### Table 1: Signal objects de ned in SignalProcessing`Support`. For the syntax of CPulse, Dirichlet, FIR, IIR, LineImpulse and Pulse, consult the on-line documentation (e.g., ?CPulse).

"... In PAGE 5: ... We now examine them in more detail. Table1 lists the twelve new functions. There are discrete and continuous versions of the impulse (Impulse and Delta), step (Step and CStep), and pulse functions (Pulse and CPulse).... In PAGE 8: ... (However, certain obvious simpli cations are carried out: for example, InvZ[z,n][Z[n,z][f]] reduces to f.) Similarly, the functions of in Table1 are not reduced to Mathematica built-in objects until they appear as arguments to TheFunction. One may wish to reduce them, for example, in order to use Mathematica apos;s built-in plotting routines to plot them.... In PAGE 8: ... One may wish to reduce them, for example, in order to use Mathematica apos;s built-in plotting routines to plot them. Naturally, some functions in Table1 , like Delta and Unit, cannot be expressed in terms of Mathematica built-in objects, so TheFunction leaves them alone. Other Features Another facility provided by SignalProcessing`Support` is the plotting of signals and transforms.... In PAGE 18: ... Transforms of exponentials in the time domain are inverse-transformed by the exponential property rule, not by table lookup. Some strategies for inverting z-transforms ( Table1 0) are similar to those applied in taking forward z-transforms, but some new ones are also needed. Two such strategies are partial fractions and power series expansion.... In PAGE 19: ... complex cepstrum: Z?1flog X(z)g ! ? 1 nZ?1 ( z X(z) d dz X(z)) *9. apply the inverse z-transform to the rst N terms of a series expansion about z = 0 Table1 0: Strategies for inverse z-transforms. An asterisk means that once the rule is applied to an expression, it will no longer be applied to any part of that expression.... In PAGE 33: ...designing/analyzing 1-D analog lters DTFT discrete Fourier analysis EducationalTool interactive version of a conference paper describ- ing educational impact of Mathematica LaPlaceTest testing procedure for Laplace transforms PiecewiseConvolution tutorial on discrete/continuous convolution README brief introduction SignalProcessingExamples interactive version of paper in the The Mathemat- ica Journal SignalProcessingIntroduction introduction to Mathematica, signal processing, and the signal processing packages SignalProcessingUsage usage information about every new object de ned by the signal processing packages zTransformI z-transform tutorial, part I zTransformII z-transform tutorial, part II zTransformIII z-transform tutorial, part III Table1 1: List of the signal processing Notebooks transforms as long as the options are set properly. The default options are biased toward DTFT apos;s: Domain - gt; Continuous, DomainScale - gt; Linear, MagRangeScale - gt; Linear, PhaseRangeScale - gt; Degree, and PlotRange - gt; All.... In PAGE 40: ...Possible Values Meaning Apart Rational, All Partial fraction decomposition only applies to polynomials with real or rational coe cients Definition True, False Use the transform de nition if all else fails to nd the transform (does not apply to the inverse z or Laplace transforms) Dialogue False, True, All Ascending levels of justi cation Simplify True, False Apply SPSimplify to result Terms False or integer Number of terms in series expansion (False means none) TransformLookup list of rules Users can specify their own transform pairs, like {x[n] : gt; X[z]} or {y[t1,t2] : gt; Y[s1,s2]} Table1 2: Meaning of the Options for the Transform Rule Bases... In PAGE 41: ...Option Default Value CTFTransform Dialogue False Simplify True DFTransform Dialogue False InvDFTransform Dialogue False Terms False DTFTransform Dialogue False LaPlace Dialogue True Simplify True InvCTFTransform Apart Rational Dialogue False Simplify True Terms False InvDTFTransform Dialogue False Terms False InvLaPlace Apart Rational Dialogue True Simplify True Terms 10 InvZTransform Dialogue True Terms 10 ZTransform Dialogue True Table1 3: Options for the Transform Rule Bases. Definition always defaults to False and TransformLookup always defaults to an empty list.... ..."

### Table 4: Convergence of the error, = apos; ? apos;e, of the computed solution to the Dirichlet case, Problem 1, using the blunted cell fragment construction process, as detailed in Section 5.1. These results are quite similar to those presented for the natural cell fragment method

### Table 1: Performance of the posterior mode clustering for the six datasets: Column (a) is using the Dirichlet mixture of attribute ensembles, and (b) is using a standard Dirichlet mixture model. The results in column (c) are from average linkage dendrograms based on COSA distances, with clusters derived from on runt pruning (Steutzle 2003) with the true value of K assumed.

2004

"... In PAGE 14: ... This latter approach may run into problems if m is very large or the posterior distribution over c() is di use relative to the number of posterior samples obtained, in which case it may be possible that no clustering function c() is sampled more than once. The performance of these MAP estimates is detailed in Table1 . For each estimate of ^ c() of c(), the purity of putative cluster k is given by max 1 k0 K jfi : c(i) = k0 and ^ c(i) = kgj=ji : ^ c(i) = kj; which is the maximum fraction of objects in a putative cluster having the same true cluster mem- bership.... In PAGE 15: ... The latter method is very di erent algorithmically from the one in this paper, but has a similar clustering goal. As shown in Table1 , the standard Dirichlet process mixture model generally overestimates the number of clusters for these simulated data. This is perhaps a result of the fact that any clustering for this model will tend to reduce the within-cluster variance 2 j for all attributes j, which in turn could lead to overidenti cation of mean di erences.... ..."

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### Table 1: Convergence of the volume-weighted truncation error of the numerical Laplacian operator for the Dirichlet case, Problem 1, using the natural cell fragment con- struction process, as detailed in Section 5.1. The largest errors are consistently on the cell fragments. The 1-norm converges roughly at rst order in h, while the 1 and 2-norms converge at 2 and 1.5 respectively.

### Table 3: Convergence of the volume-weighted truncation error of the numerical Laplacian operator for the Dirichlet case, Problem 1, using the blunted cell fragment con- struction process, as detailed in Section 5.1. The 1-norm convergence is slightly better behaved in this case, compared to the results generated from the natural cell generation method. Here again, the 1-norm converges roughly at rst order in h, while the 1 and 2-norms converge at 2 and 1.5 respectively.

### Table 1. Estimated Dirichlet parameters.

"... In PAGE 6: ...33, corresponding to the weight of the region B and region A respectively. Table1 presents the Dirichlet parameters and their estimates of the two modes. Although the estimated values are near from the true parameter values, we note that this does not have to happen necessarily, since the same distribution can be modelled with difierent MODs.... ..."

### Table 1. The effectiveness (the percentage of test documents attributed with correct authorship) for 2, 3, 4, and 5-class attribution. The data is extracted from the AP collection [2], with function words as features, using Dirichlet smoothing.

"... In PAGE 1: ... Our present work arose out of experimenting with different forms of style markers in our quest to determine which works the best. Some sample results for two class or binary authorship attribution are shown in Table1 . (Technical details of the authorship attribution process is deferred to the following sections of the paper).... In PAGE 11: ... While using all types of features but FW/POS gives the best results of any three types of feature models. Table 5 shows the results of significance tests between the per- formance of the best baseline system from Table1 , and the best additive system using all feature models. The additive system performs significantly better, especially with the harder multi-class attribution tasks, with which the p-values are extremely small.... ..."

### Table 1: Convergence test for the Dirichlet formulation

2005

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### Table 1: Convergence test for the Dirichlet formulation

2005

Cited by 1