scholarly journals Using the Negative Exponential Model to Describe Changes in Risk of Smoking-Related Diseases following Changes in Exposure to Tobacco

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Peter N. Lee ◽  
John Hamling ◽  
John Fry ◽  
Barbara Forey
Keyword(s):  
Relative Risk ◽  
Half Life ◽  
Epidemiological Data ◽  
Exponential Model ◽  
Excess Relative Risk ◽  
Multiple Time ◽  
Product Switching ◽  
Negative Exponential Model ◽  
Multiple Time Points ◽  
Negative Exponential

Recently published analyses for four smoking-related diseases show that the declining excess relative risk by time quit is well fitted by the negative exponential model. These analyses estimated the half-life of this excess, that is, the time after quitting when the excess relative risk reaches half that for continuing smokers. We describe extensions of the simple model. One quantifies the decline following an exposure reduction. We show that this extension satisfactorily predicts results from studies investigating the effect of reducing cigarette consumption. It may also be relevant to exposure reductions following product-switching. Another extension predicts changes in excess relative risk occurring following multiple exposure changes over time. Suitable published epidemiological data are unavailable to test this, and we recommend its validity to be investigated using large studies with data recorded on smoking habits at multiple time points in life. The basic formulae described assume that the excess relative risk for a continuing smoker is linearly related to exposure and that the half-life is invariant of age. We describe model adaptations to allow for nonlinear dose-response and for age-dependence of the half-life. The negative exponential model, though relatively simple, appears to have many potential uses in epidemiological research for summarizing variations in risk with exposure changes.

APPLICATION OF TWO-LEVEL NEGATIVE EXPONENTIAL MODEL TO CHILDREN'S LEARNING CURVE IN READING

2002 ◽  
Vol 31 (2) ◽  
pp. 279-299 ◽  
Author(s):  
Dung-Tsa Chen ◽  
Wenyaw Chan ◽  
David J. Francis ◽  
Sally E. Shaywitz ◽  
Bennett A. Shaywitz
Keyword(s):  
Learning Curve ◽  
Exponential Model ◽  
Children’S Learning ◽  
Negative Exponential Model ◽  
Negative Exponential ◽  
Children's Learning

scholarly journals A Wave-Spectrum Analysis of Urban Population Density: Entropy, Fractal, and Spatial Localization

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Yanguang Chen
Keyword(s):  
Urban Population ◽  
Population Distribution ◽  
Wave Spectrum ◽  
Spatial Dynamics ◽  
Exponential Model ◽  
Urban Morphology ◽  
Wave Number ◽  
Entropy Maximization ◽  
Negative Exponential Model ◽  
Negative Exponential

The method of spectral analysis is employed to research the spatial dynamics of urban population distribution. First of all, the negative exponential model is derived in a new way by using an entropy-maximizing idea. Then an approximate scaling relation between wave number and spectral density is derived by Fourier transform of the negative exponential model. The theoretical results suggest the locality of urban population activities. So the principle of entropy maximization can be utilized to interpret the locality and localization of urban morphology. The wave-spectrum model is applied to the city in the real world, Hangzhou, China, and spectral exponents can give the dimension values of the fractal lines of urban population profiles. The changing trend of the fractal dimension does reflect the localization of urban population growth and diffusion. This research on spatial dynamics of urban evolvement is significant for modeling spatial complexity and simulating spatial complication of city systems by cellular automata.

scholarly journals Dung decomposition of cattle grazing from mixed pastures of Signalgrass (Brachiaria decumbens Stapf.) and tree legumes

2019 ◽  
pp. 1943-1949
Author(s):  
Carolina C. Lira ◽  
Jose C. B. Dubeux ◽  
Jr., Erick R. S. Santos ◽  
Mércia V.F. dos Santos ◽  
Erinaldo V. de Freitas
Keyword(s):  
Gliricidia Sepium ◽  
Exponential Model ◽  
Dry Forest ◽  
Co2 Evolution ◽  
Brachiaria Decumbens ◽  
Forest Region ◽  
Negative Exponential Model ◽  
In Situ Decomposition ◽  
Negative Exponential

The mineralization rate of ruminant manure may influence the fertilization management of pastures. This study aimed to evaluate feces decomposition of heifers grazing signalgrass (Brachiaria decumbens Stapf.) fertilized or not with N, or intercropped with legumes in the dry forest region. Two experiments were conducted; the first one was a CRD that evaluated the evolution of CO2 from a mixture of soil and feces (10:1) during 22 days of incubation in a hermetically sealed bucket with a solution of NaOH 0.5 mol L-1. The second one was a RCBD that evaluated the in situ decomposition of feces in nylon bags in time periods 4, 8, 16, 32, 64, 128 and 256 days after incubation above ground. The single negative exponential mathematical model was adequate (P ≤ 0.0001) to quantify the CO2 evolution of the mixture of soil and feces, indicating that 78% of CO2 was released at the beginning of the incubation, especially for the feces collected in the signalgrass pastures intercropped with Gliricidia sepium (Jacq.) Kunth ex Walp. (gliricídia). After the first 5 days, CO2 evolution was more stable. Remaining biomass in the litterbag along decomposition fitted the single negative exponential model (P < 0.001). Greater relative decomposition rate (k) of bovine fecal biomass occurred for the N-fertilized signalgrass treatment (k = 0.0031 g g-1 day-1) and a lesser rate for the treatment intercropped with Mimosa caesalpiniifolia Benth. (sabiá) (k = 0.0018 g g-1 day-1). Nitrogen fertilization in signalgrass pasture favored the decomposition of bovine feces at the end of 256 days of incubation.

How long does it take for different seeds to dry?

2010 ◽  
Vol 37 (6) ◽  
pp. 575 ◽  
Author(s):  
James P. Hill ◽  
Will Edwards ◽  
Peter J. Franks
Keyword(s):  
Seed Mass ◽  
Structural Features ◽  
Exponential Model ◽  
Moisture Loss ◽  
Negative Effects ◽  
Desiccation Rate ◽  
Seed Moisture ◽  
Moisture Deficit ◽  
Negative Exponential Model ◽  
Negative Exponential

Reduction in rainfall and intensification of dry season moisture deficit threaten to expose desiccation-sensitive seeds in the seasonal tropics to greater potential negative effects of desiccation. A determinate affecting the recruitment of species under increased aridity is how quickly desiccation-sensitive seeds dehydrate. We investigated the rate of seed moisture loss in 24 species that produce desiccation-sensitive seeds in a seasonal tropical forest and tested the common hypothesis that seeds conform to a simple negative exponential model of moisture loss with time. A negative exponential model described moisture loss in 14 species, but was not the best model for the remaining 10 species. Moisture loss in eight species was best described by a double-negative exponential model and by a double-linear model in the remaining two species. We then tested the hypothesis that seed mass could predict the rate of desiccation between and within species. Within species the time to a given state of desiccation could be predicted by seed mass for eight species. Between species there was no relationship between desiccation rate and seed mass. We conclude that different modes of water loss and seed structural features may be more important than seed mass in prolonging desiccation.

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