Output Functions

The output function determines the value that is transferred to the neurons linked to a particular one. In the same way as each biological neuron receives a lot of inputs (maybe one per dendrite) but outputs only a signal through the 

Going back to the main issue of this book, multivariate calibration, the most common situation is to accept the value of the activation function without further processing. In this case, the output function has no effect and it just transfers the value to the output (this can be considered as an identity function). Recall that the final response of the ANN has to be scaled back to obtain concentration units. 

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The. succeeding letter indicates the display or output function ... 

Next, one must determine the amount of gain needed by the error amplifier to bring the control-to-output function up to 0 dB at the closed-loop cross-over frequency ... 

JLo(.v) is the Laplace transform of the output function, or system response. 

BPCS/SIS functions that produce a trend analysis of input and output functions. Graphic video displays set-up to indicate process conditions and valve positions assure that the status of the process conditions is announced to the board operator, who may then verify the conditions with the field operator. 

A network that is too large may require a large number of training patterns in order to avoid memorization and training time, while one that is too small may not train to an acceptable tolerance. Cybenko [30] has shown that one hidden layer with homogenous sigmoidal output functions is sufficient to form an arbitrary close approximation to any decisions boundaries for the outputs. They are also shown to be sufficient for any continuous nonlinear mappings. In practice, one hidden layer was found to be sufficient to solve most problems for the cases considered in this chapter. If discontinuities in the approximated functions are encountered, then more than one hidden layer is necessary. 

FIGURE 3.2 General curve for an input/output function of the rectangular hyperbolic form (y = 50x/( 1 Ox + 100)). The maximal asymptote is given by A/B and the location parameter (along the x axis) is given by C/B (see text). 

These, such as the black box that was the receptor at the turn of the century, usually are simple input/output functions with no mechanistic description (i.e., the drug interacts with the receptor and a response ensues). Another type, termed the Parsimonious model, is also simple but has a greater number of estimatable parameters. These do not completely characterize the experimental situation completely but do offer insights into mechanism. Models can be more complex as well. For example, complex models with a large number of estimatable parameters can be used to simulate behavior under a variety of conditions (simulation models). Similarly, complex models for which the number of independently verifiable parameters is low (termed heuristic models) can still be used to describe complex behaviors not apparent by simple inspection of the system. 

In general, a model will express a relationship between an independent variable (input by the operator) and one or more dependent variables (output, produced by the model). A ubiquitous form of equation for such input/output functions are curves of the rectangular hyperbolic form. It is worth illustrating some general points about models with such an example. Assume that a model takes on the general form... 

Adenosine A2a receptors are localized to the indirect striatal output function and control motor behavior. Istradefylline is a novel adenosine A2a receptor antagonist, which demonstrated a clinically meaningful reduction in motor fluctuations in L-DOPA-treated patients with established motor complications, and is safe and well tolerated. 

The other problem-dependent boxes in Fig. 8 relate to reading input and writing output - tasks that are clearly application-specific. We view writing post processing files to be part of the output function. It is usually inefficient to force the code that computes the solution to perform simultaneously all the interpretive functions. Moreover, if the solution itself is saved, then any number of post-processing functions can be exercised without requiring the problem to be solved again. 

If X (0 and Xjit) are the input and output functions in the time domain (for example, the contents in the reservoir and in the plasma compartment), then XJj) is the convolution of Xj(r) with G(t), the inverse Laplace transform of the transfer function between input and output ... 

Neurons have one or more inputs, an output, oiy an activation state, Aiy an activation function, facU and an output function, fout. The propagation function (net function)... 

The output Oft) of the neuron is estimated by means of the output function fout... 

Often the identity function is chosen as output function. Then the output becomes... 

THEOREM 6.21 Every partial recursive function from non-negative integers to ncn-negative integers can be expressed as f(n) = val(P,I,n) for P a Ianov scheme and I an interpretation permitting only functions px and x/p and predicate " P divides x " for every prime p, constant 1, and special input function 2X and output function logjX. ... 

