I expected to find some evidence of the project's exponential growth rolling over into the inevitable logistic curve; I hoped for a leading indicator, perhaps-- a sort of canary.
12.
If Player A has a rating of R _ A and Player B a rating of R _ B, the exact formula ( using the logistic curve ) for the expected score of Player A is
13.
:If Player A has true strength R _ A and Player B has true strength R _ B, the exact formula ( using the logistic curve ) for the expected score of Player A is
14.
More quantitatively, as can be seen from the analytical solution, the logistic curve shows early exponential growth for negative argument, which slows to linear growth of slope 1 / 4 for an argument near zero, then approaches one with an exponentially decaying gap.
15.
The Resilience Alliance, as illustrated by the work of C . S . Holling and L . H . Gunderson, shows how the logistic curve of the r phase positive feedback, becoming replaced by the K negative feedback strategy is an important part of adaptive capacity.
16.
Fitting data to the logistics curve is notoriously hard; the parameters are very sensitive to small changes in the data in some ranges ( which is a backwards way of saying that the function values may change very little for big changes in the parameters, at least in some regions ).
17.
In his classic 1957 Ph . D . dissertation, " Hybrid Corn : An Exploration in the Economics of Technological Change ", published as an article in the October 1957 issue of " Econometrica ", Griliches demonstrated that the penetration of corn seeds followed the logistic curve.
18.
When graphed, the rate of adoption formed what came to typify the Diffusion of Innovations model, a logistic curve ) The graph shows a cumulative percentage of adopters over time slow at the start, more rapid as adoption increases, then leveling off until only a small percentage of laggards have not adopted.
19.
:: : : : : I agree a logistic curve would be a better model, but when I tried fitting the sigmoids, they were nearly identical-- within a few percent-- to the exponential model out to 2030, and did not cusp until long enough that the amount of electricity being produced was unrealistic . talk ) 01 : 20, 16 March 2012 ( UTC)
20.
Among the subjects were the transit of Mercury, the Aurora Borealis, the figure of the Earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometer, and various problems of spherical trigonometry.
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