### Table 2: Method of lines solution for transport equation.

"... In PAGE 10: ... The simulation is allowed to run for t from 0 to 2. The results displayed in Table2 are the maximum error at the final time evaluated on a fine evaluation mesh, along with an indication of the h-convergence rate of the method. We see that the use of a more accurate quasi-interpolant pays off and results in higher accuracy.... ..."

### Table 1. Stratified sampling message updating and belief computing algorithm

"... In PAGE 5: ... We adopt a stratified sampler similar to PAMPAS but in its sequential version. The stratified sampling propagation that consists of message updating and belief computation, detail is described in Table1 . Each message in BP is represented by a set of weighted particles, i.... In PAGE 8: ...337 Then following equations from (17-19), message propagation and belief computa- tion is described in Table1 . the sequential Monte Carlo belief propagation is shown in Table 2.... ..."

Cited by 1

### TABLE A4. Pseudopopulation Created by Inverse Proba- bility of Treatment Weighting from a Point-Treatment Study with Dichotomous Treatment A0, Stratified by the Con- founder L0

2000

Cited by 6

### Table 1: Inverse Table

1998

"... In PAGE 4: ...e., truncn(sd; 8), page 11) in Table1 . The table maps each of the 128 8-bit non-0 signi cands to an 8-bit approximation of its reciprocal.... In PAGE 7: ... At line 6 the variable sd2 is assigned a 32,,17 oating point number that (we will prove) is 1=d with a relative error less than 2?28. This is done by obtaining an initial approximation via Table1 and then re ning it with two iterations of an easily computed variation of the Newton-Raphson method, sdi+1 = sdi(2 ? sdi d) (0 i 1): The variation is obtained by making the following transformations on the equation above. Instead of d we use the oating point number obtained by rounding d with the mode [away 32], i.... In PAGE 26: ...26 It is helpful to generalize away from the particulars of Table1 . Therefore, consider any table mapping keys to values.... In PAGE 26: ... Thus, if a table is quot;-ok and it contains a value v for truncn(d; 8) then jdv ? 1j lt; quot;. It is easy to con rm by computation that Table1 is quot;-ok for quot; = 3=512 and that it contains an entry assigning a value for the 8-bit truncation of every 1 d lt; 2 (e.g.... In PAGE 26: ...roved. Q.E.D. Perhaps the most interesting aspect of checking this proof mechanically is the quot;-ok prop- erty of Table1 . Just as described above, we de ned this property as an ACL2 (Common Lisp) predicate and proved the general lemma stating that any table satisfying that predicate gives su ciently accurate answers.... In PAGE 26: ... Just as described above, we de ned this property as an ACL2 (Common Lisp) predicate and proved the general lemma stating that any table satisfying that predicate gives su ciently accurate answers. When the general lemma is applied to our particular lookup, the system executes the predicate on Table1 to con rm that it has the required property.... In PAGE 27: ...27 var = value error bounds sd0 = (1=d)(1 + quot;sd0(d)) j quot;sd0(d)j lt; 2?8 + 2?9 sdd0 = 1 + quot;sdd0(d) quot;sd0(d) quot;sdd0(d) quot;sd0(d) + 2?30 sd1 = (1=d)(1 ? quot;sd1(d)) 0 quot;sd1(d) quot;sd0(d)2 + sdd1 = (1 ? quot;sdd1(d)) quot;sd1(d) ? 2?30 quot;sdd1(d) quot;sd1(d) sd2 = (1=d)(1 ? quot;sd2(d)) 0 quot;sd2(d) quot;sd1(d)2 + Table 2: Error Analysis for Lines 1-6 ( = 2?29 + 2?31 + (9=512)2?31) the particulars of Table1 are involved in the proof is when the predicate is executed. This example illustrates the value of computation in a general-purpose logic.... ..."

Cited by 27

### Table 3 Inverse probability weighing

2002

"... In PAGE 25: ... Consider again the censored exponential survival times. In Table3 we compare the complete case estimator of to various estima- tors of obtained from weighted estimating equations with weights either known ( True weights ) or estimated using a model only depending on X... In PAGE 27: ... The results are reported in Table 4; the rst row uses estimated weights (qfXg) depending on X only, the second row weights depending on X and the survival data (T ^ C; 1ft Cg). We see that adding a term leads to a considerable improvement over the complete case estimator (see Table3 ); in fact the ef ciency is very close to the ef ciency of the maximum likelihood estimator obtained in sub- section 3.2 (obtained via the EM algorithm).... ..."

### Table 1. Performance Goals for the RWSL Runway Entrance Lights*

### Table 3: Rendering performance in seconds per frame including shadows from 2 point lights. For all scenes, shadow rays use 4- tuples for subdivision while primary rays use 8-tuples.

2007

"... In PAGE 6: ...3 Ray casting with shadows Primary rays, however, tend to exhibit higher coherence than other types of rays. In Table3 , we investigate our performance for sec- ondary rays with simple shadows from 2 point light sources. The results demonstrate that packets are already beginning to lose some... ..."