Discrete responses

Table 7.2 shows the discrete response x ikT) to a unit step function and is compared with the continuous response (equation 3.29) where... 

From Table 7.2, it can be seen that the discrete and continuous step response is identical. Table 7.3 shows the discrete response x kT) and continuous response x t) to a unit ramp function where Xo t) is calculated from equation (3.39)... 

In Table 7.3 the difference between Xo(kT) and Xo(t) is due to the sample and hold. It should also be noted that with the discrete response x kT), there is only knowledge of the output at the sampling instant. 

Figure 7.25 shows that the continuous and discrete responses are identical, both with ( = 0.5. The control algorithm can be implemented as a difference equation... 

As in the case of C(t) or E(t), the integral form in each equation is used for a continuous response, and the summation form for discrete response data. The result for / from equation 19.3-7 serves either as a second check on the accuracy of the tracer study, since / = V/q for constant density, or as a means of determining f, if the true value of V is unknown. 

The PD models fall under two categories graded or quantal of fixed-effect model. Graded refers to a continuous response at different concentrations, whereas the quantal model would evaluate discrete response such as dead or alive, desired or undesired and are almost invariably clinical end points. 

Figure 2.10 Response surface showing an inherently discrete response (number of lines in the Lyman series) as a function of an inherently continuous factor (excitation energy).

The equation y = asin(fex) describes a sine wave of period 360/b. If a = 1 and b = 10, evaluate y at = 0, 40, 80,. .., 320 and 360. Plot the individual results. What is the apparent period of the plotted data Do these discrete responses give an adequate representation of the true response from the system ... 

In the BMD approach, a curve is fitted to discrete responses (binary, dichotomous/quantal data, i.e., yes/no) or to continuous mean effect values (a response such as weight that can assume any value in a range). The curve is usually fitted to data using the maximum likelihood approach. 

For discrete responses, the BMR is typically chosen at 10% above the control response, the BMD 10 as an excess risk of 10% is considered to be at or near the limit of sensitivity in most carcinogenicity studies and in some noncarcinogenicity studies as well. If a study has greater than usual sensitivity, then a lower BMR can be used, although the BMDio and BMDLio should always be presented for comparison purposes. 

A discrete factor is a factor that can take on only a limited number of values within a given domain. A discrete response is a response that can take on only a... 

Liang KY, Zeger SL (2000) Longitudinal data analysis of continuous and discrete responses for pre-post designs. Sankhya - The Indian Journal of Statistics Series B 62 134-148. 

McFadden, D., and Train, K.E., 2000, Mixed MNL models for discrete response. Journal of Applied Econometrics, 15(5) 447 70. 

Hanemann, W.M., 1984, Welfare evaluations in contingent valuations e q)eriments with discrete responses, American Journal of Agricultural Economics, 66(3) 332-341. 

Hanemann, W.M., and Kanninen, B., 1996, The statistical analysis of discrete-response CV data, Department of Agricultural and Resource Economics, University of California at Berkeley, Working paper n. 798. 

Assume that discrete response data are available at No(< Nd) observed DOFs, i.e., some selected components of x(f) and/or their linear combinations. Use At to denote the sampling time step. Due to measurement noise and modeling error, referred to hereafter as prediction error, the measured response y 6 (at time t = nAt) will differ from the model response LoX(nAf) corresponding to the measured degrees of freedom where Lo denotes an Ng x Nd observation matrix, which is determined by the configuration of the sensing system. Therefore ... 

Assume that discrete response data are available for No < N ) instrumented DOFs and use Ar to denote the sampling time step. Because of measurement noise and modeling error, referred to hereafter jointly as prediction error, the measured response y e at time t = nAt differs... 

Regression analysis is not applicable for modelling discrete response data such as biodegradability (classifying compounds either readily degradable or non-readily degradable ), because two-point correlations are the inevitable result (Figure 3.2). 

FIGURE 28. Classifier with continuous or discrete response. 

The discrepancy can be seen at various places along the eurves and is small in absolute terms. However, the difference is systematieally large in relative terms at concentrations approaching zero, a feature that would lead to potentially serious errors in the determination of low-concentration analytes. Analysts need to avoid this trap, by calibrating the analytical system over a much smaller range than that shown when near-zero concentrations are important. In reality, the quadratic curve would be estimated from discrete responses corresponding to a small number of calibration points and the ensuing random errors would be combined with these systematic discrepancies. 

This paper proposed a dynamic reliability modeling method of DBN, in order to find out the solutions of comprehensive system reliability modeling issues such as the above problems with discrete responses. Using this method to build reliability models of complex mechanical systems can reduce complexity. 

The dynamic stiffness matrices and shape functions used in SEM are exact within the scope of the underlying physical theory, and the method allows a reduced number of degrees of freedom. The matrices are depended on frequency, but using spectral analysis, the dynamic response can be easily composed by wave superposition. Harmonic, random, or damped transient excitations can be decomposed using the discrete Fourier transform (DFT). The discrete frequencies are used to calculate the spectral matrix and discrete responses. Then, the complete dynamic response is computed by the sum of frequency components (inverse DFT). As FEM, SEM uses the assembly of a global matrix using elementary matrices and spatial discretization. However, differently from FEM, only discontinuities and locations where loads are applied need to be meshed (Ahmida and Arruda 2001). 

The fundamental idea of steerable filter is to apply basis filters that correspond to a fixed set of orientations and interpolate between each discrete response. As defined in [6] the steering constraint is formulated as ... 

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