And, in addition, we would also call these SFs on the BTs of the ADLD the BSFs.

From Figure 2(a), it is easy to see that there are two SFs in the ADLD of the sequence pair (chimpanzee, human); one is ASF1, that is, the line segment from the point (1,1) to the point (32,32), and the other is [BSF.sup.1.sub.-4], that is, the line segment from the point (35,31) to the point (125,121).

Observing Figure 2(b), we can easily find that there are also two SFs in the ADLD of the sequence pair (human, gorilla).

Through analysis, we can know that, for a given protein sequence pair, if there exist some deletions or insertions of amino acid segments between the two protein sequences, then there will exist some misalignments of SFs in their ADLD; that is, some ASFs on the AT will be transformed into BSFs on some BTs.

From the above descriptions, it is easy to know that the ADLD of any given protein sequence pair obtained by our above proposed method reflects some inner and specific differences between these two protein sequences in the given protein sequence pair, which may be useful in the similarity/dissimilarity analysis of protein sequence pairs.

For a given protein sequence pair {[[psi].sub.a], [[psi].sub.1]}, a e {1,2, ...,N}, b [member of] {1,2, ..., N}, we can obtain their ADLD through adopting the method proposed in Section 2.6, and then we can obtain all of the SFs (including ASFs and BSFs) and FPs in the ADLD.

Suppose that there are totally [L.sub.1] different ASFs such as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]} different BSFs such as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] different FPs such as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]} in the ADLD. And, in addition, for each [ASF.sup.i] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] let their length be length" and length., respectively, where i [member of] {1,2, .., [L.sub.1]} and j [member of] {1,2, ...

Observing Figure 7, we can clearly find that the total length of all of the SFs in each of these three ADLDs satisfies the total length of all of the SFs in the ADLD of Figure 7(a) > the total length of all of the SFs in the ADLD of Figure 7(b) > the total length of all of the SFs in the ADLD of Figure 7(c).

Moreover, from Figure 7, we can also intuitively identify that the two protein sequences in the protein sequence pair (human, gorilla) are very similar to each other, since the total length of all of the SFs in the ADLD of Figure 7(a) looks very long.

Additionally, observing Figures 2(a) and 2(b), hardly can we distinguish the total length of all of the SFs (including ASFs and BSFs) in the ADLD of Figure 2(a) and that in the ADLD of Figure 2(b), since the total lengths of all of the SFs in these two ADLDs look nearly the same.

Next, in Sections 2.2-2.6 we will introduce the details of constructing the ADLDs and obtaining some of the numerical characteristics of them.

According to the above assumptions, in Figure 2, we show the two ADLDs corresponding to the ASDs illustrated in Figures 1(a) and 1(b) while letting [delta] = 3.