### Table 1: Results of the experiments with neural networks Recurrent neural networks has the best performance for the Reference voltage and FBM data sets. Both data sets represent time series with very fast changing values without long-term trend. The recurrent neural network has worst performance for the time series with trend. In that case the MP and FIR-MP networks better identify the underlying system, as we can see from the results of the experiments for Lorenz and

"... In PAGE 7: ...ection) were used. The best equation was then chosen that minimizes the RMSE on the test training set. IV. 3 Results The results of the experiments for neural networks and equation discovery system Lagramge are given in Table1 and Table 2, respectively. The architecture of the MP neural network is represented with x?y?z, where x, y and z denote numbers of neurons in rst, second and third layer, respectively.... ..."

### Table 5 Time-series estimation of the relation between SEO long-run abnormal returns and interest rates at the time of SEO Time -series regression results with 4th-order residual correlation. The 312 monthly observations between 1970 to 1995 are weighted by the square root of the number of offerings in the respective month. The 10 months without any offerings receive no weight in the regression. The dependent variable is the mean 36- month abnormal return for all SEOs for the respective month. Interest rate is the annualized 30-day Treasury Bill yield. Dividend yield is the mean dividend yield for all SEOs for the respective month. Aggregate SEO Volume is total dollar amount of primary seasoned equity offered over months t-2 to t divided by the total market capitalization of all CRSP-listed stocks. January is an indicator variable with value of 1 for January and 0 for other months. T-statistics are in parentheses. * and ** denote rejection of the null hypothesis at the 5 percent and 1 percent level, respectively.

"... In PAGE 18: ... Four observations are deleted from the time- series since no offerings occur during these months. The time-series results are presented in Table5 . For all three abnormal return measures and all specifications, the slope coefficient on interest rates is negative, implying that a one- percentage point increase in annual interest rates is associated with SEO 3 year performance that is roughly between 1% and 3% worse.... ..."

### Table 8. Tests performed using the long-gap method

2002

"... In PAGE 76: ... Series 1-4 test results comparison Cable Series 1 Series 2 Series 3 Series 4 A, White 253 No failure 257 No failure No failure 884 B, Yellow 1 6 615 1021 C, Green 144 257 163 1220 D, Blue 2 257 No failure No failure N/A E, Red 2 163 No failure 296 F, Purple N/A N/A N/A2 1020 VIII. LONG-GAP TESTS WITH 10 KVRMS SUPPLY Three series of tests were performed on the cables as shown in Table8 . The use of a current limiting resistance increases the time to failure due to the decreased current magnitude.... ..."

### Table 3 Long and Short Run Terminal Costs

"... In PAGE 6: ... We also had the added benefit of using a panel, which reduces the problems associated with either exclusive time series or cross-sectional data. Table3 presents the final estimates for both short and long run terminal costs. Alternative functional forms, as well as dummy variables for some airports, were tested in the estimations but were insignificant in the final outcome.... In PAGE 6: ... The simple arithmetic relationship had the best statistical fit. The long run cost relationship is illustrated in Table3 in which total costs, capital plus operating costs, were regressed on values for passengers. We were not able to distinguish between domestic and international passengers.... In PAGE 7: ...45 per passenger. For the short run costs in Table3 the constant term is significant, indicating the presence of fixed costs and the parameter estimates on the linear and second order term are both statistically significant at the 10 percent level. The results indicate that short run marginal costs are rising at a relatively constant rate; the second order coefficient is non- significant.... ..."

### Table 2: robustness performance comparison If the RNN is a perfect model of the Henon time series model, then y0(k) = y00(k) = x(k+1). However, as the RNN is only an approximation to the model, the series y0(k) and y00(k) are di erent and deviate from x(k + 1). The second extrapolation measure is very di cult for a chaotic series prediction model, as chaotic series have the properties of long term unpre- dictability, and they are sensitive to initial conditions.

1995

"... In PAGE 3: ... The length of the random walk was 4. Table2 is the results that can be used to com- pare the robustness between the RTRL and the cel- lular GA. When the temporal length is 2, the RTRL has no di culties in training the RNNs correctly.... In PAGE 3: ... As the temporal length increases, the performance of the RTRL becomes worse. From Table2 , the success rate of the RTRL increases as the number of nodes (i.e.... ..."

Cited by 3

### Table 2: robustness performance comparison If the RNN is a perfect model of the Henon time series model, then y0(k) = y00(k) = x(k+1). However, as the RNN is only an approximation to the model, the series y0(k) and y00(k) are di erent and deviate from x(k + 1). The second extrapolation measure is very di cult for a chaotic series prediction model, as chaotic series have the properties of long term unpre- dictability, and they are sensitive to initial conditions.

1995

"... In PAGE 3: ... The length of the random walk was 4. Table2 is the results that can be used to com- pare the robustness between the RTRL and the cel- lular GA. When the temporal length is 2, the RTRL has no di culties in training the RNNs correctly.... In PAGE 3: ... As the temporal length increases, the performance of the RTRL becomes worse. From Table2 , the success rate of the RTRL increases as the number of nodes (i.e.... ..."

### Table 2 Computation time versus computer characteristics for the studied configuration Computer Type specifications Simulation time for 1 shot*

2001

"... In PAGE 12: ... For instance, as a compromise between complexity and speed of the delivery, in this study we had to step back from a preferred 12 tank-in-series plug-flow system to a 3 tank-in-series complete-mix configuration. Table2 summarises the calculation time required to run a 1-year shot on three different PCs... ..."

Cited by 2

### Table 1. Four modes of operation designed for the zeus software. An asterisk indicates that the mode has not been fully implemented or tested.

"... In PAGE 1: ... This allows zeus to be used for segmenting difierent epochs within a long time-series signal, or for producing a pixel-by-pixel classiflcations within an image. Thus, zeus is designed for use in four separate modes, as described in Table1 : time series forecasting, time series classiflcation, image classiflcation, pixel-by-pixel classiflcation within an image. Although the problems that characterize these modes are quite difierent in character, many of the same tools are used in their solution, and zeus provides a framework for incorporating those tools in a way the permits them to be used for a wide range of applications.... ..."

### Table 1 Characteristics for several long thin problems.

2002

"... In PAGE 36: ... Both series of problems use a structure- preserving translation so that the maximum number of variables per clause is three. The test results for these problems are given in Table1 and Table 2. It is interesting that cmpadd64 with a good renumbering can have an average cost of cut of only 11; some of our other renumberings reduced this value to 8.... In PAGE 36: ...n section 9. These problems have a maximum clause size of four. The cuts have very small cost, indicating the importance of the problem formulation and the ordering. The test results for the maxmin and dpmaxmin problems can also be found in Table1 and Table 2. Here again QsatCNF far outperforms SATO and GRASP, and gives small solution times.... ..."