"... In PAGE 3: ... Algorithm 1 Updating Slicing Information Procedure Update(a33 ) 1: a34a36a35a37a33a39a38a41a40 = a42a36a33a19a43 ; 2: a44a19a33a39a45a46a40a48a47 a33a50a49 = a44a19a33a39a45a46a40a26a34a51a44a53a52a54a45a56a55 ++; 3: for (each use a57 in a58a59a34a60a40a11a47 a33a50a49 ) do 4: a34a36a35a37a33a39a38a41a40 = a34a36a35a37a33a39a38a41a40a62a61a64a63a48a40a66a65 a34a60a35a67a33a21a38a51a40a11a47 a57a68a49 ; 5: end for 6: a63a11a38a51a63 = the statement a34 in a69a59a70a71a47 a33a39a49 which has the maximum a44a19a33a39a45a46a40a48a47 a34a51a49 value; 7: a34a36a35a37a33a39a38a41a40 = a34a36a35a37a33a39a38a41a40a72a61a46a34a36a35a37a33a39a38a41a40a11a47 a63a11a38a51a63a73a49a21a47 a35a74a40a36a33a75a47 a63a11a38a76a63a73a49a77a49 ; 8: a34a36a35a37a33a39a38a41a40a11a47 a33a50a49a78a47 a35a74a40a36a33a75a47 a33a50a49a79a49 = a34a36a35a37a33a39a38a41a40 ; 9: a35a74a40a36a33a75a47 a33a39a49 ++; 10: for (each definition a63 in a70a14a40a66a65a80a47 a33a50a49 ) do 11: a63a48a40a66a65 a34a36a35a37a33a39a38a41a40a11a47 a63a73a49 = a34a36a35a37a33a39a38a51a40 ; 12: end for Forward computation of dynamic slices for example in Fig. 1 is shown in Table1 . In the execution step of a20a34a17a81a2 , which is a0a82a30a83a10 a20 a85a84a39a86 a11 a76a87 a11 a76a0a3a88 , a0 is defined, a4 a86 a11a76a87 a11a76a0a89a5 are the variables that are used.... ..."

"... In PAGE 16: ... First use the parameters quot;j, j = 1; 2; :::; 7; to approximately compute the forward temperature tf i;k, for each unit. This procedure is described in the algorithm forward-temp, see Table4 . In the al- gorithm unit(k) = V P U means the test to check if quot;unit k is a VPU quot;.... In PAGE 18: ... To summarize, the economic dispatch problem (63) is implemented in 28 m- les using about 2600 lines of code. The start-value algorithm in Table 3 and the forward-temp algorithm in Table4 are implemented in two m- les. To solve the nonlinear programming problem (63) we have used two general purpose solvers, NPSOL [GMSW86] and CONSTR from MathWorks Optimization Toolbox [Gra93].... ..."

"... In PAGE 7: ... Similar to the de nition of , we can de ne t(i; j) = ProbfOt+1; Ot+2; ON; Lt = jjct = ig; which is computed using the backward recursion N(i; j) = (L; j)b(i; j; O); t(i; j) = Pk t+1(k; j + lk)Probfct+1 = kjct = i; Lt = jgb(k; j + lk; O); 8t = N ? 1; ; 1: (7) To update HMM parameters, we de ne t(i; j) = Probfct = i; Lt = jjOg = t(i; j) t(i; j) ProbfOg ; (8) t(i; k; j) = Probfct = i; ct+1 = k; Lt = jjOg; = Pl t(i; l)Probfct+1 = ijct = k; Lt = jg t+1(l + lk; k)b(k; l + lk; O) ProbfOg ; (9) where ProbfOg = Pi T(i; L). We can update the distribution of the rst codeword to f 0g and the probabilities for codewords to fp0 ikg, using: 8 lt; : 0(i) = 1(i); p0 ik = Pt=1; T?1;j=1; ;L;Probfct+1=mjct=i;Lt=jg gt;0;8m t(i;j;k) Pt=1; T?1;j=1; ;L;Probfct+1=mjct=i;Lt=jg gt;0;8m t(i;j) : (10) Table4 provides an example of the results of source distribution estimation. The re- sults in the table are based on one packet containing 100 symbols from the VLC x1=0, x2= 10, and x3=11, transmitted over a AWGN channel with di erent noise powers.... In PAGE 8: ...Of course, even if hard decisions are used for the estimation, the original soft observations need to be retained in memory so that the SISO VLC decoding algorithm de- scribed in the previous section can be utilized. Simulations with other codeword alphabets produced result consistent with Table4 and con rm that the approach in equation (10) can produce an accurate estimate of the source distribution, even in the presence of a very low SNR. Table 4: Source distribution estimation with forward-backward iteration Estimated probabilities with/without hard decision (SNR)... ..."

"... In PAGE 7: ...n this rst step, we want to compute x := V T xj for all 2 T(I). If is not a leaf, i.e., if S( ) 6 = ;, we have V T xj = X 02S( ) B 0; T V 0T xj 0 = X 02S( ) B 0; T x 0; so the algorithm shown in Table2 can be used to compute all coe cients. Now we want to analyse the complexity of this algorithm.... ..."

"... In PAGE 5: ... As with the Forward algorithm, pieces were ranked in order by the score of their highest-ranking theme. Table1 shows the rank of the correct answer, broken down by rank scoring method. The table shows HMM-based ranking using the Forward algorithm clearly outperforms ranking based on edit- distance with the simple string matcher.... ..."

"... In PAGE 11: ...Table2 for an operational scheme of the forward and backward simulations). 11 255 260 265 270 275 Figure 4 shows comparisons between adjoint and BF horizontal advection sensitivities.... In PAGE 14: ... As a result: (a) the same numerical scheme can be used to horizontally diffuse concentrations and adjoints in forward and backward simulations; and (b) continuous and discrete horizontal diffusion adjoints are identical. We use the same subroutine for horizontal diffusion of adjoints with an internal decoupling from (division by) densities (see Table2 ). Adjoint and BF sensitivity fields show good agreement in Figure 7 where only horizontal diffusion in one direction is included in the simulations and sensitivities of final ozone at the 21st x-cross section with respect to initial ozone at the 20th column are shown.... In PAGE 15: ... This leads to significant computational savings when multiple backward simulations are performed. In general, the order in which processes are called during the backward simulation is reverse of that in the forward simulation ( Table2 ). As only chemistry requires knowledge of concentrations in the current implementation, checkpoints are written and read before each chemistry call.... ..."