### Table 2: Additional Examples Proved using Test Set Method.

1991

"... In PAGE 27: ... Our implementation failed to compute JK(R8) due to lack of space after one hour of running time, so we do not know the size of JK(R8). Table2 is a list of inductive theorems proved using the test set method. Since these theorems involve nonconstructor symbols and no new constructor rules were generated, the test set method and the ground-reducibility method perform in the same way.... ..."

Cited by 11

### Table 3: Result of adding knapsackcover inequalities to CFL.

1996

"... In PAGE 18: ... Note that these inequalities can also be derived for subsets K #12 N of the clients. The cover inequalities have proved very useful computationally, as is illustrated in Table3 . In the table we report on the number of branch-and-bound nodes and the time needed to verify optimum if we use the linear relaxation of CFL only, compared to if we use the linear relaxation and added violated lifted knapsackcover inequalities.... ..."

Cited by 4

### Table 3. Wealth inequality measures using HUS and HINK data.

"... In PAGE 10: ... 4. The inequality of wealth Table3 compares three different inequality measures computed for both data sources. To preserve comparability between the two data sets the definitions of gross and net wealth are the more limited ones excluding consumer durables and condominiums.... In PAGE 11: ... If owner occupied houses and condominiums are valued at market prices and if the wealth invested in consumer durables are included, the inequality measures drops considerably. The same result is found if the inequality measures of Table 4 using the extended wealth definition are compared to the measures of Table3 . For instance, the Gini coefficient for the extended net wealth concept is about 70 per cent of the Gini for the more limited wealth definition.... ..."

### Table 1. Benchmark problems solved by MiniSat+. GAC SAT: results from MiniSat+ with all CNF clauses; SAT: results from MiniSat+ with all CNF clauses but clause (4); Mono: results from a CP solver using the monolithic propagator; Decomp: results from a CP solver using the decomposition; |A|: number of activities; #: problem number; m: number of employees; sol: number of worked hours (boldfonted if best solution found amongst the different methods); time (s): CPU time in seconds to find and prove the optimality of a solution. Times are omitted when the search is suspended by a lack of memory; bt: number of backtracks (boldfonted if least back- tracks amongst methods that prove optimality); opt: solution was proved optimal. ILog solver did not prove any problems optimal within one hour of computation.

"... In PAGE 12: ... ILog solver was halted after one hour of computation as it never proved the optimality of a solution. Table1 presents the results for 17 satisfiable instances of the benchmark involving one or two activities. The CP model performed very well at finding a good solution.... ..."

### Table 7: Regional Inequality in Illiteracy Rate and Infant Mortality Rate (IMR)

2003

"... In PAGE 10: ... Moreover, it appears that the gender gap has increased between 1990 and 1995. Table7 further displays the spread in the illiteracy rate across rural and urban areas, with the Gini and Generalized Entropy (GE) as inequality measures. The GE 2 The data in 1964, 1981 and 1990 are from the census, while the information in 1995 is from a one percent population survey.... In PAGE 11: ... Inequality is calculated using the population weighted values of illiteracy for spatial units at the highest level of disaggregation for which data is available. In the top panel of Table7 , the first two columns show that the Gini and the GE at the national level declined from 1964 to 1981 and then increased from 1981 to 1995. The same pattern holds true for inequalities across rural areas, as shown in the third column for the GE measure.... In PAGE 11: ... As is well known, the GE family of inequality measures can be decomposed into the sum of a within and a between group component, for any given partitioning of the population into mutually exclusive and exhaustive groups. The fifth and sixth columns of Table7 present the evolution of the within and the between group components of inequality. Both components rose in the post-reform period.... In PAGE 11: ...nequality. Both components rose in the post-reform period. Using the within-inequality and between-inequality, we can calculate the polarization index following the method outlined by Zhang and Kanbur (2001).4 As shown in the last column in Table7 , rural and urban areas became increasingly polarized from 1981 to 1995. The above inequality analysis, based on more disaggregated data, offers a snapshot for each of four years.... In PAGE 12: ...and district level as shown in Table7 . The rural regional income inequality, measured by the Gini coefficient, increased by from 13.... In PAGE 12: ... Using the data set, we can further examine the regional distribution of IMR. As shown in the lower panel of Table7 , overall regional inequality increased from 1981 to ... ..."