FACT III If Ianov schemes are restricted to the interpretation I above, only a small subclass of the recursive functions are computed in the sense that g(n) = 1 + val(P,I,n) for (P,I,n) convergent and g(n) = 0 for (P,I,n) divergent is a total recursive function and "most" total recursive functions cannot be so expressed. However, if one selects as interpretation I the interpretation with functions px and x/p and predicates "p divides x" for every prime p and constant 1 as well as special input function 2X and output function log2x then every partial recursive function f(n) can be expressed as val(P,I,n) for a Ianov (single register) scheme P and this particular interpretation I. ... 

When the evolution of the thermal phenomenon is fast, a rather large number of coefficients r, must be considered in Eq. (29) in order to define correctly the linear operator. The total amount of heat produced is still easily determined since it can be shown that proportionality of the areas under the input and output functions is a general property of linear systems,... 

The input function is the product of amount in the central compartment Aj and the entry rate constant the output function is given by the amount in the effect compartment Ae and... 

The input and output functions are then Fourier-transformed and divided to give the system transfer function in the frequency domain The details of one procedure for accomphshing this Fourier transformation are discussed in the following sections, and a little digital computer program that does this job is given in Table 14.1. Alternative methods include the use of Fast Fourier Transforms, which are available in most computing centers. 

Therefore would be simply the Fourier transformation of the output function. No division by a small number would be required. 

Powering all output functions such as alarms, extinguishing system releases, etc. 

Make sure that YMAX is selected as in the dialog box above. This function instructs PSpice to sort the output according to the maximum difference from the nominal value. We found that the nominal value of the gain was 0.5. YMAX specifies the output function ... 

TS Wind OUTPUTS (functions of position and time) p resin viscosity T composite temperature a degree of cure F Fiber tension u, Fiber position... 

OUTPUTS (functions of position and time) p resin viscosity... 

As in our example here there is only a neuron at the exit layer (we are considering only calibration), the activation function yields a value that is the final response of the net to our input spectrum (recall that the output function of the neuron at the output layer for calibration purposes is just the identity function) ... 

In most applications, the input, activation and output functions are the same for all neurons and they do not change during the training process. In other words, learning is the process by which an ANN modifies its weights and bias terms in response to the input information (spectra and concentration values). As for the biological systems, training involves the destruction , modification... 

Before training the net, the transfer functions of the neurons must be established. Here, different assays can be made (as detailed in the previous sections), but most often the hyperbolic tangent function tansig function in Table 5.1) is selected for the hidden layer. We set the linear transfer function purelin in Table 5.1) for the output layer. In all cases the output function was the identity function i.e. no further operations were made on the net signal given by the transfer function). 

The system is shown in Fig. 21.7. It is described by two concentrations (state variables), CA and CB, by two zero-order input functions, JA and JB (input per volume and time), by two first-order output functions, kACA and kBCB (output per volume and time), and by the first-order transformations from A to B and vice versa. The inputs and outputs can be the sum of two or more processes, for instance, the sum of the input through different inlets and from the atmosphere (as in Eq. 21-7a), or the sum of the output at the outlet and by exchange to the atmosphere (as in Eq. 21-7b.). 

Let us first consider the problem of an appropriate degree of coupling of oxidative phosphorylation in the cell. The solution to this question depends entirely on what output function is to be optimized. We might for example require a maximal net flow of ATP at optimal efficiency (Jp) opt. As is evident from Fig. 4 there is a unique degree of coupling qf, which corresponds to the maximum of this output function (see also Table I). Such a low value of the degree of coupling has never been experi-... 

General output function /(a) = tg" (a/2) cos a-constant with a = sin-1 ([Pg.146]

Fig. 4, Mitochondrial output functions. Plot of the output function /(a) = tg" cos a...

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