### Table 1: Parameterized vertices

"... In PAGE 9: ... How- ever, each vertex is given as the intersection of hyperplanes defined by the constraints with faces of A1BG. Figure 2 shows the general position of these intersection points, and Table1 presents them as a list. The third column of Table 1 states the conditions on the parameters for when the intersection point is an actual vertex of the polytope.... In PAGE 9: ... Figure 2 shows the general position of these intersection points, and Table 1 presents them as a list. The third column of Table1 states the conditions on the parameters for when the intersection point is an actual vertex of the polytope. Such conditions we will subsequently encounter in great numbers; they are formally introduced by the following definition.... In PAGE 10: ...(r)=0.4, I(s)=0.2 (0,0,1,0) (0,0,1,0) I(r)=0, I(s)=0 (0,0,1,0) Figure 1: Polytopes for different parameter values 3 5 2 4 8 6 7 1 Figure 2: General vertex positions problem statement for generating a complete parameterized vertex list can now be refined as follows: given input constraints BV, we have to find a list DACY BM APCY B4BD AK CY AK C5B5 (13) where each DACY is a parameterized vertex as in (7), and the APCY are lists of p-constraints, such that for every parameter instantiation C1 the set of vertices of A1B4C1B4BV B5B5 is just CUC1B4DACYB5 CY C1 satisfies APCYCV (where, naturally, C1 satisfies AP iff for every APCX AH D4CX AO BC BE AP: C1B4D4CXB5 AO BC). Table1 provides this list for the input constraints (9) and (10). To obtain a systematic method for generating such a list it is convenient to consider one by one the different faces of A1BEC3, in... In PAGE 12: ...icularly suitable method is fraction free Gaussian elimination (see e.g. [7]). This is a variant of Gaussian elimination that avoids divisions, which is useful for us, as otherwise we would have to divide by symbolic expressions that might be zero for some parameter values and nonzero for others, thereby requiring us to make a number of case distinctions. As an illustration for the working of the algorithm we retrace how vertex 8 in Table1 was generated. This vertex is the solution of the system (14)-(16) defined by CS BP BE, C0 BP CUBDBN BEBN BFCV and the (then mandatory) selection of both constraints CRBDBN CRBE for (16).... In PAGE 14: ... To illustrate the general method, we continue with our example, taking C8 B4BMBT CY BUB5 to be the target probability of the inference rule to be derived. The probability of BMBT given BU at the vertices listed in Table1 is evaluated by computing DABFBPB4DABDB7DABFB5, which leads to the values listed in Table 4. Note that the possible values of C8 B4BMBT CY BUB5 are still annotated with the parameter constraints on the vertices at which they are attained, and that for vertices 5 and 8 the new p-constraint D7 BO BD has been added.... In PAGE 21: ... Minimal irredundant sets of values for minimization and maximization of C8 B4BT CY BU CM BWB5 are indicated by the +-marks in the columns 8 and 9, respectively. The final bound functions we obtain now are C4B4D6BN D8BN D9BN DAB5 BP minCJD6BPDA BM AQ BN DA BQ BCCL (40) CDB4D6BN D8BN D9BN DAB5 BP maxCJBC BM D6 BP BCBN DA BP BDBN BD BM AQ BN D9 AK D6BN D6 BQ BCBN BD BM AQ BN D9 AK D8BN D8 AK DABN D8 BQ BCBN BD BM AQ BN D6 AK D9BN D9 AK D8BN D9 BQ BCBN BD BM AQ BN DA AK D8BN DA BQ BCBN D8BPD9 BM AQ BN D8 AK D9BN D9 BQ BCCLBM (41) where the p-constraints AQ suppressed in Table1 have been reinstated. Remembering the con- ventions min BN BP BDBN max BN BP BC, and taking into account that the conditions D6 AK D8BN D9 AK DA are taken for granted in (29), these functions can be seen to be the same as (30) and (31).... ..."

Cited by 1

### Table 2: Surface Parameterization for business jet problem

1997

"... In PAGE 12: ... Six design variables were used whose associated mode shapes were combinations of 3 chordwise functions and 2 spanwise functions. The selected design variables result in a wing parameterization given by equation (36) and the functions fi and gj for this case are listed in Table2 . Note that the chordwise functions are given by a shear function (which is similar to a twist variable for small geometry perturbations), and two Hicks-Henne functions.... ..."

