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  • Springer  (89,255)
  • 2020-2024
  • 1990-1994  (62,697)
  • 1985-1989
  • 1965-1969  (26,558)
  • 1992  (62,697)
  • 1966  (26,558)
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  • 2020-2024
  • 1990-1994  (62,697)
  • 1985-1989
  • 1965-1969  (26,558)
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  • 1
    Electronic Resource
    Electronic Resource
    Composting of explosives and propellant contaminated soils under thermophilic and mesophilic conditions (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 137-144 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569746
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  • 2
    Electronic Resource
    Electronic Resource
    Purification and properties of extracellularβ-fructofuranosidases fromAureobasidium sp. ATCC 20524 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 145-147 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569747
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  • 3
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    Electronic Resource
    Insect fungal symbionts: A promising source of detoxifying enzymes (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 149-161 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569619
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  • 4
    Electronic Resource
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    Biosensors for process monitoring (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 163-172 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569620
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  • 5
    Electronic Resource
    Electronic Resource
    Ecology ofVibrio vulnificus in Galveston Bay oysters, suspended particulate matter, sediment and seawater: Detection by monoclonal antibody — immunoassay — most probable number procedures (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 219-223 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569626
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  • 6
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    Conversion of sodium cyanide to carbon dioxide and ammonia by immobilized cells ofPseudomonas putida (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 235-238 
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    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569629
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  • 7
    Electronic Resource
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    Changes in protein composition ofSaccharomyces brewing strains in response to heat shock and ethanol stress (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 229-234 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569628
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  • 8
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    Isolation and characterization of a novel polysaccharide fromBacillus licheniformis NCIB 11634 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 239-245 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569630
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  • 9
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    Announcement from the publisher (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 269-269 
    Details
    ISSN: 1476-5535
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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    URL: http://dx.doi.org/10.1007/BF01569634
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  • 10
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    Effect of deglycosylation on the properties of β-fructofuranosidaseP-1 fromAureobasidium sp. ATCC 20524 (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 251-255 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01569632
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  • 11
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    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 333-345 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is a sequel to a paper by the author entitled “Restricted Transition Probabilities and Their Applications to Some Problems in the Dynamics of Biological Populations” (Bull. Math. Biophysics, 1966,28, 315–331). The paper is divided into two parts. In part one some aspects of the maximum size attained by the population during a finite time interval are studied for the case the stochastic process underlying the evolution of the population is a birth process. Two interesting by-products emerge from the study presented in part one; namely a combinatorial method of finding solutions to the Kolmogorov differential equations in special cases, and secondly, a set of criteria for the optimum allocation of genotypes in the host population of a host-pathogen system. The optimum allocation of genotypes in the host population is a problem of practical importance in controlling plant pathogens. In part two the theory of restricted transition probabilities developed in the companion paper is applied in finding the distribution of the time to the appearance of the first mutation for the case of a two dimensional birth process. The distribution of the time to the appearance of the first mutation is of importance in understanding the role mutation plays in the evolution of a population, particularly in the pathogen population of a host-pathogen system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476814
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  • 12
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    The motion of the left ventricle. I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 355-362 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476816
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  • 13
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    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 347-354 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Le modèle de Nelson peut-être considéré comme une approximation du modèle de Hodgkin-Huxley. Moins précis, il est plus maniable. Le modèle de Nelson peut également être considéré comme une généralisation du modèle de Hodgkin-Huxley. En effet, il introduit des liaisons synaptiques localisées ou diffusantes, et un processus de facilitation. Le mécanisme des liaisons synaptiques ne se traduit pas facilement dans le langage de Hodgkin-Huxley. Par contre, le processus de facilitation s'interprète facilement. Nelson's model can be taken as an approximation of Hodgkin-Huxley's model. Its precision is lesser, but it is more usable. Nelson's model can also be taken as a generalization of Hodgkin-Huxley's one; for it introduces localized or diffusing synaptic connexions and a facilitating process. The mechanism of synaptic connexions cannot be easily translated into Hodgkin-Huxley's language. On the contrary, the facilitating process is easily interpreted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476815
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  • 14
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    The theory of the left ventricular aneurysm (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 363-370 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A spherical model for the human left ventricle with two different types of aneurysms, circular and rectangular-square, is proposed and meaningful relations are derived between the parameters of the aneurysms and ventricle. Such ventricular parameters as stroke volume, end-diastolic volume, and end-systolic volume are given normal human values to compute values for end-systolic radius and percentage shortening of muscle for various sized circular and rectangular-square aneurysms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476817
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  • 15
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    A note on crime control (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 375-378 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Volterra theory of two competing populations is extended to the contemporary social problem of crime control. Domains of stability for the time dependence of the numbers in the criminal and enforcement groups are exposed by a numerical example. Both augmentation and reduction of enforcement can produce a stable system. Average values of the ratio of members in each group show great sensitivity to the control policies adopted by the remaining sector of the total population.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476819
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  • 16
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    Interactions in enzymatic reactions (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 379-390 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper deals with interactions of substances via an enzymatic reaction (Bull. Math. Biophysics,25, 141–154, 1963). The substances are the activators, inhibitors and/or substrates of the reaction. Due to the bimolecularity of the processes in the reaction, the quantitative relation between the steady state amount of complexes and the amounts of the substances assumes a typical form. In multiple enzymatic reactions this form is more complicated, though basically similar. Because the substances may influence the steady state amounts of the complexes in opposite directions, the compensation and blocking effects are the properties of enzymatic reactions. The substances with the same direction of influence may potentiate each other. In the enzymatic reaction here considered, the potentiation is always non-negative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476820
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  • 17
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    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 391-409 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476821
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  • 18
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    On the derivation of a mean growth equation for cell cultures (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 411-416 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract IfN(t) is the expected number of cells in a culture at timet, $$\dot N(t)$$ the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation $$\dot N(t) = 2\int_{ - \infty }^t {f(t - \tau )\dot N(\tau )d\tau }$$ for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.
