisfy the following requirements: regularity, impulse-free response and rankÊ arbitrary eigenvalues assignment. This parametric characterization conveniently organizes the nonunique gain matrixK to modify the dynamic response of the systems. The result can be used for discrete-time descriptor systems, in which a zero-value eigenvalue may well be a desired closed-loop eigenvalue. One illustrative example is included.
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    Circuits, systems and signal processing 12 (1993), S. 453-464 
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    Notes: Abstract An efficient bi-state stochastic gradient is proposed for spontaneous constrained time delay estimation. The quantized stochastic gradient is an approximation of the polarity of the instantaneous delay estimation error. It is adjusted in such a way that it has a much higher probability to move in the correct direction at each iteration so as to enable a speed-up in the delay estimate to converge to global minimum in steady state. The performance of the delay estimator is evaluated statistically and an analytical solution for its convergence behavior is established. It is demonstrated that the proposed algorithm has at least a two-fold improvement in convergence speed when compared with the conventional approach, and this is verified by extensive simulation results.
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    Circuits, systems and signal processing 12 (1993), S. 503-531 
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    Notes: Abstract In this work, we extend the coding theory approach to error control in redundant residue number systems (RRNS). The concept of erasure correction capability in RRNS is introduced. We derive the relationship between the minimum distance and the error detection and error/erasure correction capability. New computationally efficient algorithms are derived for simultaneously correcting single errors and multiple erasures and detecting multiple errors. These algorithms reduce the computational complexity of the previously known algorithms by at least an order of magnitude. Another attractive feature of the algorithms is that all the arithmetic operations are modulo operations. Consequently, the need to process large valued integers is avoided.
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    Circuits, systems and signal processing 12 (1993), S. 579-587 
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    Notes: Abstract This paper presents a general expression relating the complex-normalized scattering matrix of ann-port network to that of its augmentedn-port network normalizing to then 1 −Ω resistances, where the Darlington equivalent network may be either reciprocal or nonreciprocal.
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    Circuits, systems and signal processing 12 (1993), S. 211-221 
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    Notes: Abstract Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper • Rigorously establishes the robustness of feedforward network realizations. • Uses a theorem of Wiener and ideas of translation invariant subspaces to provide conditions for universal approximations toL 1 andL 2 functions by networks, for quite general activation functions. The second result extends and simplifies some of the recent results of Stinchcombe and White, at least for the special cases ofL 1 andL 2 functions.
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    Circuits, systems and signal processing 17 (1998), S. 85-102 
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    Notes: Abstract In this paper, we present a hybrid space-time-filtered Viterbi receiver using multiple antennas for co-channel interference (CCI) reduction and intersymbol interference (ISI) equalization in a slow Rayleigh fading channel. In this approach, a space-time filter is first applied at the antenna outputs to maximize the signal-to-interference-plus-noise ratio (SINR), and the scalar output is then sent to a Viterbi equalizer. We propose a closed-form solution to jointly determine the weight vector for the space-time filter and the channel vector for the Viterbi equalizer. We also examine the need for a whitening filter prior to the Viterbi equalizer and show that it only marginally improves the performance. Simulation results are provided to validate our approach and to compare the performance of our receiver with that of different existing receivers.
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    Circuits, systems and signal processing 17 (1998), S. i 
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    Circuits, systems and signal processing 17 (1998), S. 123-136 
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    Notes: Abstract Prosthetic heart valves have been responsible for extending the life spans and improving the quality of life of many people with serious heart conditions. Even though the heart valves are extremely reliable, eventually they are susceptible to the long-term fatigue and structural failure effects expected for mechanical devices operating over long periods of time. In [2] a classification procedure was developed using spectral features obtained from acoustic signals to determine the condition of the prosthetic heart valve. Although this classification procedure has produced very encouraging results, this method still lacks a fundamental physical description of the sounds produced by the valve during normal operation. In order to obtain a better understanding of the valve acoustic response, we have performed a set of anechoic tests. In this paper, we describe the anechoic experiment and also present limited transient response results. This transient information will eventually be used to identify and improve the features used to classify the valve condition.
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    Circuits, systems and signal processing 17 (1998), S. 195-218 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this two-part study we present a new design methodology for neural classifiers. The design procedure utilizes a multiclass vector quantization (MVQ) algorithm for information extraction from the training set. The extracted information suffices to specify the hidden layer in a canonical neural network architecture. The extracted information also leads to the specification of neuron inhibition rules and subsequently the design of the hidden layer-to-output map. In Part I of the study we focus attention on the MVQ algorithm and how it is used to extract information from a training set. The extracted information is referred to as thecodebook. The codebook is used to directly specify the hidden layer. This specification can take the form of a perceptron layer, a radial basis layer, or a heterogeneous layer involving a mixture of neuron types. These and otherh-layer specifications are determined directly from the same extracted information. The MVQ codebook also suffices to scale the activation function of each neuron. In Part II we consider the nonsimplistic hidden layer-to-output map design. We note that the MVQ algorithm, as it extracts information, decomposes the design set into disjoint neighborhoods. For each neighborhood we identify subsets of the hidden layer neurons, which are significant sensors for the neighborhood. For each such subset we construct an output map. Inhibition rules are established to ensure that the proper output map is activated. In benchmark simulations the overall design exhibits excellent performance, to the extent that we are hard pressed to identify bounds on performance, if any.
