FIGURE 6-11 Complete program for the nonlinear predictor in .NET Drawer QR-Code in .NET FIGURE 6-11 Complete program for the nonlinear predictor FIGURE 6-11 Complete program for the nonlinear predictorRecognize QR Code ISO/IEC18004 In .NETUsing Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in .NET applications.Neural Networks with Memory Make Quick Response Code In .NETUsing Barcode encoder for VS .NET Control to generate, create QR image in Visual Studio .NET applications.Vector signal = signal{-1} | signal[1] = sTRUE Vector x = x{-1} | x[1] = signal[m] ------------Vector vv = tanh(WW1 * xx) | -note bias Vector y = WW2 * vv | -no limiter needed on output! -Vector error = sTRUE - y | -backpropagation Vector vvdelta = WW2% * error * (1 - vv^2) DELTA WW1 = WW1gain * vvdelta * xx DELTA WW2 = WW2gain * error * vv ----------------------------------------------------------ERRORx5 = 5 * error[1] - 05 * scale dispt y[1], ERRORx5, sTRUEQR Code JIS X 0510 Decoder In VS .NETUsing Barcode scanner for .NET Control to read, scan read, scan image in .NET applications.FIGURE 6-11 (Continued)Bar Code Generation In VS .NETUsing Barcode creator for .NET framework Control to generate, create bar code image in .NET framework applications.to produce the current predictor input s(t) = signal[m] The simulated predictor then tries to predict sTRUE(t) by minimizing the sample average of g = (y sTRUE)2 with the backpropagation algorithm of Section 6-12a Prediction results necessarily depend on the frequency content of the input signal To provide a fairly difficult prediction task, sTRUE = sTRUE(t) is the Mackay Glass chaotic time series [17] defined by17Bar Code Recognizer In VS .NETUsing Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.Sd(t) = sTRUE(t tau) (d/dt) sTRUE = a Sd/(1 + Sdc) b sTRUE Encoding QR-Code In Visual C#.NETUsing Barcode creation for VS .NET Control to generate, create QR Code ISO/IEC18004 image in Visual Studio .NET applications.Figure 6-12 shows the future signal value sTRUE, the predictor output y, and the prediction error sTRUE y during training and recall We used 20 training runs with a total of 250,000 training steps to learn prediction m = 20 steps aheadCreating Quick Response Code In .NETUsing Barcode creator for ASP.NET Control to generate, create Denso QR Bar Code image in ASP.NET applications.In Figure 6-11, this is programmed with Creating QR-Code In VB.NETUsing Barcode maker for Visual Studio .NET Control to generate, create QR-Code image in .NET applications.tdelay Sd = DD, sTRUE, tau sTRUEdot = a * Sd/(1 + Sd^c) - b * sTRUE d/dt sTRUE = sTRUEdot Print Barcode In .NETUsing Barcode encoder for .NET framework Control to generate, create barcode image in .NET framework applications.where tdelay is a library time-delay routine that implements Sd(t) = sTRUE(t tau) by storing samples of its input sTRUE in an array DD declared in the experiment protocol; one sample for each DT step of the simple Euler integration routine (Section 1-7a) used here The example mglasslst in the book CD lets you experiment with the generatorEncoding Barcode In Visual Studio .NETUsing Barcode creator for Visual Studio .NET Control to generate, create barcode image in VS .NET applications.Vector Models of Neural Networks Draw Code 39 Full ASCII In VS .NETUsing Barcode creation for Visual Studio .NET Control to generate, create Code 3 of 9 image in Visual Studio .NET applications.sTRUE, y Printing 2/5 Interleaved In Visual Studio .NETUsing Barcode maker for .NET framework Control to generate, create ANSI/AIM I-2/5 image in .NET framework applications.sTRUE GS1 - 13 Creation In Visual Studio .NETUsing Barcode drawer for ASP.NET Control to generate, create EAN-13 image in ASP.NET applications.y 0 0Read UPCA In VS .NETUsing Barcode reader for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.error x 5 error x 5 1e+03 scale = 3 125e+03 15e+03 y[1],ERROR 5,sTRUE vs t 105e+04 scale = 3 108e+04 11e+04 y[1],ERROR 5,sTRUE vs tDraw Barcode