### Table 2: Initial parameters for linear transformation components.

1999

"... In PAGE 18: ...Since such degenerate matchings are not very interesting in a comparison, the method using the one-way Hausdor distance had its transformation space restricted to exclude arbitrary small scalings. Table2 shows which initial parameters were used to constrain the linear part of transformation space for both implementations. In each test the accuracy was set to one pixel.... ..."

Cited by 20

### Table 2: Initial parameters for linear transformation components.

"... In PAGE 18: ...Since such degenerate matchings are not very interesting in a comparison, the method using the one-way Hausdor#0B distance had its transformation space restricted to exclude arbitrary small scalings. Table2 shows which initial parameters were used to constrain the linear part of transformation space for both implementations. In each test the accuracy was set to one pixel.... ..."

### Table 3 Median Filter Linear Transform Shearing

2001

Cited by 3

### Table 1. Descriptive statistics of the research variables (n=110)

"... In PAGE 14: ...2 Measurement The measures of environmental uncertainty, strategy, structure and performance originate from concepts developed in the organization theory and strategic management literature, and have had their validity confirmed in prior empirical studies. As presented in Table1 , all variables show an adequate level of reliability in terms of their alpha coefficient. Environmental Uncertainty.... ..."

### Table 2. Results for the Linear and Transformed, and VAR Models DATA SET

2000

"... In PAGE 18: ...17 Table2 shows the results of the analyses for the Follow-the-Leader Hypothesis and the Price Effect Hypothesis. For each hypothesis, the results of both the transformed linear model and the VAR model are described.... ..."

Cited by 6

### Table 2: Variety of Non-linear Transformations and Rotation by

1997

Cited by 2

### Table 2: Results for symmetry reduction and linear transformations Symmetry reduction (Murphi) Linear transformations (DiVinE) Model Full Reduced Model Full Reduced

2005

"... In PAGE 17: ...3 Symmetry reduction Symmetry reductions based on permutations can, in theory, achieve reduction up to D2AX where D2 is the number of symmetrical entities. Table2 presents practical results. Experiments were done in the tool Murphi on the set of model which was used by Dill and Ip [27].... In PAGE 18: ... The effect of the reduction is proportional to the size of domain of linearly transformable variables. Table2 presents results for three protocols. The run-time overhead is neglible, but the static detection of a set of lineary transformable variables is not easy.... ..."

### Table 3: Linear transformations to which some s-box output bits are invari- ant

"... In PAGE 5: ...round is given by: ri = LT (S0 i(ri 1 ki)) : If a function f is applied to the input, the output would become: ri = LT (S0 i(f(ri 1) ki)) which, if f is linear in the XOR operation and ki is not changed by the transformation, becomes ri = LT (S0 i(f(ri 1) f(ki))) = LT (S0 i(f(ri 1 ki))) : A program was written to search for linear transformations f for which at least one output bit of Si(x) is the same as the corresponding bit of Si(f(x)) for all x. Table3 lists, for each s-box Si, the linear transformations f with the property that at least two output bits of Si(x) are the same as the corresponding output bits of Si(f(x)). The linear mapping f is described in the table by four 4-bit binary numbers.... In PAGE 7: ... In explicitly choosing the s-boxes to be resistant to differential crypt- analysis, the designers of Serpent ensured that an input difference would lead to a specific output difference with a probability of at most 1 4. How- ever, as shown in Table3 , these same s-boxes admit linear transformations of the input that lead to output differences with probabilities greater than 1 4. Although this property could possibly be exploited in the first round of the cipher, it is not clear that it could be extended to multiple rounds.... ..."

### Table 4: Inputs for which at least two output words are the same in the linear transformation

"... In PAGE 8: ... Is it ever the case that the output also has several equal 32-bit words? A search through the 232 inputs for which all four input words are the same shows that the output is the same in at least two words exactly 11 times. It is interesting to note from Table4 that it is most often the last two words of the output that are the same (8 times out of 11).... ..."