### Table 1: A list of dot product kernels.

2004

"... In PAGE 3: ... (5) Since the input to kD is a dot product, we call this type of kernels as dot product kernels. A list of kD functions is provided in Table1 . The positive definiteness of these kernels 1 can be verified by applying the aforementioned kernel construction rules.... ..."

Cited by 2

### Table 1: Means and variances of dot products of common

1995

"... In PAGE 5: ... Unfortunately, these do not apply exactly to circular convolution. The means and variances for dot products of some common circular con- volution products are given in Table1 in Section VIII.A.... In PAGE 10: ... The equivalent expressions in rows (5) to (10) are derived from the following identityofconvolution algebra: ~ a~ ~ b~ ~ x ~ y = ~ a~ ~ b~ ~ y ~ x = ~ a~ ~ b ~ x~ ~ y These means and variances are used as follows: Sup- pose that ~ a;; ~ b;; ~ c;; ~ d;; and ~ e are random vectors with el- ements drawn independently from N(0;; 1 n ). Then the value of ~ a ~( ~ a~ ~ b+ ~ c~ ~ d) ~ b will have an expected value of 1 and a variance of 7n+4 n 2 (= 6n+4 n 2 + 1 n using rows 6 and 10 in Table1 ). The value of ~ a ~( ~ a~ ~ b + ~ c~ ~ d) ~ e will have an expected value of 0 and a variance of 3n+2 n 2 (= 2n+2 n 2 + 1 n using rows 8 and 10 in Table 1).... In PAGE 19: ... The means and variances of all the signals are also shown, together with the number of each of these signals that must be tested to probe exhaustively for eachpairin the trace. The variances were calculated by adding the appropriate variances from Table1 , ignoring the terms of order 1=n 2 .Thecovariance between all terms in the signals (e.... In PAGE 20: ...mark gives X mark = ~ s 1 ~agt eat 1 p 3 id mark = 1 p 3 (eat + agt eat ~mark = +obj eat ~the sh)~agt eat 1 p 3 id mark = 1 3 (eat = +agt eat ~ 1 p 3 (being + person + id mark ) +obj eat ~the sh)~agt eat id mark = 1 3 eat~agt eat id mark + 1 3 p 3 agt eat ~being~agt eat id mark + 1 3 p 3 agt eat ~person~agt eat id mark + 1 3 p 3 agt eat ~id mark ~agt eat id mark + 1 3 obj eat ~the sh~agt eat id mark The expectations and variances of these terms can be found by consulting Table1 . It is not necessary to ex- pand the vectors agt eat , obj eat or the sh, as the com- ponents of these are independent of the other vectors appearing in the same terms.... In PAGE 20: ... It is not necessary to ex- pand the vectors agt eat , obj eat or the sh, as the com- ponents of these are independent of the other vectors appearing in the same terms. The expectation of the fourth term is 1 3 p 3 (row 4 in Table1 ), and all the expec- tation of the remaining terms is zero. These veterms are independentandthus the variance of the sum is the sum of the variances.... In PAGE 20: ... These veterms are independentandthus the variance of the sum is the sum of the variances. The variance of the rst term is 1 9n (row 3 in Table1 ), the variance of the second and third terms is 2n+2 27n 2 (row 8), the variance of the fourth term is 6n+4 27n 2 (row 6), and the variance of the fth term is 1 9n (row 10). These terms are uncorrelated, so their expectations and variances can be summed to give E(X mark )= 1 3 p 3 ;; var(X mark )= 16n +8 27n 2 0:593=n: The expectations and variances of Y p and Z can be calculated in a similar manner.... ..."

Cited by 79

### Table 2: The logic grammar for the Dot Product problem

### Table 1: Stability Classifications Of Edges Edge Type Dot Product Orientation

2004

"... In PAGE 5: ... Therefore we consider this to be an un- stable non-silhouette edge. Table1 presents the possible edge classifications. Table 1: Stability Classifications Of Edges Edge Type Dot Product Orientation... ..."

Cited by 4

### Table 7: Similarities (dot-products) among the frames.

1995

Cited by 79

### Table 7: Similarities (dot-products) among the frames.

1995

Cited by 79

### Table 7: Similarities (dot-products) among the frames.

1995

Cited by 79

### Table 4. Dot products of the reference spectra with the top 5 categories. The bold values indicate the reference spectra that have the highest dot products for each category spectrum.

2006