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# Download A Cautionary Note on Likelihood Ratio Tests in Mixture by Seidel W., Mosler K., Alker M. PDF

By Seidel W., Mosler K., Alker M.

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The equation for sigmoid function is: f (ui) = 1 / (1 + e-ui) (4) The sigmoid activation function given in Equation (4) is popular for ANN applications since it is differantiable and monolithic, both of which are a requirement for training algorithms like as the backpropagation algorithm. Perceptrons must include a training rule for adjusting the weighting coefficients. , 1996). 2 Network architectures There are mainly two types of ANN architectures: feedforward and recurrent (feedback) architectures.

G(q) is the gravity vector as given below; 6 G(q ) = τ g (q ) = T T W g (32) where Wg are wrenches vector due to gravity: T T T W g = [ W 1 g , W 2 g ,..... W 13 g ] T = [ 0 , m 1 g T ,. 0 , m 13 g T ]T (33) where 0 is 3x1 zero vector, g is the vector of acceleration of gravity. 4. Controller emulation by using Elman networks In this stage, it is aimed to implement an application of ANN to emulate the operation of an existing PID controller in a Stewart manipulator control system. com). The block diagram of the control system is given in Fig.

Then the homogeneous coordinates L(t ) of the point L at any t are given by L(t ) = H (t )L(t0 ) . So its velocity is given by L(t ) = H (t )H −1 (t )L(t ) . The element H (t ) determines the tangent vector at H (t ) and def H (t )H −1 (t ) is a right translation by H −1 (t ) . Then Y (t ) := H (t )H −1 (t ) belongs to the Lie algebra e(3) . The velocity of the motion L(t ) = H (t )L(t0 ) determined by H (t ) at t0 and the velocity of the motion L(s ) = exp(sY (t0 ))L(t0 ) determined by exp(sY (t0 )) at s = 0 are the same.