### Table 3. Running time and number of violated inequalities. For each PALI dataset, times and number of inequalities are reported for computing the epsilon1 of Table 2. Columns report the median and extreme values across the binary search iterations.

2006

"... In PAGE 14: ... Notice also that with varying substitution scores, one can consistently come very close to optimal on every dataset. Finally, Table3 gives running times and number of violated inequalities for the cutting-plane algorithm on the experiments of Table 2. Running times are wall-clock times in seconds to solve Inverse Near-Optimal Alignment for a given epsilon1 during the binary search for the smallest epsilon1.... ..."

Cited by 7

### Table 7: Inequations for

"... In PAGE 15: ... Table 6 contains the standard inequations for testing from [20, 28]. The laws in Table7 state that process is less de ned than every PAL process (UND1) and assert the strictness of all binary operators (strictness of follows from IC4). The laws in Table 8 are essentially concerned with the PAL parallel operators, and show that parallel operators, when applied to nite terms, can be replaced by more primitive ones, namely nil, , [] , , in(t): and out(t):nilb .... ..."

### Table 7: Inequations for

"... In PAGE 15: ... Table 6 contains the standard inequations for testing from [21, 30]. The laws in Table7 state that process is less de ned than every PAL process (UND1) and assert the strictness of all binary operators (strictness of follows from IC4). The laws in Table 8 are essentially concerned with the PAL parallel operators, and show that parallel operators, when applied to nite terms, can be replaced by more primitive ones, namely nil, , [] , , in(t): and out(t):nilb .... ..."

### Table 1. Benchmark problems solved by MiniSat+. GAC SAT: results from MiniSat+ with all CNF clauses; SAT: results from MiniSat+ with all CNF clauses but clause (4); Mono: results from a CP solver using the monolithic propagator; Decomp: results from a CP solver using the decomposition; |A|: number of activities; #: problem number; m: number of employees; sol: number of worked hours (boldfonted if best solution found amongst the different methods); time (s): CPU time in seconds. Times are omitted when the search is suspended by a lack of memory; bt: number of backtracks (boldfonted if least backtracks amongst methods that prove optimality); opt: solution was proved optimal. ILog solver did not prove any problems optimal within one hour of computation.

"... In PAGE 12: ... 10.4.8 and ILog Solver on a AMD Dual Core Opteron 2.2 GHz with 4 Gb of RAM. The reader should be careful when comparing the times as the clock speeds of the computers are slightly different. Table1 presents the results for 17 satisfiable instances of the benchmark involving one or two activities. The CP model performed very well at finding a good solution.... ..."

### Table 3 Income and Expenditure Inequality Decomposition by Sources Sources Percentage (%)

"... In PAGE 10: ... We next apply the Shorrocks (1982, 1984) method to decompose the overall income and expenditure inequality into factor components. Table3 presents the results of inequality decompositions by income source. The uneven distribution of agricultural income is the second most important factor contributing to the overall income inequality while local income from nonfarm jobs and wage jobs ranks as the first one.... In PAGE 10: ... Although incomes from blood sales provide farmers with necessary cash and help smooth consumption, in the long run selling blood, however, hurts the health status which in turn may affect their income generating capacity. Table3 also decomposes expenditure inequality according to agricultural inputs, rural nonfarm inputs, and consumption expenditures. Living expenditures account for over 70% of total variation while agricultural inputs explain another 17%.... In PAGE 14: ... Among the last group of variables on household assets, per capita arable land area (a measure of quantity) and the number of draft animals are both highly significant. As shown in Table3 , agricultural income is still the important source of overall inequality within a village. In the Guizou Province, because land has not been readjusted since the rural reform in the early 1980s, the land distribution has become increasingly uneven due to demographic change.... ..."