The WNN employed in this paper is designed as a three-layer structure with an input layer, a wavelet layer, and an output layer. The topological structure selleck kinase inhibitor of the WNN is illustrated in Figure 1. In this WNN model, the hidden neurons have wavelet activation functions of different resolutions and ��i is the weight connecting the hidden layer and output layer. For an input vector x = [x1, x2, ��., xn], the output of the i th wavelet layer neuron is described as follows:��k(x)=��i=1n exp(?(xi?dktk)2/2)cos(5?xi?dktk)(3)where xi is the i th input vector and k is the number of wavelet node. Inhibitors,Modulators,Libraries dk and tk are translation parameter and the dilation parameter, respectively.Figure 1.Wavelet Neural Network Structure.The output of the third layer is the weighted sum of ��k(x)y(x)=��m=1k ��m ��m(x)(4)3.2.

Training of WNNWavelet network training consists of minimizing the usual least-squares Inhibitors,Modulators,Libraries cost function:E=12��j=1s (yj?oj)2(5)where s is the number of training samples for each class and oj is the optimal output of the j th input vector.Due to the fact that wavelets are rapidly vanishing functions, a wavelet may be too local if its dilation parameter is too small and it may sit out of the domain of interest if the translation parameter is not chosen appropriately.Therefore, it is inadvisable to initialize the dilations and translations randomly, as is usually the case for the weights of a standard neural network with sigmoid activation function. We use the following initialization procedure, setting.

The same value to dilation parameter dk is given randomly Inhibitors,Modulators,Libraries at the beginning, and initializing the translation parameter tk is as follows:tk=(k��s)/K, k=0,1,2?K?1(6)where s is the number of training samples for each class and K is the number of nodes in the wavelet layer.The partial derivative of parameters d, t, �� are as follows:?E?dm=��j=1s 2(yj?oj)?(��m=1k ��m exp(?(x?dmtm)2/2) Inhibitors,Modulators,Libraries ((x?dmtm2) cos(5?x?dmtm)+5tmsin(5?x?dmtm)))=��j=1s 2(yj?oj)?(��m=1k ��m exp(?sm22) (sm cos(5sm)+5 sin(5sm))tm)(7)?E?tm=��j=1s 2(yj?oj)?(��m=1k ��m exp(?(x?dmtm)2/2) x?dmtm2 (x?dmtm cos(5?x?dmtm)+5sin(5?x?dmtm)))=��j=1s 2(yj?oj)?(��m=1k ��m exp(?sm22) smtm (sm cos(5sm)+5sin(5sm)))(8)?E?��m=��j=1s ��m=1k ��m 2(yj?oj)(9)where sm=x?dmtmWe adjust the parameters by the following equation:��n=��n?1?������(10)where �� = (d,t,��)T is vector of the parameters d, t and ��, a is learning Brefeldin_A rate between 0.

1 and 0.9.4.?ExperimentsWe applied the proposed method to two SAR images sized 256 �� 256 pixels [Figure 2(a)] to demonstrate the differences between the Morlet and Mexihat procedures; thes
In recent either developments, micropumps utilizing piezoelectric actuation have been commonly employed for directing the fluid purposes especially in BioMEMS and microfluidic systems [1�C6]. One of the essential features of micropump is the ability to direct the fluid flow as to flow in only one direction and this could be enhanced with the introduction of a check valve.