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  • 93
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    Circuits, systems and signal processing 17 (1998), S. 361-389 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A transform domain image tagging orwatermarking method that survives image cropping (and, hence, is “holographic”) was proposed at Bell Labs in September 1994. This report analyzed in detail the various properties of this method and introduces an optimal procedure for watermark recovery.
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  • 94
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    Circuits, systems and signal processing 17 (1998), S. 483-493 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract An algorithm for the exact computation of the frequency responses of linear interval systems is obtained. For the computation a sectoring stage is added to an elimination algorithm to eliminate interior curves. It is shown that the intersection of a ray and the frequency response set is an empty set or a line segment whose endpoints are extrema of the functions defined. Required mathematical analysis tools for the development of the sectoring algorithm and an illustrative example are provided.
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  • 95
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    Circuits, systems and signal processing 17 (1998), S. 559-574 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The geometric theory of the domain of an ordered pair (F, G) of matrices or the geometry associated with matrix pencils provides a unifying framework for the study of algebraic, dynamic and feedback properties of linear singular systems. The key concepts and tools of the geometry are the notions of the (F, G)-, (G, F)-invariance and a set of subspace sequences. In this paper, an alternative characterization of these sequences is given based on the properties of the partitioned null spaces of appropriate sequences of Toeplitz matrices defined by the (F, G) pair. The results provide a simple procedure for the computation of the limit spaces of these sequences and clearly cover corresponding problems of the singular, implicit systems theory.
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  • 96
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    Circuits, systems and signal processing 17 (1998), S. 667-682 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a new concept of narrowband and broadband active noise compression (ANCom) systems which improves the conventional active noise equalization (ANE) technique to meet some practical requirements. By using a variable equalization coefficient, the narrowband ANCom system can automatically switch among the four different operating modes of narrowband ANE, according to the primary noise power. As a result, it can “compress” the narrowband noise into a desired power range when the primary noise power varies drastically. Compared to a conventional broadband ANE system, the novel broadband ANCom system not only has the ability to shape the residual noise power spectrum, but can also compress the residual noise power into a predetermined dynamic range as the narrowband AN-Com does. Theoretical analyses are conducted for both the narrowband ANCom and broadband ANCom systems. Simulation results show that the proposed algorithms work well in both static and dynamic situations.
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  • 97
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    Circuits, systems and signal processing 17 (1998), S. 703-708 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The cornerstone of the theory of discrete-space single-input single-output linear systems is the idea that every such system has an input-output mapH that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight, which, for the case of bounded inputs mapped continuously into bounded outputs, was recently corrected by adding an additional term to the representation. Here we give a more general result that addresses an important larger family of inputs.
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  • 98
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    Circuits, systems and signal processing 17 (1998), S. 737-755 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper the problem of robust stabilizing a linear, time-invariant singular system is studied. The characterization is given in terms ofH ∞-bounded perturbations to the numerator and denominator factors of its normalized left coprime factorization. An optimal stability margin is provided in terms of the definition of the Hankel norm of a singular system. The Hankel norm is computed using two generalized Lyapunov equations.
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  • 99
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    Circuits, systems and signal processing 17 (1998), S. 1-27 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A novel computationally efficient realization of sharp linear-phase finite impulse response (FIR) bandstop filters is proposed. The synthesis scheme for the bandstop filters is derived from variations of the frequency-response-masking technique. Five realization structures are presented in this paper for the synthesis of five different classes of bandstop filters. Approximate expressions for the optimal value of the impulse response up-sampling ratio (M) and the corresponding number of multipliers are derived.
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  • 100
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    Circuits, systems and signal processing 17 (1998), S. 29-49 
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Estimating the covariance sequence of a wide-sense stationary process is of fundamental importance in digital signal processing (DSP). A new method, which makes use of Fourier inversion of the Capon spectral estimates and is referred to as theCapon method, is presented in this paper. It is shown that the Capon power spectral density (PSD) estimator yields an equivalent autoregressive (AR) or autoregressive moving-average (ARMA) process; hence, theexact covariance sequence corresponsing to the Capon spectrum can be computed in a rather convenient way. Also, without much accuracy loss, the computation can be significantly reduced via an approximate Capon method that utilizes the fast Fourier transform (FFT). Using a variety of ARMA signals, we show that Capon covariance estimates are generally better than standard sample covariance estimates and can be used to improve performances in DSP applications that are critically dependent on the accuracy of the covariance sequence estimates.
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