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Machine Learning
Published in Michael Ljungberg, Handbook of Nuclear Medicine and Molecular Imaging for Physicists, 2022
where ∘ denotes function composition. For this network architecture there is first an affine mapping from m dimensions to n1, followed by a non-linear activation function. The result is a vector with n1 elements. Then follows another affine function from n1 dimensions to n2 dimensions, followed by a non-linear activation function. The final results are obtained by a third affine mapping from n2 dimensions to n dimensions, followed by the softmax function. The output vector fw(x) consists of n positive numbers that sum to 1. The parameters w of the artificial neural network consists of all the parameters of the affine layers, that is, w = (w1,w2,w3).
Functional Dependency Network Analysis
Published in C. Ariel Pinto, Paul R. Garvey, Advanced Risk Analysis in Engineering Enterprise Systems, 2016
C. Ariel Pinto, Paul R. Garvey
The equation for Pp was fashioned by a composition of operability functions. Function composition is when one function is expressed as a composition (or nesting) of two or more other functions.* Function composition applies in FDNA when the operability function of one node is a composition of the operability functions of two or more other nodes. Next, we discuss forms the operability function f might assume. Selecting a specific form is central to FDNA and a major flexibility feature of the approach.
Scheduling and control of high throughput screening systems with uncertainties and disturbances
Published in Production & Manufacturing Research, 2022
Adetola Oke, Laurent Hardouin, Xin Chen, Ying Shang
The operator denotes function composition, i.e. means that is a function of .