By Tang X.

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**Extra info for 3/2-global attractivity of the zero solution of the food limited type functional differential equation**

**Example text**

The signal template s will be the weight vector, and the observation x is applied as its input. The bias term is threshold, and the output = 1 if the presence of the signal is detected. A multilayer perceptron can also be used to implement a nonlinear matched filter if the output activation function is a threshold function. By the same token, a support vector machine is also a plausible neural network structure to realize a nonlinear matched filter. 6 Time Series Modeling A time series is a sequence of readings as a function of time.

In the following layers, each unit sums its inputs and adds a bias or threshold term to the sum and nonlinearly transforms the sum to produce an output. This nonlinear transformation is called the activation function of the unit. The output layer units often have linear activations. In the remainder of this chapter, linear output layer activations are assumed. The layers sandwiched between the input layer and output layer are called hidden layers, and units in hidden layers are called hidden units.

The resulting mean square error Et , after we compress the M outputs down to M , is given by M Et = Et + λi i=M +1 where λi s are the ith singular values of the desired outputs’ covariance matrix. For each value of i, the sizing algorithm generates all possible MLP configurations and their predicted training MSE using M values between 1 and M. The algorithm sifts through these potential configurations and saves those that have the lowest training MSE for a given number of hidden units. The final output of our algorithm is the sequence of ordered pairs, Et (i), Nh (i) .

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