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    URL: http://dx.doi.org/10.1007/BF02476822
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  • 19
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    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 417-432 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model of the dissolution kinetics of powdered enamel is developed based on the kinetic rate termq, $$q = K'H - k'C \cdot P_1$$ , whereH=[H +],C=[Ca ++] andP 1=[HPO 4 = ]. The differential equations describing the rate of mineral dissolution (and the linearly related rate of appearance of calcium and phosphate in solution) have been derived and solved for three basic cases: (1) when thepH of the solution and surface area of the enamel are considered constant, (2) when thepH is assumed constant, but the reduction in surface area during dissolution is considered, and (3) when the rise ofpH resulting from the buffering effect of the dissolved enamel is considered along with the change in surface area. Analytical solutions have been obtained for cases (1) and (2), while a numerical solution has been found for case (3). Data from a study on enamel dissolution are presented that agree with the theory of case (3), and it is noted that apH rise as large as 0.5 can occur, as has been shown elsewhere in the literature.
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    URL: http://dx.doi.org/10.1007/BF02476823
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  • 20
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    Reward and punishment in learning with possible reference to punishment for crime (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 477-481 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.
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    URL: http://dx.doi.org/10.1007/BF02476827
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  • 21
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    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02476828
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  • 22
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    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02476829
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  • 23
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    Operations research around the world meetings (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 485-485 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02476830
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  • 24
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    Dimensional anlaysis and the equations of electrophoresis (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 501-510 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.
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    URL: http://dx.doi.org/10.1007/BF02476857
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  • 25
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    Categories of (ℓ, ℛ)-systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 511-517 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
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    URL: http://dx.doi.org/10.1007/BF02476858
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    The origin of lift forces in fluttering flight (1966)
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    Bulletin of mathematical biology 28 (1966), S. 487-500 
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    Notes: Abstract A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.
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    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
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    Bulletin of mathematical biology 28 (1966), S. 519-536 
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    Notes: Abstract Certain types of cortical electrical events are non-propagated so that the associated electric fields must have standing wave characteristics. However, cortical electric events typically are generated by neurone populations which cannot be activated simultaneously on impulse driving. Hence the sum of the standing wave fields due to asynchronous activation of adjoining regions of cortical neurones must give the appearance of a traveling wave. Analysis of cortical waveforms is further complicated by curvature in cortical surfaces. A model is presented that shows the effects of curvature and time lag in activation on the form of the potential at points in space around a laminar array of elements simulating a population of cortical neurones. The results are compared with waveforms evoked by single-shock stimulation of the prepyriform cortex in cats.
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    A continuity equation for cell populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 545-554 
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    Notes: Abstract A continuity equation for cell-number density in a population of cells is derived, and a system of equations for eliminating parameters between the general solution and the initial distribution obtained.
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    The behavior of the weakening and failing myocardium (1966)
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    Bulletin of mathematical biology 28 (1966), S. 537-544 
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    Notes: Abstract Use of an electrical model of the left ventricle of the heart and the arterial system permits analysis of the changes which take place as the capacity of the myocardium for generation of force decreases. The model is simple in structure, and its construction and practical testing would not be difficult. It demonstrates that, as the heart muscle weakens, the peak of intracardiac force occurs later in systole, and the difference between the intracardiac pressure and the aortic pressure in the second half of systole is much greater than for the normal heart. The feedback mechanisms which are proposed to affect myocardial contractility would affect this compensation for cardiac weakening. Indices to categorize the behavior of the normal, compensated though weakened, and decompensated myocardium are proposed.
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    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 555-566 
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    Notes: Abstract The frequency distribution in a population of cells of the quantityCD (defined as the amount of some chromosomal substance in a cell which containsC chromosomes) is calculated using the distribution in the population of the amount per chromosome,D, and the distribution of chromosome number,C.
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    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 567-574 
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    Notes: Abstract The rate of chromosomal DNA synthesis in an exponentially growing population of cells having chromosome-number dispersion is calculated using DNA histogram data, chromosome-number distribution data, and the assumptions that the synthesis rate is constant and DNA double exactly.
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    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
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    Bulletin of mathematical biology 28 (1966), S. 575-584 
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    Notes: Abstract An estimate is made of the rate coefficient for linear DNA synthesis with exact doubling in an exponentially growing population of Ehrlich ascites tumor cells having chromosome-number dispersion. Comparison of calculated and experimental results suggest that the assumptions used in the calculation are tenable, but further experimental evidence is needed to prove this.
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    A sociological approach to biology (1966)
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    Bulletin of mathematical biology 28 (1966), S. 655-661 
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    Notes: Abstract The paper develops further some suggestions made previously (Bulletin of Mathematical Biophysics,28, 283–308, 1966) that certain biological phenomena may be more easily interpreted from a “sociological” point of view by considering the organism as a social aggregate of cells and a cell as a social aggregate of genes. In this light the problems of origin of life on earth, of aging, and of parasitism and symbiosis are discussed. The notion of social aggregates of different orders is introduced.
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    Theorems on random evolution (1966)
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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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    A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure (1966)
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    Bulletin of mathematical biology 28 (1966), S. 585-643 
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    Notes: Abstract A theoretical and experimental study was made of the mechanical behavior of the cornea. The theoretical analysis included an analytical solution for the symmetrical constraint of a thin, shallow, spherical shell by a rigid indenter. The experimental study investigated the rheology of the cornea with particular emphasis on its compliance with the requirements of the Boltzmann Superposition Principle. Representative results of tests on twenty enucleated hog eyes and two human eyes have been reported. The corneas of the human and hog eyes behaved as linear viscoelastic solids; the human eyes differed from the hog eyes in having a long term creep component. Several eyes were tested at the site of procurement, six to seven minutes after the animal's death, and it was established that creep is not an artifact due to aging or enucleation. The analytical and experimental results were combined to study some instruments used to detect the level of pressure in the eye. The theoretical analysis predicted that a type of elastic instability occurs during the process of flattening a small portion of the cornea; this is discussed with reference to the Goldmann and Mackay-Marg tonometers. The role of corneal creep was considered with reference to the response of the Schiøtz indentation tonometer during the time dependent process known as tonography.
