### Table 1. Examples of gene expression time series published in literature including unevenly sampled time series. Non-time series data points (e.g. mutants) published with the studies are not described

in warping

"... In PAGE 1: ...ner et al., 2000; Golub et al., 1999) is now commonplace. An important area of application of these techniques is the study of biological processes that develop over time by collecting RNA expression data at selected time points and analyzing them to identify distinct cycles or waves of expression (see Table1 ). Progress in the development of high throughput protein level assays (Gygi et al.... In PAGE 2: ... These conditions are easily met when sampling speech data through appropriate electronics and data processing, but not for RNA expression level data where collection of data at a time point involves laborious and costly steps. Examples of unevenly and sparsely sampled RNA expression time series are common in the literature (see Table1 ), and this will surely be true of protein time series as well. As a result, time warping algo- rithms developed for speech recognition cannot generally be directly applied to typical expression level time series.... ..."

### Table 2: Tests of the time-series properties of the dataa

"... In PAGE 7: ...ppendix 1. The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Appendix 2. Table2 : Tests of the time-series properties of the data .... In PAGE 16: ... Both the ADF test and the modified Phillips-Perron test allow us to test formally the null hypothesis that a series is I(1) against the alternative that it is I(0). The results from the tests of the time-series properties of the data can be found in Table2 in Appendix 2. ADF critical values are generated to account for the finite-sample distribution of the series by performing Monte Carlo simulations with 5,000 replications for the level of inventories, the level of new orders, capacity utilization, the price of raw materials and the yield spread.... In PAGE 16: ... Evidence was found that capacity utilization contains a moving-average component, while the yield spread appears to follow an autoregressive moving- average process.9 Table2 (Appendix 2) indicates that both the ADF and the tests suggest that inventories, new orders, and raw material prices are non-stationary or I(1) processes in levels. The ADF test rejects the null hypothesis of a unit root in the level of the yield spread at conventional levels of significance and also provides evidence that capacity utilization is characterized as a stationary or I(0) process.... ..."

### Table 2: Results from runs with 30 data points per wave, distributed among one time series (upper table), three time series (second table), and five time series (third table). The correct network, from which the artificial data was generated, is shown in the lowermost table.

2000

"... In PAGE 7: ... In the second set, ten points per wave were measured from each of three different trajectories, and in the third set, six points per wave were measured from each of five different trajectories. The results together with the network from which the data were generated are shown in Table2 . For the single time series used in the first set of runs, whose results are shown in the uppermost table, the expression level curves were monotonous, containing only very little information to constrain the parameters.... In PAGE 8: ... In both cases, the time constants were very close to their correct values. When presented in the form used in Table2 , the results are far from transparent and also difficult to compare. In order to facilitate the comparison, the results are presented again, in a different form, in Table 3.... ..."

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### Table 3: Main requirements for gene expression time-series clustering and proposed solution.

"... In PAGE 25: ... Table3 presents the main requirements for gene expression time-series cluster- ing and the proposed solutions. As commented in the previous paragraph, given the particular objectives of the proposed algorithm, the number of clusters is inherent in the data set.... ..."

### Table 1 Hypothetical Time Series Data

"... In PAGE 3: ...n the ordered autoregression. Tsay (1989) suggests using m H11015 (n/10) H11001 p. A simple example is employed to illustrate the key steps of arranging the ordered autoregression. Table1 gives a hypothetical time series with n H11005 24 observations. For illustrative purposes, we assume p H11005 3 and d H11005 1.... In PAGE 3: ... H11005 3 and d H11005 1. The symbol (i) represents the time index of the ith smallest observation of {Y3,..., Y23}. The values of (i) are obtained for this example; see Table1 .... ..."

### Table 1. Time series used in the experimental evaluation.

"... In PAGE 3: ... In this work, 12 time series with real- world data were used in order to try to establish a general ranking among the models tested. The names and sizes of the used time series are shown in Table1 . All data are differentiated and then the values are rescaled linearly to between 0.... ..."

