### Table 1: Schematic characterization of the test functions

"... In PAGE 13: ...he full matrix A can be found at http://www.wi.leidenuniv.nl/CS/ALP/alea.html. Our experiments aim at investigating the e ect of increasing the number of parents on these functions, and relating this e ect to function character- istics. Table1 shows that there are four functions in the multi-modal and non-separable category; the reason for this is that this category is supposed to contain the most challenging functions. In this category we divide func- tions further into two sub-categories: f4 and f5 have a regular arrangement of the local optima, while the arrangement of f6 and f7 is determined by random matrices, and is thus irregular.... ..."

### Table 1: Schematic characterization of the test functions

"... In PAGE 13: ...he full matrix A can be found at http://www.wi.leidenuniv.nl/CS/ALP/alea.html. Our experiments aim at investigating the e ect of increasing the number of parents on these functions, and relating this e ect to function character- istics. Table1 shows that there are four functions in the multi-modal and non-separable category; the reason for this is that this category is supposed to contain the most challenging functions. In this category we divide func- tions further into two sub-categories: f4 and f5 have a regular arrangement of the local optima, while the arrangement of f6 and f7 is determined by random matrices, and is thus irregular.... ..."

### Table 1: Characterizations of some function classes

1997

"... In PAGE 4: ... ~x 2 if and only if (~x; ) 2 . In Table1 we give a list of function classes with their defining generators. Note that most of the characterizations are easy to see from the original definitions, so we mention the appropriate papers within the list.... In PAGE 4: ...2 in [VW95]. For the notations in Table1 let ~x be a tuple of k components and let index variables range between 1 and k. We define a function span+ as span+(~x) =def #(fx1; : : : ; xkgnf0g).... In PAGE 11: ...roof. Suppose that such an oracle A does not exist, i.e. for H1(~x) =def min j xj gt; 0 , H2(~x) =def span+(~x) (see Table1 ) and for all s we have (H1; ) FPL; c:w: s?m (H2; ) by Theorem 5.... In PAGE 12: ...) For the case of c# P this means that functions from this class are defined by Turing machines where accepting paths are neighboured. The classes c# P, c# NP and c# coNP are characterized in Table1 in Sect. 3.... In PAGE 12: ...heorem 6.2. There is an oracle A such that max NPA 6 c# coNPA. Proof. Again, suppose that such an oracle A does not exist, so for the generators (H1; ) and (H2; ) from Table1 of max NP and c# coNP, respectively, and for all s we have (H1; ) FPL; c:w: s?m (H2; ). Let s(x) =def 2x and d1; d2 2 FPL witness the reduction for all ~x 2 s.... ..."

Cited by 6

### Table 14: Characterization of the application kernels

"... In PAGE 15: ... The application kernels of the benchmark suite is intended to cover a wide variety of scienti c applications typically implemented on parallel machines. Table14 captures some of the essential features by which many application codes are classi ed. Many nite di erence codes using explicit solvers require emulation of grids on one or several dimensions.... In PAGE 15: ... Depending on the layout of the associated arrays, the interprocessor may or may not correspond directly to the dimensionality of the data arrays. Table14 speci es the interprocessor communication implied in the application kernels. The application kernels contain one code for unstructured grid com- putations, fem-3D, pure particle codes, n-body and md, and codes that make use of both regular... In PAGE 31: ... The DPF suite includes three application kernels that make extensive use of the FFT: ks-spectral and pic-simple perform FFTs on two{dimensional grids, while wave-1D performs FFTs on a one{dimensional grid. The above characterization of the application kernels is summarized in Table14 . Table 15 lists the data representation and layout for the arrays used in the dominating computations in the application kernels and Table 16 summarizes the communication patterns in the codes.... ..."

### Table 8: Characterization of the application kernels.

"... In PAGE 10: ... The application kernels of the benchmark suite is intended to cover a wide variety of scienti c applications typically implemented on parallel machines. Table8 captures some of the essential features by which many application codes are classi ed. Many nite di erence codes using explicit solvers require emulation of grids on one or several dimensions.... In PAGE 10: ... Depending on the layout of the associated arrays, the interprocessor may or may not correspond directly to the dimensionality of the data arrays. Table8 speci es the interprocessor communication implied in the application kernels. The application kernels contain one code for unstructured grid computations, fem-3D, pure particle codes, n-body and md, and codes that make use of both regular grid structures and particle representations, mdcell, pic-simple and pic-gather-scatter.... In PAGE 19: ... The HPFBench suite includes three application kernels that make extensive use of the FFT: ks-spectral and pic-simple perform FFTs on two{dimensional grids, while wave-1D performs FFTs on a one{dimensional grid. The above characterization of the application kernels is summarized in Table8 . Table 9 lists the data representation and layout for the arrays used in the dominating computations in the application kernels and Table 10 summarizes the communication patterns in the codes.... ..."

### Table 5. Explicit representation vs. regular expressions in dataset one

2002

"... In PAGE 10: ... In this way we generated eight test sets for each training set for a total of 9*8=72 test results. Table5 depicts example test results using dataset number one as a training set. We applied a one-tailed t-test to the two distributions, one using an explicit representation and the second using regular expressions.... ..."

Cited by 2

### TABLE II. Explicit Formulae for Two-Center ERI Classes.

### Table 5. The types of objects that may be used with each function. Explicit Implicit

"... In PAGE 14: ... Here, again, we had to give the parent classes all the specializations of their derived classes. Table5 indicates when the functions are allowed. An error condition is raised at run-time if the functions are used incorrectly.... ..."

Cited by 17

### Table 1: The explicit and implicit methods.

"... In PAGE 8: ... The computations were carried out on a PC with an Intel PIII-1GHz CPU, RAM of 256 MB, and Windows 2000 OS. Table1 contains computation times for the two different methods, for a number of small instances. The instances are characterized by that there is a demand between every node-pair and that link capacities are uni- formly distributed over {10, 20, 30, 40, 50}.... In PAGE 8: ... For the first 7 instances there are two paths per demand, and for the 5 last instances there are three paths per demand. The results of Table1 suggest that the implicit method is slightly faster than that of the explicit method. If we sum up the usage of variables and constraints for the MIP corresponding to iteration k in the two different approaches, this is reasonable to expect.... In PAGE 9: ...0770 Table 2: The distribution approach. computation times given in Table1 and Table 2, strongly suggests that the distribution approach should be used whenever its deviation from the true optimum is acceptable. Certainly, such an error tolerance will depend on the details of the application.... ..."