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    Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver (1966)
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    Bulletin of mathematical biology 28 (1966), S. 645-654 
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    Notes: Abstract Following previous studies, differential equations are established which determine the variation of the stimulus towards a corrective turn of the steering wheel and its effect on the excitation of the centers in the brain which results in the production of the corrective turn. The equations are derived under the highly oversimplified assumption that all excitation thresholds are so small that they can be neglected. Under these assumptions it is found that the tracking curve of a car is a sinusoid with negative damping, that is, with an ever increasing amplitude. Driving under these assumptions is imposible since the car will always eventually jump off the road. The possible effects of the threshold as well as stimuli towards corrective turns other than the distance from the edge of the lane are very briefly discussed. In spite of the negative results of the paper, its interest lies in the circumstance that with the complication of the model, we find that driving depends not only on the reaction times as the only “purely biological” parameter, but on three other neurobiophysical constants. In a subsequent paper (Rashevsky, 1967) it is shown how the introduction of one or more purely biological parameters of the driver makes a stable driving regime possible.
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    The motion of thhe left ventriele: I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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    Modularity and reliability in the organization of organisms (1992)
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    Bulletin of mathematical biology 54 (1992), S. 1-20 
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    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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    Maximum-likelihood estimation of the statistical distribution of Smith-Waterman local sequence similarity scores (1992)
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    Bulletin of mathematical biology 54 (1992), S. 59-75 
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    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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    A general theory for host seeking decisions in mosquitoes (1992)
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    Bulletin of mathematical biology 54 (1992), S. 401-412 
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    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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    Rate maximizing and state variable theories of diet selection (1992)
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    Bulletin of mathematical biology 54 (1992), S. 413-422 
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    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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    Components of uncertainty in clutch-size optimization (1992)
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    Bulletin of mathematical biology 54 (1992), S. 445-464 
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    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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    Intra-specific competition and density dependent juvenile growth (1992)
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    Bulletin of mathematical biology 54 (1992), S. 503-519 
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    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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    Analysis of volume regulation in an epithelial cell model (1992)
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    Bulletin of mathematical biology 54 (1992), S. 537-561 
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    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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    Book reviews (1992)
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    Bulletin of mathematical biology 54 (1992), S. 687-694 
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    Modeling immune reactivity in secondary lymphoid organs (1992)
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    Bulletin of mathematical biology 54 (1992), S. 649-672 
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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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    On the kinetics and optimal specificity of cytotoxic reactions mediated by T-lymphocyte clones (1992)
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    Bulletin of mathematical biology 54 (1992), S. 839-873 
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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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    Compartmental models with Erlang distributed residence times and random rate coefficients (1992)
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    Bulletin of mathematical biology 54 (1992), S. 929-938 
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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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    Nonlinear phenomena and chaos in a Monte Carlo simulated microbial ecosystem (1992)
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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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    A mathematical model of the P-glycoprotein pump as a mediator of multidrug resistance (1992)
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    Bulletin of mathematical biology 54 (1992), S. 1023-1038 
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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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    Initiation and stability of reentry in two coupled excitable fibers (1992)
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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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    Use of a flexible logistic function to describe axial growth of plants (1992)
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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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    Analysis of weighted median filters based on inequalities relating the weights (1992)
    Springer
    Circuits, systems and signal processing 11 (1992), S. 115-136 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    URL: http://dx.doi.org/10.1007/BF01189223
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    Signal and image processing using three-dimensional binary ranking transforms (1992)
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    Circuits, systems and signal processing 11 (1992), S. 137-151 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    URL: http://dx.doi.org/10.1007/BF01189224
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    On the performance of stack filters and vector detection in image restoration (1992)
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    Circuits, systems and signal processing 11 (1992), S. 153-169 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Losslessness and stability of LDI ladders and filters (1992)
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    Circuits, systems and signal processing 11 (1992), S. 325-352 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    On construction of coprime factorizations for nonlinear feedback control systems (1992)
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    Circuits, systems and signal processing 11 (1992), S. 285-307 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we 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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    URL: http://dx.doi.org/10.1007/BF01293677
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    Improved neural networks for analog-to-digital conversion (1992)
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    Circuits, systems and signal processing 11 (1992), S. 387-398 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we 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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    URL: http://dx.doi.org/10.1007/BF01190983
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    On observability of singular systems (1992)
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    Circuits, systems and signal processing 11 (1992), S. 421-430 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Rotationally invariant pecstrum: A rotationally invariant object descriptor based on mathematical morphology (1992)
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    Circuits, systems and signal processing 11 (1992), S. 455-492 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    URL: http://dx.doi.org/10.1007/BF01219503
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    Close-form coefficient expressions of typical two-dimensional band-select linear-phase FIR filters (1992)
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    Circuits, systems and signal processing 11 (1992), S. 493-508 
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    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    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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    Beneficial changes in random variables under multiple sources of risk and their comparative statics (1992)
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    The Geneva risk and insurance review 17 (1992), S. 7-191 
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    ISSN: 1554-9658
    Keywords: Risk ; Insurance Demand ; Deterministic Transformations ; Stochastic Dominance ; Expected Utility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract The consequences of a change in a random parameter are determined for a decision model with more than one source of randomness. The two cases of independent and stochastically dependent sources of risk are discussed. Four comparative static theorems are given. These state the effect of first degree stochastically dominant shifts or risk decreases for one random variable while the other random variable is held fixed. Deterministic transformations are used to represent random parameter changes. The results are presented in the context of the coinsurance demand model with a risky insurable asset and background risk.
