### Table 4.5a : Phoneme recognition using a 3-state continuous density HMM.

### Table 1. Pdf apos;s, Moments, and Equivalent Density Functions for Some Continuous Random Variables Equivalent

1989

"... In PAGE 3: ... 3. DOUBLY STOCHASTIC REPRESENTATIONS FOR THE IRRADIANCE DISTRIBUTIONS A number of continuous probability-density functions (pdf apos;s) of interest in our study, and their direct moments, are presented in Table1 . Various equivalent representations for the pdf apos;s are also shown.... In PAGE 4: ...4) As indicated above, the K apos; distribution, G(x, 13, U) A G(u, a, N), is symmetric in the two degrees-of-freedom parameters, a and 1. The distribution denoted GI in Table1 , a compounding of the gamma and the noncentral x2 distributions, is also a compounding of two gamma distributions with a Poisson distribution. This can model the smearing of laser light that has a coherent component and an interfering chaotic compo- nent.... In PAGE 5: ... This operation leads to the distributions presented in Table 2, in which the corresponding factorial moments are also given. Note that the factorial moments in Table 2 are identical to the direct moments of the correspond- ing continuous distributions in Table1 , as noted in Section 2. The exception is the noncentral negative-binomial distribu- tion,3437 which includes a gain factor in the Poisson distribu- tion.... In PAGE 5: ... Some well-known density functions27 are included in Table 2 for ease of comparison. The three K distributions in Table1 , K0, K, and K apos;, trans- form to three discrete distributions denoted PKO, PK, and PK apos;. By the associative property of the smearing operation, calculation of these discrete distributions may proceed in any order desired.... ..."

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### Table 4: Derivative E ects by Group Using the Conditional Density Estimation Technique | continued

2000

"... In PAGE 31: ... Bootstrapped standard errors are after the derivatives at each point and are in parentheses. The rst panel in Table4 displays how age e ects vary by gender. At age 20, for example, men appear to increase health expenditures by $4.... In PAGE 32: ...Table4 : Derivative E ects by Group Using the Conditional Density Estimation Technique Evaluation Point Mean Std.Error Mean Std.... In PAGE 34: ...until they are 45 years old. The second panel of Table4 explores how the income e ects vary by race and gender. For each of the four groups, additional income has the largest impact on health expenditures at the lowest income levels.... In PAGE 34: ... But these point estimates for both whites and non-whites are relatively small and not signi cantly di erent from zero. The second panel in Table4 also contains how the e ects of changing the coinsurance rate vary by race and gender. Except for non-white males, the largest reduction in health expenditures occurs when the coinsurance rate is raised from zero.... In PAGE 34: ... Presumably, even a small copayment can reduce substantively average health expenditures. The third panel of Table4 examines the coinsurance and health e ects on expenditures as a function on income level. Somewhat surprisingly, a rise in the coinsurance rate from zero reduces health expenditures more for those with average incomes ($30K) than for those with quite low incomes ($10K).... In PAGE 34: ... The nal three sets of results indicate that the CDE models can easily estimate constant e ects across levels of characteristics. The bottom of the third panel in Table4 indicates that the impact of health status, as measured by the general health index, does not vary by income level. Likewise, the fourth panel in Table 4 indicates that the e ect of the coinsurance rate on expenditures does not vary across health levels.... In PAGE 34: ... The bottom of the third panel in Table 4 indicates that the impact of health status, as measured by the general health index, does not vary by income level. Likewise, the fourth panel in Table4 indicates that the e ect of the coinsurance rate on expenditures does not vary across health levels. The nal panel of this table shows that there is almost no di erence by race in the male-female expenditure di erential.... ..."

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### Table 3. (continued) 1) Positions and flux densities measured by fitting Gaussians to the image, instead of fitting a quadratic surface and integrating over the component region.

### Table 3: Estimated L1 norm between power spectrum density of true and reconstructed trajectories. Decoder CL-sequential LA-continuous CL-continuous

"... In PAGE 7: ...can be assessed by calculating the L1 norm between the power spectrum densities of the true and reconstructed hand trajectories. The estmated values of this quantity in our experiments are shown in Table3 . These results reflect the relationship shown in Figure 2 (a typical case).... ..."

### Table 3: Estimated L1 norm between power spectrum density of true and reconstructed trajectories. Decoder CL-sequential LA-continuous CL-continuous

"... In PAGE 7: ...can be assessed by calculating the L1 norm between the power spectrum densities of the true and reconstructed hand trajectories. The estmated values of this quantity in our experiments are shown in Table3 . These results reflect the relationship shown in Figure 2 (a typical case).... ..."

