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for details on neural network topology and operation. Figure 6.5 provides a basic diagram of a simple neural network. The feedforward nature of the network restricts the network to a single direction of ow and does not allow looping or cycling. The neural network is composed of two or more layers, although most networks consist of three layers: an input layer, a hidden layer, and an output layer. There may be more than one hidden layer, although most networks contain only one, which is suf cient for most purposes. The neural network is connected completely, meaning that every node in a given layer is connected to every node in the next layer, although not to other nodes in the same layer. Each connection between nodes has a weight (e.g., W1A ) associated with it. At initialization, these weights are randomly assigned to values between zero and 1. How does the neural network learn Neural networks represent a supervised learning method, requiring a large training set of complete records, including the target variable. As each observation from the training set is processed through the network, an output value is produced from the output node (assuming that we have only one output node). This output value is then compared to the actual value of the target variable for this training set observation, and the error (actual output) is calculated. This prediction error is analogous to the residuals in regression models. To measure how well the output predictions are tting the actual target values, most neural network models use the sum of squared errors: SSE =

Figure 14.2b illustrates the backoff ow for MBS. In this scheme, the CW value for the successful data delivery in the previous superframe is recorded to predict the initial value of the CW for the current superframe. The coordinator announces the initial CW value for the current superframe to end devices via the beacon frame. In Fig. 14.2b, device A obtains the channel access in the ith superframe by using a suitable CW and successfully transmits its data frame. Then as the next superframe [i.e., the (i+1)th superframe] starts, the size of CW will not be reset to CWmin. The coordinator informs end devices the CW value with that device A successfully transmits its data frame in the ith superframe. Suppose that devices A and D intend to send the frames in the (i+1)th superframe. The two devices probably select different backoff times due to a relatively large CW, and the probability of the data collision may decrease. To avoid the backoff window expanding too quickly in MSB, a window-shrinking operation is designed. That is, if three consecutive successful transmissions occur with the 2k-slot CW (which implies that the CW may be too large), the initial window value for the next superframe is decreased to 2k 1. The MBS is fully compatible with the existing IEEE 802.15.4 implementations. In MBS, bits 7 9 for the frame control eld in beacon and ACK frames (shown in Fig. 14.5) are used to carry the exponent of the CW value. Once the coordinator receives an ACK frame, the CW value in the ACK frame for this successful frame transmission would be maintained in the coordinator. As the next superframe starts, the coordinator announces the initial CW value to all end devices based on all CW values collected in the current superframe.

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The following basic information inequality can be used to prove many of the other inequalities in this chapter. Theorem 17.1.7 (Theorem 2.6.3: Information inequality) two probability mass functions p and q, D(p||q) 0 with equality iff p(x) = q(x) for all x X. Corollary For any two random variables X and Y , I (X; Y ) = D(p(x, y)||p(x)p(y)) 0 (17.11) For any (17.10)

or of ces, and the feel, look, and use of the facilities becomes most apparent especially when there is a mismatch.

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