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    URL: http://dx.doi.org/10.1007/BF00941954
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    Comparative statics under multiple sources of risk with applications to insurance demand (1992)
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    The Geneva risk and insurance review 17 (1992), S. 21-33 
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    ISSN: 1554-9658
    Keywords: Insurance Demand ; Multiple Sources of Risk ; Comparative Statics ; Increases in Risk
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract In this paper we propose an answer to the following problem of comparative statics in models with multiple sources of risk: How a risk averse agent will change his coinsurance demand when the distribution of the insurable loss is shifted? To answer the question, we first comment on Jack Meyer's results and then we show how an alternate approach leads to more definitive comparative statics.
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    Pricing insurance and warranties: Ambiguity and correlated risks (1992)
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    The Geneva risk and insurance review 17 (1992), S. 35-60 
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    ISSN: 1554-9658
    Keywords: Ambiguity ; Pricing ; Actuaries ; Decision Processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract This paper reports on the results of a questionnaire study of pricing decisions made by professional actuaries when the probabilities of a loss are either ambiguous or nonambiguous. Theoretical hypotheses derived from the expected utility model were compared with the implications of procedures described by practicing actuaries. Actuaries were asked to act as consultants to a computer manufacturer concerning the price of a warranty. The suggested prices were considerably higher when probabilities were ambiguous than when they were well-specified. These pricing decisions were consistent with the procedures described by actuaries but inconsistent with predictions from expected utility theory when the risks are perfectly correlated. Further insight into the actual decision process is provided by interviews with actuaries and an analysis of comments written on the questionnaire forms.
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    Saving under uncertainty: A bivariate non-expected utility approach (1992)
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    The Geneva risk and insurance review 17 (1992), S. 61-75 
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    ISSN: 1554-9658
    Keywords: Saving ; Borrowing ; Increases in Risk Aversion ; Increases in Risk ; Multivariate NonExpected Utility Model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract We adopt the multivariate non-expected utility approach proposed by Yaari [1986] to provide a characterization of the comparative statics effects of greater risk aversion and of mean-preserving increases in risk on saving and borrowing in the presence of income and interest rate risk. We show that in Yaari's model, it is possible to extend the applicability of the Diamond and Stiglitz [1974] and Kihlstrom and Mirman [1974] (DSKM) single-crossing property to establish a relationship between greater risk aversion and saving (or borrowing) on the basis of the individual's ordinal preferences as long as the two risks are independent. We also demonstrate that the comparative statics effects of a joint mean-preserving increase in random income and interest rate on saving and borrowing can be determined by an extension of the DSKM single-crossing property.
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    Plasmid incidence and linear alkylbenzene sulfonate biodegradation in wastewater and pristine pond ecosystems (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 37-43 
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    ISSN: 1476-5535
    Keywords: Linear alkylbenzene sulfonate ; Biodegradation ; Plasmid ; Detergent ; Gene probe
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Linear alkylbenzene sulfonate (LAS) is a widely used anionic surfactant. Although approximately 1 million metric tons of LAS are produced annually, relatively little is known about the bacteria or the genetic factors that control LAS degradation in the environment. The objectives of this research were to: i) compare bacterial populations in wastewater and pristine pond systems; ii) determine the frequency of plasmids in bacteria from these sites; and iii) compare the frequency of DNA sequences coding for aromatic catabolism in isolates from these two sites. Plate counts indicated that exposure to wastewater resulted in higher levels of both heterotrophic bacteria and bacteria capable of growing on LAS containing medium (LAS/YEPG). In addition to higher numbers, a higher proportion of heterotrophs from the wastewater system were capable of growth on LAS/YEPG medium. Thus, the high levels of LAS in the wastewater system apparently selected fro organisms that were able to tolerate and/or degrade, it. Mineralization of14C-ring labelled LAS in any habitat related to the presence of organisms that grew on LAS/YEPG. Although may of these isolates could carry out primary degradation, no isolate, could mineralize14C-ring LAS in pure culture. A higher incidence of plasmids was found in bacteria from the wastewater pond and among bacteria that grew on LAS containing medium. However, the presence of plasmid, DNA did not necessarily confer the ability to degrade LAS nor was the ability to degrade LAS dependent on the presence of a plasmid. The incidence of selected genotypes for aromatic catabolism was similar among isolates on LAS/YEPG at both sites, suggesting that LAS ring degradation may be present in other populations or encoded by alternative sequences. In conclusion, LAS mineralization is mediated by a consortium and the evidence that initial attack of LAS is plasmid mediated is inconclusive.
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    10-Hydroxy-8(Z)-octadecenoic acid, an intermediate in the bioconversion of oleic acid to 7,10-dihydroxy-8(E)-octadecenoic acid (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 103-107 
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    ISSN: 1476-5535
    Keywords: Fatty acid bioconversion ; hydroxy octadecenoic acid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Previously, we reported the discovery of a new compound, 7,10-dihydroxy-8(E)-octadecenoic acid (DOD) which was produced from oleic acid by a new bacterial isolate PR3 [6,7]. The reaction is unique in that it involves a hydroxylation at two positions and a rearrangement of the double bond of the substrate molecule. Now, we have isolated another compound from the reaction mixture determined by GC/MS to be 10-hydroxy-8-octadecenoic acid (HOD). NMR and IR data indicate that the unsaturation is probablycis. The optimum pH and temperature for the production of HOD by strain PR3 were 6.5 and 30°C, about the same as those for DOD. However, the amount of HOD detected remained small throughout an 48-h reaction period during which the amount of DOD increased sharply. At 48 h of reaction, the ratio between HOD∶DOD was 1∶10. HOD may be an intermediate in the biosynthesis of DOD from oleic acid.
