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With enough neurons in the first layer, even a two-layer network is theoretically a universal approximator, that is, an output activation y[i] can approximate any desired continuous function of the inputs x[k] [7,8] Typically, there is more than one optimal set of connection weights If too many hidden-layer neurons are used, one might match the training-sample pairs accurately but make matches for new test samples worse ( overtraining hurts generalization ) This problem is treated in substantial detail in References [11] and [32] Unfortunately, backpropagation training is often slowed by flat spots and/or stopped by local minima in the mean-square error function A frequently useful partial fix (momentum learning) declares two extra state-variable matrices

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H (t ) =

However, that doesn t mean that I don t think about going the third-party route, and as a dedicated Flickr user I sometimes use it as an image host. It is convenient and saves both time as well as bandwidth and space. Despite all I ve said so far, those are hard facts to argue with.

where t is the elapsed time after the client has entered the media streaming system and t is the time relative to the start of media stream. The upper bound of this client buffer requirement is 37% of the size of the media stream. Note that this is only a suf cient condition so it is still possible for a periodic broadcasting scheme to achieve lower client buffer requirement at the expense of increased latency or bandwidth.

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The way to add more layers can be seen from the program for a three-layer network with two hidden layers:

Starting from this section, we use an open-loop algorithm called Consonant Broadcasting (CB) to illustrate the design and trade-offs of open-loop multicast streaming algorithms. An important feature of CB is that it can be used in networks with limited client access bandwidth, which is the norm in typical metropolitan broadband networks. Figure 18.1 shows CB s broadcasting schedule and reception schedule. We divide a media stream into N equal-size segments and repeatedly broadcast them in separate variable-bandwidth multicast channels, i.e., media segment L i is multicast in the ith logical channel, for i = 0, 1, . . . , N 1. Thus CB belongs to the category of xed-segment variable-bandwidth schemes. We assume the media stream is constant-bit-rate encoded and thus the playback duration for each media segment is the same, denoted by U seconds.

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Flickr ( ickr.com) is probably the most popular photo-sharing site out there. It lets you upload photos for free, up to a limit, and if you want to upload more photos you can purchase a pro account. It also works very well with blogs, and you can even share your Flickr photos (and those of others) directly to your blog. This is done in your account settings, and WordPress is just one of many types of blogs that Flickr can let you share photos to. To share photos on your blog using Flickr: 1. Sign in to Flickr and go to the Your Account page. 2. Click the Extending Flickr tab, and then click the edit link to the right of Your Blogs (see Figure 14-3).

Vector v1 = tanh(W1 * x) Vector v2 = tanh(W2 * v1) Vector y = tanh(W3 * v2) Vector error = Y y Vector delta3 = error * (1 y^2) Vector delta2 = W3% * delta3 * (1 v2^2) Vector delta1 = W2% * delta2 * (1 v1^2) DELTA W1 = lrate1 * delta1 * x DELTA W2 = lrate2 * delta2 * v1 DELTA W3 = lrate3 * delta3 * v2

Shaded region represents the reception schedule of a client that enters the system at time t0 Logical channel 0 L0 L0 L0 L0 L0 L0

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Example bptest2lst in the book CD shows the time histories of some hidden neurons in a three-layer backpropagation network 11 In this case, the activation-function derivative factor (1 y^2) in Eq (6-28) is omitted, since all its vector components equal 1

T: m: L: Li : N: N Startup latency Configurable parameter Length of video Video segment number (0,1, ,N 1) Total number of segments

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MATRIX Dw1 = lrate1 * delta1 * x + mom1 * Dw1 MATRIX Dw2 = lrate2 * delta2 * v1 + mom2 * Dw2 DELTA W1 = Dw1 | W2 = Dw2

b: i: j: t0 :

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