In computer graphics and real-time rendering, some of the sigmoid functions are used to blend colors or geometry between two values, smoothly and without visible seams or discontinuities. In biochemistry and pharmacology, the Hill and Hill–Langmuir equations are sigmoid functions. In audio signal processing, sigmoid functions are used as waveshaper transfer functions to emulate the sound of analog circuitry clipping. In artificial neural networks, sometimes non-smooth functions are used instead for efficiency these are known as hard sigmoids. The van Genuchten–Gupta model is based on an inverted S-curve and applied to the response of crop yield to soil salinity.Įxamples of the application of the logistic S-curve to the response of crop yield (wheat) to both the soil salinity and depth to water table in the soil are shown in modeling crop response in agriculture. When a specific mathematical model is lacking, a sigmoid function is often used.
Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. Inverted logistic S-curve to model the relation between wheat yield and soil salinity Ī sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0.Įxamples Plot of the error functionĪ sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.Ī common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: S ( x ) = 1 1 + e − x = e x e x + 1 = 1 − S ( − x ).
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