### (Table(J+ l) := Table(J);

1971

"... In PAGE 3: ...(Table... ..."

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### Table 1: Edge-de ning patterns for A( ^ G1; ^ G2)

"... In PAGE 10: ... Given two weighted sequence graphs ^ G1 = (V1; E1) and ^ G2 = (V2; E2), the graph A = A( ^ G1; ^ G2) has the node set f(i; j) i 2 V1 and j 2 V2g. The weighted edges of A are de ned by the patterns in Table1 . An edge from the source to the target node is de ned in A for all edges e1 = (i0; i; l1) 2 E1, e2 = (j0; j; l2) 2 E2 and l 2 0, when the edge label is distinct from h ?x ? i , x 2 .... In PAGE 11: ... Proof. The edge labels in Table1 represent all patterns for a terminal column of a regular fork alignment between any ^ s1 2 S( ^ G1(i)) with any ^ s2 2 S( ^ G2(j)). Notice that, since ^ G1 and ^ G2 are acyclic, the graph A, as de ned in Table 1, is acyclic, too.... ..."

### Table 3: Operational semantics for L

1998

"... In PAGE 8: ... For instance, a term B not referring to instance i in any of its events (and not containing )mayalways signal termi- nation of i;; it in fact has no information on i and assumes it to be terminated. Table3 gives the structural operational semantics of L MSC . This gives rise to a transition system semantics for each L MSC -term.... In PAGE 9: ... In this way,weavoid that a choice can be resolved by the termination of an instance not partici- pating in an execution. For instance, using the rules in Table3 , we can derive (e@1+e 0 @2) e 00 @3 ; e 00 @3 ;;;! (e@1+e 0 @2) quot; rather than (e@1+e 0 @2) e 00 @3 ; e 00 @3 ;;;! e@1 quot; or (e@1 + e 0 @2) e 00 @3 ; e 00 @3 ;;;! e 0 @2 quot;. Process names behave according to their instantiation by .... In PAGE 14: ... Two transition systems T i = hS i ;; !;;q i i for i =1;; 2 are called bisimilar, denoted T 1 T 2 , if there exists a relation R S 1 S 2 suchthat (q 1 ;;q 2 ) 2Rand whenever (s 1 ;;s 2 ) 2Rwehave { s 1 ; @i ;; ! s 0 1 implies 9s 0 2 : s 2 ; @i ;; ! s 0 2 suchthat(s 0 1 ;;s 0 2 ) 2R;; { s 2 ; @i ;;! s 0 2 implies 9s 0 1 : s 1 ; @i ;;! s 0 1 suchthat(s 0 1 ;;s 0 2 ) 2R. Note that our operational semantics ( Table3 ) as well as the standard one (Table 6) fall into the SOS format of [21], and therefore bisimulation is a congruence. Consistency of the semantics holds for all well-formed MSC def- initions, which we de ned above to mean that for every outgoing message, a corresponding incoming one is speci ed as w ell.... ..."

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### Table 6.3. Pairs dependent on Theorem 6.4

in Identical parallel machines vs. unit-time shops and preemption vs. chains in scheduling complexity

1998

Cited by 13

### Table 3. Parameters for L-J potentials

"... In PAGE 5: ... The Coulombic interaction is the sum of 16 pairs of point charges. The potential function between water molecules and carbon atoms are represented by Lennard-Jones function (with parameters in Table3 ) and the quadropole interaction term [15]. One (10, 10) SWNT with length 20.... ..."

Cited by 2

### Table 1. Relations j= l and 6 j= l for partial DB states.

"... In PAGE 9: ... De nition 6 Anexpansion operator ; is optimal if for all compatible and ;( ;; ) up = max and 0 ;( ;; ) ic for no 0 such that ( 0 ;; 0 ) 2 Equ( ;; ) for some 0 : The update expansion operators in [8] propagate into the initial update = (D + ;;D ; ) and so de ne the set of literals l whichitrequires ( j= l), and those to whichitcontradicts ( 6 j= l). Table1... ..."

### Table 1: Data augmentation in the spectral model. For all variables, j 2 J , l 2 L, and s 2 S.

"... In PAGE 3: ... 3.2 DA in the Spectral Model Table1 de nes a hierarchy of augmented data structures used to construct simple sampling and mode nding al- gorithms for the spectral model. In the notation of Ta- ble 1 more dots in the accent represent greater degrees of augmentation; variables with fewer dots are (sometimes stochastic) functions of those with more dots.... In PAGE 3: ... Two things are important here. First, each level of augmented data follows a standard distribution given and the data in the rows lower in Table1 ; e.g.... In PAGE 4: ... Thus, the E-step of EM and the corresponding draw of the DA algorithm are straightforward. Second, given the data in Table1 , the posterior distribution of is a set of independent standard distributions. For example, given Y k iid N( k; 2 k), it is easy to compute the posterior of (~ k; k; 2 k), using the Poisson nature of the length of Y k for ~ k, k 2 K.... In PAGE 5: ... For simplicity here we assume K = 0 and g( A; Ej) = 1 for each j. In this case, we use only the bottom three rows of Table1 in our DA scheme to derive Q( j (t)) = J X j=1 hE( _ Y C j jY obs; (t)) log C j ? C j i ? 1 2 J X j=2 !j( C j ? C j?1)2 : (3) Once we have computed the expectation in (3), we need only optimize Q( j (t)) as a function of . Unfortunately, this is not an easy task if ! gt; 0.... In PAGE 8: ... Given the computation cost of the outer E-step and hierarchical structure of the DA, nesting is an obvious strategy. The inner iteration of the nested EM algorithm xes _ Y s j for s 2 S; j 2 J and updates only the rst two rows of Table1 in the (inner) E-step and in the M-step. If this inner EM converges slowly (e.... ..."

### Table 3: Data for ? = O(2), = D 2, = D 1 in the (v; )-subsystem

1998

"... In PAGE 17: ... Notation: MRW = modulated rotating wave Veri cation of the entries in Table 2 Since dim V = 1, there is a unique axial subgroup J o Z2k, namely the subgroup of D 1 Z2 that acts trivially on V . The subgroups J together with the data p and L?p in the (v; )-subsystem are listed in Table3 . Applying Proposition 3.... In PAGE 19: ... Notation: MRW = modulated rotating wave, MTW = modulated traveling wave The veri cation of the entries in Table 4 is similar to that for Table 2. In particular, the entries in Table3 are unchanged. The main di erence is that we have Z( bif)0 = R in the V+ cases and Z( bif)0 = SE(2) in the V? cases.... ..."

Cited by 6