### Table 1. A recurrence arising from unpublished work with J. Byskov on graph coloring algorithms.

2003

"... In PAGE 2: ... Similar but somewhat more complicated multivariate recurrences have arisen in our algorithm for 3-coloring [10] with variables counting 3- and 4-value variables in a constraint satisfaction instance, and in our algorithm for the traveling salesman problem in cubic graphs [12] with variables counting vertices, unforced edges, forced edges, and 4-cycles of unforced edges. These examples of recurrences have all had few enough terms that they can be solved by hand, but Table1 depicts a recurrence, arising from unpublished work with J. Byskov on graph coloring algorithms, that is complex enough that hand solution seems unlikely.... In PAGE 8: ... Both due to our use of exact real arithmetic, and due to the implementation in Python, a relatively slow interpreted language, our exact arithmetic implementation is not fast, taking several hours on a laptop computer to solve moderately sized 3-variable recurrences to 64 bits of precision. However our floating point implementation is able to run at interactive speeds, taking roughly one or two seconds on a recent- model laptop to solve recurrences such as the one in Table1... In PAGE 11: ... Perhaps it would also be possible to automatically perform some of the case analysis used to design backtracking algorithms, and to determine the appropriate variables to use in setting up the recur- rences used to analyze those algorithms, before automatically solving those recurrences, at least for simple constraint satisfaction type problems. It would also be of interest to find ways of specifying algorithms of this type in such a way that their correctness can be proven automatically, especially in situations where re- peated refinement based on our analysis tools has led to highly complex case analysis such as that appearing in Table1 . Also, while we can find tight worst-case bounds on the solution of the recurrence derived from an algorithm, it may not always be possible to construct an instance causing the algorithm itself to have that worst case time bound; it would be useful to determine conditions under which this recurrence-based analysis is tight.... ..."

### Table 6.1 Seasonal Adjustment/Trend Analysis of Some Foreign Trade Series

### Table 3. Upper bounds for e G(k): smaller k.

"... In PAGE 10: ...Table3... In PAGE 11: ... We note that the methods underlying the last two bounds can be adapted to give explicit bounds for e G(k) when k is of moderate size. Thus the method of Ford yields a bound for e G(k) that is superior to the best recorded in Table3 as soon as k 9, and indeed unpublished work of Boklan and Wooley pushes this transition further to k 8. The bounds recorded in Tables 3 and 4 are likely to be a long way from the truth.... ..."

### Table 2. Summary information for the pro-2-groups

"... In PAGE 3: ...2 is such a group. We report here on an extensive investigation of the 2-groups of coclass 3 and prove that there are 70 such families; in Table2 we identify 54 families which have nilpotency coclass 3. (Unpublished work of James agrees with this.... In PAGE 8: ...s shown (see Theorem 6.1). To distinguish between these, we say that the pro-2- groups obtained as extensions by Z2 have rank 1?. In Table2 we summarise some properties of the 82 pro-2-groups. For each pro- 2-group G, we record its coclass and rank; d is its minimal number of generators; jRGj is the order of the root for its associated family.... ..."

### Table 2 Comparison of MML and AIC on the task of selecting a polynomialapproximationtoanon-polynomialfunction.Adapted from (Wallace [unpublished]).

"... In PAGE 26: ... The difference between the two methods is especially stark when the amount of data is small. The results of one such experiment are shown in Table2 , adapted from (Wallace [unpublished]).26 This experiment shows the average results over 1000 cases for approximation of a trigonometric function with only 10 data points,27 under conditions of low noise.... ..."

Cited by 3

### Table V. Known Ramsey numbers R (Cn , Km ), results from unpublished manuscripts are marked with a *.

1994

### Table 2: The charged B states. Masses and widths come from theoretical estimates and ALEPH data (unpublished).

1996

### Table 2: The charged B states. Masses and widths come from theoretical estimates and ALEPH data (unpublished).

1996

### Table V. Known Ramsey numbers R (Cn , Km ), results from unpublished manuscripts are marked with a *.

### Table 3: Description of previously unpublished linkage markers placed on the integrated bovine chromosome 15 map.

2004