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    Cultivation ofCandida blankii in simulated bagasse hemicellulose hydrolysate (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 109-113 
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    ISSN: 1476-5535
    Keywords: Candida blankii ; Biomass ; d-Xylose ; l-Arabinose ; Acetate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary All fourCandida blankii isolates evaluated for growth in simulated bagasse hemicellulose hydrolysate utilized the sugars and acetic acid completely. The utilization ofd-xylose,l-arabinose and acetic acid were delayed by the presence ofd-glucose, but after glucose depletion the other carbon sources were utilized simultaneously. The maximum specific growth rate of 0.36 h−1 and cell yield of 0.47 g cells/g carbon source assimilate compared with published results obtained withC. utilis. C. blankii appeared superior toC. utilis for biomass production from hemicellulose hydrolysate in that it utilizedl-arabinose and was capable of growth at higher temperatures.
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    Laboratory-scale biosynthesis ofTrichoderma mycolytic enzymes for protoplast release fromCochliobolus lunatus (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 115-119 
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    ISSN: 1476-5535
    Keywords: Mycolytic enzymes ; Trichoderma viride ; Protoplasts ; Cochliobolus lunatus ; Fermentation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Microorganism useful for the induction of enzymes lytic towards walls of filamentous fungusCochliobolus lunatus were studies. Production of specificTrichoderma viride mycolytic enzymes was studied in a laboratory fermentor. The product with high chitinase and relatively low protease activity gave better yields ofC. lunatus protoplasts than commercial Novozym 234.
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    Optimized protocol for the pilot-scale preparation of fungal cellulase (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 121-125 
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    ISSN: 1476-5535
    Keywords: Trichoderma viride ; Cellulase production ; Optimized production medium and parameters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary A 25-l scale protocol is devised for the optimal secretion and recovery of fungal cellulase. Using a selected higher yieldingTrichoderma viride SMC strain, a protocol consisted of: a) an optimized production medium rich in microcrystalline cellulose (MCC), fortified with 1% (w/v) ammonium sulphate, 0.5% (w/v) soybean flour, 0.1% (v/v) Tween-80 and other trace nutrients; b) optimized physical parameters of production, such as an inoculum containing a homogeneous suspension of 6×107 conidia per 1,28±1°C, pH 4.0±0.5, 300±20 rpm, 11000±1000 l/h aeration, and 170–220 h duration; c) optimal recovery through a filter press (450 l/h rate of filtration) followed by precipitation with 2.5–3.0 volumes of acetone (15°C and basket centrifugation (27°C, 1700 rpm)); and d) vacuum drying (35°C, 4–6 h). This afforded 70% recovery of cellulase in the form of white fluffy powder containing 20000±2000 carboxy methyl cellulase and 1000±50 units filter paperase per g activities, with raw material cost of US$ 8–10 per million carboxy methyl cellulase units. During storage for 18 months at 4°C, ambient temperature and 37°C, the cellulase preparation was found to retain 100, 75 and 60% of its initial activity, respectively.
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    Production ofLactococcus lactis biomass by immobilized cell technology (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 131-135 
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    ISSN: 1476-5535
    Keywords: Cheese ; Starters ; Production ; Alignate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Calcium alginate beads containingLactococcus lactis cells were used for three batch fermentations of milk or a commercially available growth medium (Gold Complete, Nordica) with the aim of producing concentrated cultures. Repeated fermentations did not significantly increase bead CFU counts which were between 3.3–7.8×1010 CFU/g. During the second and third fermentations, which lasted 6 h each, the bead populations decreased if the incubation was extended over 2 h. There was cell release from the beads. Fermentation media and fermentation time all had an effect on free cell counts, but none of these factors statistically interacted. Free cell counts were higher at the end of fermentations 2 and 3 than in the first fermentation and approximately 50% of the population was in the free state. Free cell counts were higher when the beads were incubated in Gold complete than in milk. Although the total bacterial population of a standard free cell fermentation was always higher than those having immobilized cells, immobilized cell technology did enable the production of dense cultures.
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    Immobilization ofβ-fructofuranosidase fromAureobasidium sp. ATCC 20524 on porous silica (1992)
    Springer
    Journal of industrial microbiology and biotechnology 9 (1992), S. 247-250 
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    ISSN: 1476-5535
    Keywords: Fructosyl-transferring enzyme ; 1-Kestose ; Fructo-oligosaccharide ; Continuous production
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary β-Fructofuranosidase P-1 fromAureobasidium sp. ATCC 20524, which produces a fructo-oligosaccharide (1-kestose) from sucrose, was immobilized covalently onto alkylamine porous silica with glutaraldehyde at high efficiency (44.4%). Optimum pore diameter of porous silica for immobilization of the enzyme was 91.7 nm. The enzymatic profiles of immobilized enzyme were almost identical to the native one except its stabilities to temperature and metal ions were improved. 1-Kestose was produced continuously and selectively from 40% (w/v) sucrose at fast flow rates by a column packed with the immobilized enzyme for up to 26 days, and the effluent concentration of 1-kestose remained in the range 113–135 mg ml−1.
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    Production of microbial levan from sucrose, sugarcane juice and beet molasses (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 257-260 
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    ISSN: 1476-5535
    Keywords: Polysaccharide ; Fructan ; Gum ; Fermentation ; Bacillus polymyxa ; Sweetener
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary Bacillus polymyxa (NRRL-18475) produced a levan-type fructan (B, 2→6 fructofuranoside) when grown on sucrose, sugarcane juice, and sugarbeet molasses. The organism converted about 46% of the fructose moiety of sucrose to levan when grown on sucrose medium, however, the yields of levan from sugarcane juice and beet molasses were much less than sucrose solution. Such sugarcane juice and beet molasses can be made a good substrate for levan production by various modifications. Adding peptone to sugarcane juice or passing beet molasses through a column of gel filtration media improved levan yield to a level almost comparable to that obtained from sucrose.
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    Etude des premiers etages sensoriels (1966)
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    Bulletin of mathematical biology 28 (1966), S. 1-10 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Résumé Les premiers étages sensoriels sont étudiés en utilisant notre modèle de neurone et en supposant que les réseaux responsables de la perception sont particulièrement solides, stables, économiques. Nous montrons que les premiers neurones doivent être spontanément périodiques et autorégulés. La nécessité fonctionnelle des premiers étages de la voie visuelle est démontrée. Par analogie, nous étudions la voie auditive.
