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A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t ...
Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed for use in both relativity and ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The graph of the function a cosh(x/a) is the catenary, the curve formed by a uniform flexible chain, ... Sigmoid function; Soboleva modified hyperbolic tangent;
The hyperbolastic functions can model both growth and decay curves until it reaches carrying capacity. Due to their flexibility, these models have diverse applications in the medical field, with the ability to capture disease progression with an intervening treatment.
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Hyperbolic spiral; Lituus; Logarithmic spiral; Nielsen's spiral ...
The curve represents xy = 1. A hyperbolic angle has magnitude equal to the area of the corresponding hyperbolic sector, which is in standard position if a = 1. In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy = 1 in Quadrant I of the Cartesian plane.
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. [1] More precisely, the reciprocal function 1 / x {\displaystyle 1/x} has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x → 0 {\displaystyle x\to 0} is infinite: any ...