### Table 1: PN (the probability of necessary causation) as a function of assumptions and available data. ERR stands of the excess-risk-ratio 1 ? P (yjx0)=P (yjx) and CERR is given in Eq. (49). The non-entries (|) represent vacuous bounds, that is, 0 P N 1. Assumptions Data Available

2000

"... In PAGE 24: ...6 Summary of results We now summarize the results from Section 4 that should be of value to practicing epidemiologists and policy makers. These results are shown in Table1 , which lists the best estimand of PN under various assumptions and various types of data|the stronger the assumptions, the more informative the estimates. We see that the excess-risk-ratio (ERR), which epidemiologists commonly identify with the probability of causation, is a valid measure of PN only when two assumptions can be ascertained: exogeneity (i.... In PAGE 25: ...concerned with associations between such factors and susceptibility to expo- sure, as is often assumed in the literature [Khoury , 1989, Glymour, 1998]. The last two rows in Table1 correspond to no assumptions about exo- geneity, and they yield vacuous bounds for PN when data come from either experimental or observational study. In contrast, informative bounds (25) or point estimates (49) are obtained when data from experimental and ob- servational studies are combined.... ..."

Cited by 5

### Table 8.1: Bounds on rates for infinite families of binary codes with various separating properties.

2003

Cited by 3

### Table 8.1: Bounds on rates for infinite families of binary codes with various separating properties.

2003

Cited by 3

### Table 1. Analytical bounds.

1996

"... In PAGE 5: ... [15, 16], we place a superscript A on any variable related to the sender-initiated protocol, N1 and N2 on variables related to the receiver-initiated and RINA protocols, respectively, and H2 on tree-NAPP proto- cols. Table1 summarizes the bounds on maximum throughput for all the known classes of reliable multicast protocols. The results for sender-initiated, receiver-initiated, and tree-NAPP protocols are taken from the analysis presented by these authors [11] and Pingali et al.... ..."

Cited by 56

### Table 1. Analytical bounds.

1996

"... In PAGE 5: ... [15, 16], we place a superscript A on any variable related to the sender-initiated protocol, N1 and N2 on variables related to the receiver-initiated and RINA protocols, respectively, and H2 on tree-NAPP proto- cols. Table1 summarizes the bounds on maximum throughput for all the known classes of reliable multicast protocols. The results for sender-initiated, receiver-initiated, and tree-NAPP protocols are taken from the analysis presented by these authors [11] and Pingali et al.... ..."

Cited by 56

### Table 1. Analytical bounds

"... In PAGE 7: ... However, no class is given any relative advantage with this assumption. Table1 summarizes the bounds on maximum throughput for all the known classes of reliable multicast protocols. Our results clearly show that tree-NAPP protocols constitute the most scalable alternative.... In PAGE 14: ... We con- jecture that, once the effects of ack or nak failure, and the correlation of failures along the underlying multicast rout- ing trees are accounted for, the same relative performance of protocols will be observed. The results are summarized in Table1 . It is already known that sender-initiated protocols are not scalable be- cause the source must account for every receiver listening.... ..."

### Table 1. Analytical bounds

"... In PAGE 7: ... However, no class is given any relative advantage with this assumption. Table1 summarizes the bounds on maximum throughput for all the known classes of reliable multicast protocols. Our results clearly show that tree-NAPP protocols constitute the most scalable alternative.... In PAGE 14: ... We con- jecture that, once the effects of ack or nak failure, and the correlation of failures along the underlying multicast rout- ing trees are accounted for, the same relative performance of protocols will be observed. The results are summarized in Table1 . It is already known that sender-initiated protocols are not scalable be- cause the source must account for every receiver listening.... ..."

### Table 7.1: Bounds on rates for infinite families of binary (2,1)-SS and (2,2)-SS.

2003

Cited by 3

### Table 7.1: Bounds on rates for infinite families of binary (2,1)-SS and (2,2)-SS.

2003

Cited by 3

### Table 2: Bounds for Hash Families hash family bound source

1996

Cited by 10