### Table 2. GLM coe cients for the factor DIR in the nal GLM along with the associated direction sectors. Term Direction Sector (degrees) Term Coe cient ( 1000)

1999

"... In PAGE 5: ...berporth. To improve our model we inserted an extra wind direction sector factor variable: DIRt. (The DIRt factor has twelve levels corresponding to winds in the di erent 30 direction sectors. See Table2 for a list.) We applied a crude variable selection approach to select a subset of the K = 1022 variables: we selected an arbitrary 5% of variables which correlated best with Yt and labelled the resultant K1 = 51 variables S1 to S51.... ..."

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### Table 1. The optimal weights and corresponding relative e ciency in (1,1,1) direction in terms of r for k = 3 case.

1999

"... In PAGE 11: ...i to ui. From Theorem 2, we know that pi = p9?i. So we only need to determine p1; p2; p3; p4. Let ~ = = w. Table1 shows these weights in terms of r(= ~ i; i 1). The limiting case (r = 1) provides the lower bound of the relative e ciency of the classical design to the locally optimal design, which is 64/81 :079.... ..."

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### Table 3: Direction Predicates for point objects in terms of coordinates

"... In PAGE 8: ...X North East SW West South SE NW NE (a) De nitions of the predicates E N A B C East(B, A), NW(A, C), SW(C, B) West(A, B), NE(B, C), SE(C, A) (b) Examples of predicates Figure 3: Illustration of the predicates The direction constraints are represented as directed edges in each graph according to the symbol in the column 2 and 3 of Table3 . The edge goes from the node with smaller values to the node with larger values.... In PAGE 9: ... Graph constructGraphPoint(Set of Predicates conjunctionConstraint) f Graph constraintGraph = ;; for each entry p 2 conjunctionConstraint add a predicate point(p, amp;constraintGraph); return constraintGraph; g add a predicate point(Predicate aPredicate, Graph* aGraph ) f rstObject = getFirstObject(p); secondObject = getSecondObject(p); addNode( rstObject, secondObject, aGraph.graphX); symbol = ndXconstraint( Table3 , p); addEdge(symbol, rstObject, secondObject, aGraph.graphX); addNode( rstObject, secondObject, aGraph.... In PAGE 9: ...graphX); addNode( rstObject, secondObject, aGraph.graphY); symbol = ndYconstraint( Table3 , p); addEdge(symbol, rstObject, secondObject, aGraph.graphY); g addNode(Node n1, Node n2, Graph aGraph) f if n1 = 2 aGraph Add n1 to aGraph; if n2 = 2 aGraph add n2 to aGraph; g addEdge(char symbol, Node n1, Node n2, Graph, aGraph) f if (symbol == apos;= apos;) merge nodes n1, n2 to one; else if (symbol == apos; lt; apos;) add directed edge of (n1, n2) to aGraph; else add directed edge of (n1, n2) to aGraph; g 2.... In PAGE 10: ...predicates point relationships before lt; (A;B) A2 lt; B1 equal = (A;B) (A1 = B1) ^ (A2 = B2) overlaps o(A;B) (A1 lt; B1) ^ (A2 gt; B1) ^ (A2 lt; B2) meets m(A;B) (A2 = B1) during d(A;B) (A1 gt; B1) ^ (A2 lt; B2) starts s(A;B) (A1 = B1) ^ (A2 lt; B2) nishes f(A;B) (A1 gt; B1) ^ (A2 = B2) after bi(A;B) B2 lt; A1 overlapby oi(A;B) (B1 lt; A1) ^ (B2 gt; A1) ^ (B2 lt; A2) metby mi(A;B) (B2 = A1) duringby di(A;B) (B1 gt; A1) ^ (B2 lt; A2) startby si(A;B) (B1 = A1) ^ (B2 lt; A2) nishedby fi(A;B) (B1 gt; A1) ^ (A2 = B2) Table 4: Spatial relationships for intervals, where lt; and bi describe directional relationships and others are topological relationships spatial constraint intrinsic constraint R S Interval relationship L R1 R2 S1 S2 L1 L2 S1 S2 L1 R1 R2 L2 Before(S, R) and Meets(S, L) Figure 5: before(S; R) ^ meets(S; L) The graph is constructed according to the de nition of each predicate in Table3 . The dashed arrow represents the intrinsic constraint of the start point and end points.... ..."

### Table 2: The eigenvalues and the coe cients ci for the diagonalized directions, in terms of the operators in Eqs. (4),(22). Here the volume is 643, G = 5, and the data have been reweighted to the in nite volume critical point.

1998

"... In PAGE 21: ... (4). Diagonalizing the 4 4 matrix h(Si ? hSii)(Sj ? hSji)i for the 643 lattice ( G = 5) resulted in the eigenvalues and -vectors shown in Table2 . We observe a pronounced hierarchy of eigenvalues, similar to the previously considered case of two observables, Fig.... In PAGE 22: ...alues above it and become the second largest one (Sec. 5.3). However, for the range of volumes studied here, the hierarchy shown in Table2 was preserved.... ..."

### Table 2: Results of regression of input variables on range in direction of ow. Regression Terms Coe cients P-value

in Estimation of Contaminant Concentration in Ground Water Using a Stochastic Flow and Transport Model

### Table 3: Training Sets and Error Terms for the Various Models Forward Model Direct Inverse Model Distal Inverse Model

"... In PAGE 18: ... We initialized the inverse model with the direct inverse model apos;s nal values. See Table3 for a summary of the various error functions and training sets that... ..."

### Table 4 Break-even point for using M in one PCGLS iteration compared to a direct step. It is expressed in terms of q. Interior-point step = 2.

"... In PAGE 7: ...of computation associated with the two formulas are different. In Table4 the columns for M1 and M2 indicate the maximum q so that the number of flops for one PCGLS iteration per iterative step do not exceed the number of flops for a direct step. The quantity s% indicates the density of nonzero elements in percentage.... In PAGE 7: ...onzero elements in percentage. Sparsity density of an m-by-n matrix A is nnz(A)=mn. For a constant q, we define the break-even point for using M as the largest number of PCGLS iterations for which the cost of a PCGLS step is less than or equal to the cost of a direct step, where the cost is measured by floating point operations. From Table4 it is seen that column Aj from A is likely to be sparse. For Aj sparse, L?1 Aj is a solve with a sparse right hand side.... ..."

### Table 5: constant absolute direction

"... In PAGE 7: ...g: ~ east, ~ west, ~ north, ~ south, ~ NW, ~ NE, ~ SE, ~ SW. Table5 illustrates how we can de ne the constant directions in terms of coordinates in local embedding space. The unit vector is denoted by an ordered pair(a; b) which represents vector... ..."

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### Table 5: constant absolute direction

"... In PAGE 7: ...g: ~ east, ~ west, ~ north, ~ south, ~ NW, ~ NE, ~ SE, ~ SW. Table5 illustrates how we can de ne the constant directions in terms of coordinates in local embedding space. The unit vector is denoted by an ordered pair(a; b) which represents vector... ..."

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