In JavaUsing Barcode maker for Java Control to generate, create bar code image in Java applications.FIGURE 6-12 Time histories of the future signal sTRUE, the predictor output y, and the scaled predictor error 5(sTRUE y) during training and recallPrinting Code39 In VB.NETUsing Barcode drawer for .NET framework Control to generate, create Code 39 image in .NET applications.6-23 The Gamma Delay Line Layer J Principe and his associates [7] replaced the tapped-delay-line definition (6-45), orCode 128A Drawer In Visual C#.NETUsing Barcode printer for VS .NET Control to generate, create Code 128 image in .NET framework applications.x[i] = x[i 1] (i = 2,3, , nx) x[1] = s(t)Generate DataMatrix In JavaUsing Barcode creator for Java Control to generate, create Data Matrix 2d barcode image in Java applications.(6-48)Reading EAN / UCC - 13 In .NET FrameworkUsing Barcode reader for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.with a cascade of simple difference equations USS Code 128 Printer In .NETUsing Barcode printer for ASP.NET Control to generate, create ANSI/AIM Code 128 image in ASP.NET applications.x[i] = x[i] + mu(x[i 1] x[i]) (i = 2, 3, , nx) x[1] = s(t)(6-49a)where mu is a positive parameter Our compact vector notation models this gamma delay line with a single vector difference equation (Section 3-4)Vectr delta x = mu * (x{ 1} x) | x[1] = s(t)(6-49b)Each tapped-delay-line neuron [Eq (6-46)] remembers just one past input value But each neuron output x[i] in the gamma delay line is affected by all past input values This extra information about the past history of s(t) may allow a reduction in the number nx of delay-line sections in the block diagram of Figure 6-9 compared to that needed with a simple tapped delay line Figure 6-13 displays the tap-value responses to the initial condition x[1] = 1 for nx = 8 and two different values of mu The memory effect decreases with time The maximum time interval analyzed by a delay-line-fed neural network is nx COMINT for a simple tapped delay line For a gamma delay line, the effective memory period (memory depth) still depends on nx but is mainly determined by the difference-equation parameter mu Suitable valuesPulsed-neuron Replication mu = 0025 mu = 004 1 scale = 05 300 600 [1], [2], [3], [4], [5], [6], [7], [8] vs t 1 scale = 05 300 600 [1], [2], [3], [4], [5], [6], [7], [8] vs t FIGURE 6-13 Response of the tap outputs of an 8-tap gamma delay line to the initial condition x[1] = 1 for mu = 0025 and mu = 004 Curves in the original display were in different colors; the small squares at the bottom are color keysof this parameter are often found by trial and error; References [7] and [14] discuss automatic training The simplest static neural networks used with an input gamma delay line are again linear (weighted-sum) layers (6-46) or (6-47), which can be optimized with the LMS algorithm The tap activation functions in Figure 6-13 serve as a useful set of basis functions for regression, as in Eq (6-31) Reference [7] discusses more advanced networks and a number of applicationsPULSED-NEURON REPLICATION 6-24 Pulsed-neuron Models Biological neurons propagate electrical signals, but their actual inputs and outputs are fluctuating release rates of chemical substances (transmitters) fed into synaptic clefts between neurons [17, 23] Neuron activations in the simplified neural networks discussed in Sections 6-1 to 6-23 model running averages of pulsed-neuron inputs and outputs In the receiving neuron, a transmitter substance reacts with receptor chemicals to change the neuron-membrane permeability to ions passing into and out of the neuron Multiple excitatory and/or inhibitory inputs roughly add with different individual gains and fire the neuron when their weighted sum exceeds a threshold value Firing or ion transition through the neuron membrane produces a positive 20 to 300-mV voltage pulse across the membrane at a specific location This pulse propagates down a neuron fiber (axon)