### Table 1: Time Series data

2001

"... In PAGE 2: ...pproaches (e.g., least squares methods). To the experiments carried out in this work, a set of ten series was selected ( Table1 ), ranging from financial mar- kets to natural processes [3][14][10] (Figure 4). The last two series were artificially created, using the chaotic formulas: a0 a1 a7 a18a17a33a0 a1 a49 a22 a5a20a19 a10 a0 a1 a49 a22 a7a9a21 a0 a23a22 a7 a18a24a23a25 a26a27a21a28a17 a7 a18a29 for the quadratic series [15]; and a0 a1 a7 a30a19 a10 a31a17a33a0a2a25 a1 a49 a22 a33a32a35a34 a0 a1 a49 a25 , a17 a7 a36a19a37a25 a29 , a34 a7 a38a24a27a25 a39 , a0 a23a22 a7 a40a24a23a25a41a19a37a19 for the henon one [2].... In PAGE 3: ... - the use of decomposable information; i.e., a41 a11 a1a0a3a2 a7 a5a4a4a19 a21 a25a42 a21 a43a42 a32 a19 a8 if the series is seasonal (period a42 ) and trended; a41 a11 a1a0a3a2 a7 a5a4a4a19 a21 a25a42 a8 if the series is seasonal ; and a41 a11 a1a0a3a2 a7 a5a4 a19 a8 and a11 a1a0a3a2 a7 a5a4 a19 a21 a26 a8 if the series trended. Several FNNs, with a number of hidden nodes (a10a44a38 ) rang- ing from 0 to 13, were used to explore all sliding windows for each TS of Table1 . Each model was trained with 90% of the series elements, being the rest 10% used for the forecasts.... In PAGE 5: ... 1 2 13 12 11 8 3 Figure 3: The best model for the sunspots series. Table 5 shows the best models achieved by the GEA, for all series of Table1 . As an example, Figure 3 plots the best ANN topology for the sunspots series.... ..."

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### Table 1: Time Series data

"... In PAGE 2: ...pproaches (e.g., least squares methods). To the experiments carried out in this work, a set of ten series was selected ( Table1 ), ranging from financial mar- kets to natural processes [3][14][10] (Figure 4). The last two series were artificially created, using the chaotic formulas: DCD8 BP CPDCD8A0BDB4BD A0 DCD8A0BDB5BN DCBC BP BCBMBEBN CP BP BG for the quadratic series [15]; and DCD8 BP BD A0 CPDCBE D8A0BD B7 CQDCD8A0BE, CP BP BDBMBG, CQ BP BCBMBF, DCBC BP BCBMBDBD for the henon one [2].... In PAGE 3: ... - the use of decomposable information; i.e., AF CBCCCF BPBO BDBN C3BN C3 B7BD BQ if the series is seasonal (period C3) and trended; AF CBCCCF BPBO BDBN C3 BQ if the series is seasonal ; and AF CBCCCF BPBO BD BQ and CBCCCF BPBO BDBN BE BQ if the series trended. Several FNNs, with a number of hidden nodes (D2CW) rang- ing from 0 to 13, were used to explore all sliding windows for each TS of Table1 . Each model was trained with 90% of the series elements, being the rest 10% used for the forecasts.... In PAGE 5: ... 1 2 13 12 11 8 3 Figure 3: The best model for the sunspots series. Table 5 shows the best models achieved by the GEA, for all series of Table1 . As an example, Figure 3 plots the best ANN topology for the sunspots series.... ..."

### Table 1: Implementation results for chaotic time-series prediction

1998

"... In PAGE 4: ...Matlab neural network toolbox and trained using conventional backpropagation algorithms. A summary of the implementation results obtained are presented in Table1 . Two different simulation approaches were used for the chaotic time series prediction problem.... In PAGE 4: ...ifference between the predicted and actual results, in terms of the prediction error is illustrated in Fig. 5. This compares favourably with a conventional fuzzy approach which employed an even finer-grained partitioning strategy ranging from 15 to 29 fuzzy sets to achieve a similar accuracy [Wang92]. For further comparison, the results using a conventional neural network approach which contains 40 nodes in the hidden layer are also included in Table1 . Previous work demonstrated that this size of network resulted in a similar degree of accuracy as a conventional fuzzy reasoning approach employing seven fuzzy sets on each input domain [Wang92].... In PAGE 4: ... Previous work demonstrated that this size of network resulted in a similar degree of accuracy as a conventional fuzzy reasoning approach employing seven fuzzy sets on each input domain [Wang92]. Table1 illustrates that the FNN approach provides a more accurate prediction of the time-series as compared to the conventional neural network approach. However, these results do not highlight that the training time of the conventional neural network was more than a factor of two slower than the largest FNN employed.... ..."

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### Table 3: A coarse-grained version of table 2. The panels show the data from the runs with 1 time series (top left), 3 time series (top right), 5 time series (bottom left), as well as the actual network (bottom right).

2000

"... In PAGE 8: ... When presented in the form used in Table 2, the results are far from transparent and also difficult to compare. In order to facilitate the comparison, the results are presented again, in a different form, in Table3 . Here, weights and biases are given as 0, positive (+), strong positive (++), negative (?), or strong negative (??), with the border between positive (negative) and strong positive (negative) set, somewhat arbitrarily, at 10 (-10).... In PAGE 8: ... A weight is set to 0 if the interval formed by the standard deviation contains zero. Apart from making the comparison between different net- works simpler, this form of presentation will also be more realistic when the results obtained from real data are displayed: With the measurement accuracy presently available, one does not expect (or need) to find exact weights and therefore a coarse representation, as used in Table3 , should be sufficiently accurate.... ..."

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