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    The flow of a viscous liquid in a converging tube (1966)
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    Bulletin of mathematical biology 28 (1966), S. 11-24 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The problem of the viscous flow of an incompressible Newtonian liquid in a converging tapered tube has been solved in spherical polar coordinates. The method of the solution involves the Stokes' stream function and a technique introduced by Stokes in the study of a sphere oscillating in a fluid. The theory for the flow in a rigid tube includes: (1) the pulsatile flow with both radial and angular velocity components; (2) the steady state flow with both radial and angular velocity components and (3) the very slow steady state flow with only a radial velocity component present. For a tapered elastic tube, the velocity of the propagated pulse wave is determined. The solution given is in terms of the elastic constants of the system and the coordinates for this type of geometry. The pulse velocity is then related to the velocity in an elastic cylindrical tube with the necessary correction terms to account for the tapered tube.
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    Some multi-dimensional branching processes as motivated by a class of problems in mathematical genetics I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 25-50 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper a class of branching processes applicable to populations reproducing by some asexual means or by a simple selfing system of mating is studied. The paper is divided into three parts. In part one the mathematical model is introduced, part two is a mathematical analysis of the model, and in part three concrete applications and examples are given. Many of the proofs of the theorems in part two are omitted but will appear in a subsequent issue of theBulletin.
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    Design of neural nets with intermittent response and certain other relevant studies (1966)
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    Bulletin of mathematical biology 28 (1966), S. 51-74 
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    Notes: Abstract The application of the earlier results (Pavlidis, T. 1965. “A New Model for Simple Neural Nets and its Application in the Design of a Neural Oscillator.”Bull. Math. Biophysics,27, No. 2, 215–229) to the design of more complex neural nets is attempted. The following cases are considered: 1. Chains of neurons where it is proven that the frequency of the output pulses does not depend on the value of the input as long as it is above a certain threshold. 2. Groups of neurons with backward inhibition which present an intermittent mode of operation. 3. Neural nets with periodic facilitation which permit time sharing of certain components for different functions. 4. A neural net which can detect the sign of the input even if the main receptor is sensitive only to the absolute value of it, is presented. 5. A velocity estimating neural net which in combination with one of the nets with intermittent response provides a model for the smooth eye tracking movements.
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    Academic learning, a variational model (1966)
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    Bulletin of mathematical biology 28 (1966), S. 75-90 
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    Notes: Abstract By assigning coordinates to the information space comprising all knowledge, rigorous mathematical interpretations can be placed on such terms as academic ability, memory and creativity such that these psychometric concepts can be incorporated into a framework of functional analysis which then permits the optimization of long-term academic learning processes through the location of the teaching trajectories in information space which will maximize the knowledge accumulated in a generalized educational system composed of a complex of subject-pupil-teacher interactions. The concepts of discrete and continuous information spaces are discussed in connection with subject-subject, subjectpupil and pupil-pupil interactions, and the advantages of using variational versus dynamic programming methods of optimizing alternative educational systems are evaluated.
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    On chains of related sets (1966)
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    Bulletin of mathematical biology 28 (1966), S. 103-106 
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    Notes: Abstract IfK is a partition of a setK which is partially ordered by the relationR andR is a collection of pairs of sets ofK such that the sets of each pair are related byR in the sense of Rashevsky, thenR is a relation which partially ordersK. Necessary and sufficient conditions thatK be a chain are obtained, and ifK is a chain under these conditions, it is shown thatK is unique.
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    On multipole theory in electrocardiography (1966)
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    Bulletin of mathematical biology 28 (1966), S. 161-166 
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    Notes: Abstract This paper continues a comparison of the Taylor series and spherical harmonic forms of multipole representations initiated by Yeh (Bull. Math. Biophysics,24, 197–207, 1962). It is shown that while transformations from Taylor series form into spherical harmonic form is always possible, the inverse cannot be accomplished as suggested by Yeh; corrected transformation equations are given. It is also shown that direct measurement of Taylor coefficients, as outlined in Yeh, Martinek, and de Beaumont (Bull. Math. Biophysics,20, 203–216, 1958), is actually not possible. Accordingly, only the spherical harmonic coefficients can be determined by measurement of surface potentials, as in electrocardiography.
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    Some multi-dimensional branching processes as motivated by a class of problems in mathematical genetics II (1966)
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    Bulletin of mathematical biology 28 (1966), S. 181-190 
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    Notes: Abstract This paper is a continuation of a paper, “Some Multi-Dimensional Branching Processes as Motivated by a Class of Problems in Mathematical Genetics I,” by C. J. Mode, which appeared in a previous issue of theBulletin. Its purpose is two-fold; namely to discuss the mathematical existence of the model and to supply the mathematical proofs of some theorems in section two of the paper mentioned above. This paper should be read in conjunction with the previous paper.
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    A resolution of Rosen’s paradox for self-reproducing automata (1966)
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    Bulletin of mathematical biology 28 (1966), S. 191-194 
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    Notes: Abstract Rosen (Bull. Math Biophysics. 1959) has argued that a self-reproducing automaton of the type originally described by von Neumann is impossible because of a logical paradox inherent in its definition. The paradox is resolved by explicitly allowing errors (mutations) in the system and thus introducing evolution. There is no paradox in an automaton, originating from a slightly different ancestor through mutation. The von Neumann model thus becomes realistic and useful for a discussion of biological phenomena.
