### Table 3: Results of 3 classes segmentation based on hidden Markov models.

"... In PAGE 6: ... Two successive frames will be shifted of 512 samples. Table3 shows results of 3 classes segmentation. Quality rates are better than with simple approaches reviewed in previous section.... ..."

### Table 4: Results of 3 classes segmentation based on combination of a C-Mean classifier and multidi- mensional hidden Markov models.

### Table 2. Performance of the hierarchical Markov model

2003

"... In PAGE 5: ...e., row 1 and 2 of Table2 ) provide a reference value for performance evaluation of the hMM. It is obvious that the hMM incurs approximately 60% (Table 2 column I - row 3 and 4) over- head for the inter-arrival-rate and, therefore, is rendering unsatis- factory performance.... In PAGE 5: ...races (i.e., row 1 and 2 of Table 2) provide a reference value for performance evaluation of the hMM. It is obvious that the hMM incurs approximately 60% ( Table2 column I - row 3 and 4) over- head for the inter-arrival-rate and, therefore, is rendering unsatis- factory performance. The burst-length random variable usually takes on small values since most of the bits are not corrupted dur- ing transmission and, hence, result in small (bit error) bursts.... In PAGE 5: ... Therefore, it is important to quantify the hMM burst-length per- formance with respect to the source-based traces. It is obvious that for the burst-length random variable, the ENK distance between the hMM- and source-based traces ( Table2 column B - row 3 and 4) is much larger as opposed to the ENK between two source- based traces (Table 2 column B - row 1 and 2). We conclude that although the hMM performs adequately in characterizing hybrid (i.... In PAGE 5: ... Therefore, it is important to quantify the hMM burst-length per- formance with respect to the source-based traces. It is obvious that for the burst-length random variable, the ENK distance between the hMM- and source-based traces (Table 2 column B - row 3 and 4) is much larger as opposed to the ENK between two source- based traces ( Table2 column B - row 1 and 2). We conclude that although the hMM performs adequately in characterizing hybrid (i.... In PAGE 7: ... Table 6 enumerates the performance of the HMM. Comparing the I col- umn of Table2 (row 3 and 4) with Table 6 outlines that the HMM shows clear improvement in the inter-arrival-rate performance, for instance, 40.... In PAGE 7: ...nstance, 40.33% as opposed to 58.72% for the hMM. However, the ENK for the burst-length random variable in the HMM case (Table 6 column B ) is orders of magnitude greater than the re- spective ENK for the hMM traces ( Table2 column B - row 3 and 4). Hence we conclude that, while the HMM improves the model- ing of good bursts , (when compared to the hMM) the hidden Markov model can not approximate the bad bursts adequately.... ..."

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### Table 7 : Results obtained with Discrete Hidden Markov Model

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### (Table 2). 2.3.2 Hidden Markov Model (HMM)

"... In PAGE 5: ....3.1 Video Analysis The video analysis was performed by two expert surgeons encoding the video of each step of the surgical procedure frame by frame (NTSC - 30 frames per second). The encoding process used a code-book of 14 different discrete tool maneuvers in which the endoscopic tool was interacting with the tissue (Table2 ). Each identified surgical tool/tissue interaction, had a unique F/T pattern.... In PAGE 8: ... 1b. (a) Forces (b) Torques Studying the magnitudes of F/T applied by R1 and ES during each step of the MIS procedures for the different tool/tissue interactions (Table2 ) using the grand median analysis showed that the F/T magnitudes applied by these groups were significantly different (p lt;0.05) and task dependent (Fig.... ..."

### Table 1 State Transition Matrix for a Hidden Markov Model

"... In PAGE 25: ...alues such as Sunny = 1.0, Rainy = 0, and Foggy = 0. 2. A state transition matrix ( Table1 ) that stores the probability of going from one state to another. For example, the first row gives the probability of a sunny day following a sunny day, a rainy day following a sunny day, a foggy day following a sunny day, and so on.... ..."

### Table 2. Accuracy of Hidden Markov Models to recognize haptic gestures

### Table 4: Sizes and encoding cost of REP99-gxn for the hidden Markov models built from the sequences of REP99-gxn.

1994

"... In PAGE 16: ...tates and 169 edges, getting 1.367 bits/base. I also tried some more complex scripts that attempted to merge states, remove unneeded states and edges, and do other model manipulation. Table4 summarizes the sizes and cost/base of all the... In PAGE 22: ...Conclusions and future work 21 tgac a tca ct ga t g c a ag a t t cg tg c t tg t g a a ac ac ct ct ca ct cacag ag atg t at gc c gca tc gtctgacg c ag c at tcaatccta tc g c a a tc at tacag t t ga c a gaatgagt t t g a at t t t g c agtcagaacgt t gtcacatgctaggca agcatcgtc tac tc g t a g g c a c gt g a t a a g g c g t t ct a ct g c c g tac a g a ct g c g act ct ca a g c ga t c gt g a t g c g a ct g c t gt ga c g c g t gt gt cat ct gc c t at ct g c t t a t c ct g c ga ta ga a a c g c c t t a t c ca g g g atg c c t a c agagt ag tacg gtc cg tgac gctcagt ct a accgagt cg ta tg ta at ag a gt g c a t c ca g ga c a Figure 5: Automatically produced drawing of the hmm REP99-gxn-hmm400m, which is the most easily understood hmm of the ones listed in Table4 . The thickness of the edges is proportional to the square root of the number of times the edge was used.... ..."

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### Table 2: Log-likelihood of the experiments on the hidden Markov simulation data

"... In PAGE 13: ...009 0.005 Table2 shows the mean and the standard deviation of log-likelihood of the test set using the naive method, the log-likelihood of the gated experts and the hidden Markov experts. It indicates that the likelihood of the gated experts and the hidden Markov experts are signi#0Ccantly better than the naive model.... ..."