Cited by 29

### Table 1. Maximum Output parameterization of Adaptive Mapping and PAM DGP

2007

"... In PAGE 6: ... Each individual is a stack-based machine composed of a general-purpose stack and an output register. A program that changes the state of the machine is a list of instructions from the function set in Table1 below. When an instruction in the pro- gram is processed sequentially, the required arguments are taken from the stack, they are presented to the function, and the return value (if any) is pushed back onto the stack.... In PAGE 6: ...Hz PowerPC G4 running Mac OS X Version 10.4.4. Algorithm parameters are summarized in Table1 for both DGP algorithms. Table 1.... In PAGE 8: ... The alternative settings for this problem demonstrate the high customizability of PAM DGP and provide an example of its performance on a hard problem using a larger population (and larger probability table) than the MAX problem. Parameterizations specific to the Two Boxes problem are shown in Table 4 ( Table1 details the common parameters). Table 4.... ..."

Cited by 2

### Table 1: Parameterized motions built in our experiments.

2004

"... In PAGE 9: ... 4.4 Results and Applications We have implemented the above algorithms and used them to cre- ate a variety of parameterized motions; see Table1 for a summary. In each case we generated a thousand parameter samples using the method described in Section 4.... ..."

Cited by 55

### Table 2: Parameterized Assembly Instructions Instruction Parameters

"... In PAGE 3: ... The geno- types of our Evolutionary Algorithm were assembly plans, consisting of a sequential set of parameterized instructions to the situated development system described above in Sec- tion 2. Table2 lists the instructions used. Note that the instructions above only allow for ballistic assembly - that is, there are no commands which test in- termediate results (such as probing for the existence of a brick at a particular location), nor any ability to branch or otherwise alter behavior predicated on such a test.... ..."

### Table 2: Parameterized Assembly Instructions Instruction Parameters

"... In PAGE 3: ... The geno- types of our Evolutionary Algorithm were assembly plans, consisting of a sequential set of parameterized instructions to the situated development system described above in Sec- tion 2. Table2 lists the instructions used. Note that the instructions above only allow for ballistic assembly - that is, there are no commands which test in- termediate results (such as probing for the existence of a brick at a particular location), nor any ability to branch or otherwise alter behavior predicated on such a test.... ..."

### Table 2: Parameterized Assembly Instructions Instruction Parameters

"... In PAGE 3: ... The geno- types of our Evolutionary Algorithm were assembly plans, consisting of a sequential set of parameterized instructions to the situated development system described above in Sec- tion 2. Table2 lists the instructions used. Note that the instructions above only allow for ballistic assembly - that is, there are no commands which test in- termediate results (such as probing for the existence of a brick at a particular location), nor any ability to branch or otherwise alter behavior predicated on such a test.... ..."

### Table 2. Parameterizations considered Model Parameters

1997

"... In PAGE 37: ....1. Model Pararneterizations Considered in the Analysis The utility function, U, and Markov transition matrix, pel, used in the analysis have the following form: The parameter p is the first order autocorrelation of 0 and o is the associated standard deviation. In the benchmark parameterization, labelled parameterization (1) in Table2 , P = 1.03-0.... In PAGE 37: ... = 1.0, a = 0.3, 6 = 0.02, a = 0.23, p = 0. The relatively large value of o was chosen to guarantee that the investment constraint would bind a substantial fraction of times. For the other model parameterizations, we perturb the benchmark values in the manner indicated in rows (2)-(7) of Table2 . The perturbations were chosen to provide information about the robustness of our results.... In PAGE 60: ... Generally this accuracy criterion was hardest to meet for the financial statistics and most other statistics were within 1% of the corresponding exact values. See Table 1 for a fuller description of the computational strategies, and Table2 for a summary of the model parameter values. A common set of starting values were used for all the algorithms.... ..."

### Table 1: Parameterization/unparameterization of a single-coplanar point.

2003

"... In PAGE 11: ... Indeed, is an homogeneous vector and has therefore at least one non-zero element. Table1 shows the practical algorithm for parameterizing/unparameterizing X 2 derived from the above reasoning. In the unparameterization, we divide by j that, as said above, is always non-zero.... ..."

Cited by 12

### TABLE l Parameter values fitted by the optimization algorithms for the test problem*

1976