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    Ventricular septal defect with bidirectional shunting: Mathematical considerations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 167-179 
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    Notes: Abstract Previously proposed formulae for the quantitative estimation of bidirectional shunts across ventricular septal defects require determination of the oxygen contents of mixed venous, pulmonary artery, pulmonary venous, and aortic blood. Because these formulae do not take into account the mixing of oxygenated with unoxygenated blood within the ventricles, their use must result in underestimation of shunt flows in each direction. A mathematical model for a ventricular defect is examined, in which it is assumed that mixing of blood occurs in each of six sites in the venae cavae or right atrium, right ventricle, pulmonary artery, left atrium, left ventricle, and aorta. A total of fourteen streams of blood can flow from one to another of these mixing sites. As long as complete mixing occurs in the six specified mixing sites, any degree of mixing or non-mixing of the various streams is permitted. From the equations characterizing the model, formulae are derived in which the shunt flow in each direction is expressed in terms of the oxygen contents in the six mixing sites and the fractions of blood which enter the shunt from either side without prior mixing in a ventricular mixing site. The previously reported formulae, which apply when no ventricular mixing is allowed to occur, lead to theoretical minimum values for the shunt flows in each direction. At the opposite extreme where all the shunting blood is required to mix in a ventricle before entering the shunt, formulae for maximum possible shunt flows are also obtained. The absolute values for the left-to-right and right-to-left shunt flows, which must lie somewhere between the theoretical maximum and minimum values, cannot be computed from blood gas data alone.
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    Control of the contractility of the myocardium in a feedback system (1966)
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    Bulletin of mathematical biology 28 (1966), S. 195-205 
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    Notes: Abstract Experimental evidence strongly suggests that the contractility of the intact heart in situ, in contrast to that of striated muscle elsewhere in the body, is controlled in a close-cycle system. Thus, the variation of intraventricular pressure during systole follows a complex pattern, whose relative form remains quite constant regardless of the duration of ejection. By use of the single-chambered model of the cardiovascular system, a mathematical representation of a feasible feedback mechanism is developed. The requirement that the feedback system must satisfy mathematical principles eliminates relationships apparently reasonable from a physiological viewpoint. A clinical application which the mathematical development suggests is that early arterial hypertension may arise from an abnormal feedback mechanism with excessively large cardiac output in the initial portion of systole.
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    On the shape of a DNA molecule (1966)
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    Bulletin of mathematical biology 28 (1966), S. 207-216 
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    Notes: Abstract Due to the lack of direct X-ray evidence for base pairing being the only mechanism for the formation of double helix in a DNA crystal, an alternative explanation is suggested so that the observed DNA loop becomes essential.
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    A population growth model incorporating delayed responses (1966)
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    Bulletin of mathematical biology 28 (1966), S. 219-233 
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    A note on group ring expression of self-fertilized population (1966)
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    Bulletin of mathematical biology 28 (1966), S. 217-218 
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    Notes: Abstract Validity of group ring expression of selfed population is shown for cases in which there are differences in recombination probabilities between two sexual sides of a plant.
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    Analysis of tracer experiments: VII. General multi-compartment systems imbedded in non-homogeneous inaccessible media (1966)
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    Bulletin of mathematical biology 28 (1966), S. 261-282 
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    Notes: Abstract An integral equation analysis of generaln compartment steady state systems imbedded in static media of arbitrary complexity has been developed. A set of initial entry functions can be found which serve to determine a corresponding set of partitioned initial entry functions. The partitioned functions, in turn, can be used to predict the probabilities and time courses of various transport histories and to determine all steady state rates of flow between measured compartments. The method is quite general, being completely applicable, for example, to closed systems, to cyclic systems and to systems in which relatively rapid (but finite) exchange between compartments occurs.
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    A note on relations between sets (1966)
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    Bulletin of mathematical biology 28 (1966), S. 309-313 
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    Notes: Abstract From the definition of a strong and weakn-ary relation betweenn sets, given in a previous paper (Bulletin of Mathematical Biophysics,27, 477–492), it follows that for a given set ofn sets and givenn-ary relationR between them there can exist only one strong relation, but a large number of weak ones. An expression for the total number of possible weak relations is derived and the notion of the degree of weakness of a relation is introduced and discussed.
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    Reconstruction of protein and nucleic acid sequences: IV. The algebra of free monoids and the fragmentation stratagem (1966)
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    Bulletin of mathematical biology 28 (1966), S. 235-260 
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    Notes: Abstract The problem of determining the sequence of a biopolymer from its fragments is stated in mathematical terms. Using concrete properties of a free monoid, certain general classes of biopolymers are shown to be insolvable from fragment data produced by complete digestion where enzymes specific for any possible combination of chemical bonds are employed.
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    Physics, biology, and sociology: A reappraisal (1966)
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    Bulletin of mathematical biology 28 (1966), S. 283-308 
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    Notes: Abstract To the extent that all biological phenomena are perceivable only through their physical manifestations, it may be justified to assume that all biological phenomena will be eventually represented in terms of physics; perhaps not of present day physics, but of some “extended” form of it. However, even if this should be correct, it must be kept in mind that representing individual biological phenomena in terms of physics is not the same as deducing from known physical laws the necessity of biological phenomena. Drawing an analogy from pure mathematics, it is possible that while every biological phenomenon may be represented in terms of physics, yet biological statements represent a class of “undecidable” statements within the framework of physics. Such a conjecture is reinforced by the history of physics itself and illustrated on several examples. The 19th century physicists tried in vain todeduce electromagnetic phenomena from mechanical ones. A similar situation may exist in regard to biological and social sciences. Quite generally, the possibility of representing a class B phenomena in terms of class A phenomena does not imply that the phenomena of class B can be deduced from those of class A. The consequences of the above on the relation between physics, biology, and sociology are studied. A tentative postulational formulation of basic biological principles are given and some consequences are discussed. It is pointed out that not only can the study of biological phenomena throw light on some physical phenomena, but that the study of social phenomena may be of value for the understanding of the structures and functions of living organisms. The possibility of a sort of “socionics” is indicated.
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    Re-establishability in abstract biology (1966)
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    Bulletin of mathematical biology 28 (1966), S. 371-374 
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    Notes: Abstract It is shown that any (ℳ ℛ) has some component which cannot be re-established after it has been inhibited. If there is only one such component, it must be central, that is, its inhibition stops the whole system. These results hold even when it is not assumed that ℳ is connected.