### Table A.1: Note two items: 1) In the 2D Drift-Poisson system, the vorticity of the elec- tron motions is proportional to the electron density; 2) The Continuity Equation and the Momentum Equation are identical in form, and therefore both systems evolve identically.

### Table 3: Some comparisons between di erent continuous density HMM struc- tures. The abbreviation PWMHMM refers to the phoneme-wise tied mixture density HMMs proposed in this paper. The CDHMM and SCHMM experi- ments, reported in earlier papers of the author, use the same speech database and basicly similar training phases as set up here for PWMHMM experiments. No corrective tuning has been used in these experiments. training methods. The error rates are de ned by the sum of missing, changed and extra phonemes divided by the correct sum of phonemes. The phoneme recognition experiments are performed using the speech recognition system of the Laboratory of Information and Computer Sci- ence of Helsinki University of Technology [13]. 20 dimensional cepstral feature vectors concatenated with the energy of the signal are used as the short-time acoustical features. New feature vector is computed every 10 ms using 20 ms signal window. 5 states left-to-right HMMs with no skips are trained by the described

"... In PAGE 9: ... The di erences of the average error rates in Table 2 are so small that, for example, the Matched Pairs test does not give any signi cant statistical di erences between the various experimented training combinations, except that the experiment of SOM with zero neighborhood is worse than the others. When comparing the performance of corresponding training combination between di erent continuous density HMMs the Table3 reveals that the phoneme-wise tied HMMs provide clearly the most appealing con gu- rations, when the number of parameters, the recognition time and the error rate are compared. The recognition times per word are computed as the average of 311 di erent nnish words and do not include the pre- processing which is same for each model.... ..."

### Table 2|Continued

"... In PAGE 15: ... Table2 |Continued CalendarDate Observation Array JulianDay minus 2440000.0 A ux density (mJy) B ux density (mJy) ReductionArray 86Jul20 B 6632.... In PAGE 34: ... A Gaussian was tted to each image to determine its ux density. The nal light curves are reported in Table2 . Although the ux densities are reported in mJy, all of the real and synthetic data in this paper were converted to \dBJ quot; units for analysis.... In PAGE 34: ...onsistent with PRHb. In these units, a 2% change in S is 0.088 dBJ. Due to the deconvolution and self-calibration techniques involved in VLA data reduction, the accuracy of the ux densities listed in Table2 cannot be determined analytically. L92 estimated the errors on these measurements in three ways: as the RMS during the quiescent period (1983.... In PAGE 34: ....6 mJy for the A image, and about 0.4 mJy for the B image. Due to the di erent synthesized beams in the three VLA arrays used (A, B, C), it is possible that the errors are signi cantly di erent for these arrays. Table2 lists the VLA array at the time of observation (sometimes a hybrid array), and the array assumed during the data reduction (one of the standard arrays, either A, B, or C, whichever is most similar to the observation array). For simplicity we have assumed a homogeneous error model for each light curve, such that every data point has the same fractional error, irrespective of the array of observation.... ..."

### Table 2|Continued

"... In PAGE 14: ... Table2 |Continued CalendarDate Observation Array JulianDay minus 2440000.0 A ux density (mJy) B ux density (mJy) ReductionArray 94May07 A!AnB 9479.... In PAGE 34: ... A Gaussian was tted to each image to determine its ux density. The nal light curves are reported in Table2 . Although the ux densities are reported in mJy, all of the real and synthetic data in this paper were converted to \dBJ quot; units for analysis.... In PAGE 34: ...onsistent with PRHb. In these units, a 2% change in S is 0.088 dBJ. Due to the deconvolution and self-calibration techniques involved in VLA data reduction, the accuracy of the ux densities listed in Table2 cannot be determined analytically. L92 estimated the errors on these measurements in three ways: as the RMS during the quiescent period (1983.... In PAGE 34: ....6 mJy for the A image, and about 0.4 mJy for the B image. Due to the di erent synthesized beams in the three VLA arrays used (A, B, C), it is possible that the errors are signi cantly di erent for these arrays. Table2 lists the VLA array at the time of observation (sometimes a hybrid array), and the array assumed during the data reduction (one of the standard arrays, either A, B, or C, whichever is most similar to the observation array). For simplicity we have assumed a homogeneous error model for each light curve, such that every data point has the same fractional error, irrespective of the array of observation.... ..."