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    Restricted transition probabilities and their applications to some problems in the dynamics of biological populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 315-331 
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    Notes: Abstract In this paper a theory of a class of restricted transition probabilities is developed and applied to a problem in the dynamics of biological populations under the assumption that the underlying stochastic process is a continuous time parameter Markov chain with stationary transition probabilities. The paper is divided into three parts. Part one contains sufficient background from the theory of Markov processes to define restricted transition probabilities in a rigorous manner. In addition, some basic concepts in the theory of stochastic processes are interpreted from the biological point of view. Part two is concerned with the problem of finding representations for restricted transition probabilities. Finally, in part three the theory of restricted transition probabilities is applied to the problem of finding and analyzing some properties of the distribution function of the maximum size attained by the population in a finite time interval for a rather wide class of Markov processes. Some other applications of restricted transition probabilities to other problems in the dynamics of biological populations are also suggested. These applications will be discussed more fully in a companion paper.
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    A mathematical theory of enamel solubility and the onset of dental caries: II. Some solubility equilibrium considerations of hydroxyapatite (1966)
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    Bulletin of mathematical biology 28 (1966), S. 433-441 
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    Notes: Abstract Equilibrium solubility considerations are presented based on the assumption that equating the kinetic expressionq, developed in part I, to zero can describe the equilibrium or steady state between hydroxyapatite and salt solutions. From this expression is derived Hodge's empirical equilibrium equation,C=KH. Further, a lograithmic transformation of this equation results in an expression that accounts for the equilibrium calcium, phosphorus andpH relation found by Levinskas and Neuman. Finally, it also shows the relation between log (C·P) andpH necessary for typical artificial carious lesions as found by Coolidge, Besic and Jacobs. A discussion of a recent theory of hydroxyapatite solubility of LaMer reveals calculation errors that vitiate his results. It is shown that logK 1 (K 1 is the ratio of the rate constants inq and can serve as a solubility equilibrium constant for hydroxyapatite) varies by only 1.2 units when calculated from three diverse sets of data. This variation is less than that reported by LaMer (when the errors of calculation in that work are corrected) and considerably less than the range of 11 among attempts to calculate a conventionalpK sp , as summarized by Hodge.
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    On mass behavior (1966)
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    Bulletin of mathematical biology 28 (1966), S. 465-475 
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    Notes: Abstract In imitative behavior, as studied previously by N. Rashevsky (Mathematical Biology of Sociol Behavior, Chapter XIII, The University of Chicago Press, 1950), the reason for the majority of a society to accept a particular behavior is based on purely voluntary action (band-wagon effect). In the present paper effects of coercion of the majority by a small minority group which poses the means for coercion, are studied. More general types of equations are thus obtained and threshold effects found, which bear a resemblance to some such effects studied previously.
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    A mathematical theory of enamel solubility and the onset of dental caries: III. Development and computer simulation of a model of caries formation (1966)
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    Bulletin of mathematical biology 28 (1966), S. 443-464 
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    Notes: Abstract Part III attempts to develop a diffusion controlled model of caries in the intact enamel employing the kinetic results of the previous two parts. A model of the enamel as a granular bed with a diffusible organic matrix filling the interstices is considered. The basic equations of diffusion and simultaneous reaction are developed under the assumption that all the reactions are so rapid as compared with the diffusion rate, that they are in a quasi-equilibrium state. The resultant system of seven coupled, non-linear parabolic partial differential equations is of such complexity that only numerical solutions could be attempted. Stability restrictions inherent in the problem dictated the use of the DuFort-Frankel numerical solution for parabolic boundary problems. Numerical solutions giving the concentration of all reactants, the rate of mineral loss, and the enamel porosity were obtained for a variety of boundary conditions. It is found that departure from the equilibrium condition expressed in part II is necessary for the occurrence of an attack on the enamel. The rate and pattern of penetration is then determined primarily by the concentrations of undissociated buffer, and salts, together with the rate of diffusion in the surrounding medium. The possibility of a relatively intact surface layer persisting over a demineralized subsurface region due solely to the composition of the demineralizing medium is noted. Remineralization behavior in portions of the carious lesion occurs in the model under certain boundary conditions.
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    Editorial (1992)
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    Circuits, systems and signal processing 11 (1992), S. 3-4 
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    Topics: Electrical Engineering, Measurement and Control Technology
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    Preface (1992)
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    Circuits, systems and signal processing 11 (1992), S. 5-6 
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    Design of universal, variable frequency range FIR digital differentiators (1992)
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    Circuits, systems and signal processing 11 (1992), S. 431-439 
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    Notes: Abstract An efficient design of digital differentiators (DD), with a variable frequency range of operation at low and midband frequencies, has been proposed. Implemented as a Taylor structure, a DD designed for orderN can be made to function as a universal configuration giving optimal transfer functions for all possible ordersN, without changing the coefficients.
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    Optimisation of culture conditions for production of eicosapentaenoic acid byMortierella elongate NRRL 5513 (1992)
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    Journal of industrial microbiology and biotechnology 9 (1992), S. 11-17 
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    ISSN: 1476-5535
    Keywords: Eicosapentaenoic acid ; Mortierella elongata ; Omega-3 fatty acids
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Summary WhenMortierella elongata NRRL 5513 was cultured in shake flasks at 25°C, mycelial growth reached a stationary phase at 48 h but maximum eicosapentaenoic acid (EPA) production was observed at 6 days. When incubated at 11°C, EPA production also continued to rise during the stationary phase of growth, reaching a maximum after 10 days. An initial culture pH of 6.1 was found to be optimum for EPA production. The effect of temperature on EPA production was dependent on medium constituents. In glucose and linseed oil supplemented media, optimum temperature for EPA production was 11 and 15°C respectively. A maximum EPA yield of 0.61 g/l was obtained in linseed oil (2%), yeast extract (0.5%) supplemented basal medium. Maximum EPA content as a percentage of lipids (15.12%) was observed when the latter medium was supplemented with 0.25% urea.
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