Experiment results
We have done experiments to test the speed and sensitivity of the software.

Speed Testing
The time complexity of the algorithm is O(n2). To test the speed in practice, we use arbitrarily generated DNA and protein sequences. We ran our software on a PC with Pentium 4 3.4G CPU and 1GB memory, the result is shown in Table 3. We can see that for long DNA and protein sequences, our software can get the result in short time. For example, if the length of the sequence is 10000, it takes about 10.8 seconds and 26.9 seconds for DNA sequences and protein sequences, respectively. In some real applications, the length of sequences could be much longer than 10000. In this case, one can cut the long sequence into several short pieces and find out the repeated regions for each piece. If a region covers two pieces, then we can re-cut that segment to get that region.
Table 3  Results for the speed test of LocRepeat
Length  2000  4000  6000  8000  10000
DNA  0.5s  2.2s  4.8s  7.0s  10.8s
PROTEIN  1.1s  4.3s  10.0s  17.7s  26.9s

Sensitivity testing using real data
We applied LocRepeat to the DNA sequence gene PRNP which contains tandem repeats (GenBank:M13667). The length of the sequence is 2420. We find the local optimal pseudo-periodic region [215,327], that contains 5 pseudo-periodic units (Table 4). The pseudo-periodic region misses the first several sites of the tandem repeats, but the region and the partitions show the tandem repeats correctly.
We also applied LocRepeat to the protein sequence LGR6 (Swiss-Prot: Q9HBX8). The length of the sequence is 828. We use PAM120 as the similarity score matrix and find the local units (Table 5).
Table 4  Local optimal pseudo-periodic region for PRNP
Unit  Position  Length  Unit
1  215–238  24  ggtggtggctgggggcagcctcat
2  239–262  24  ggtggtggctgggggcagcctcat
3  263–286  24  ggtggtggctgggggcagccccat
4  287–310  24  ggtggtggctggggacagcctcat
5  311–327  17  ggtggtggctggggtca
Table 5  Local optimal pseudo-periodic region for LGR6
Unit  Position  Length  Unit
1  30–53  24  LSMNNLTELQPGLFHHLRFLEELR
2  54–77  24  LSGNHLSHIPGQAFSGLYSLKILM
3  78–101  24  LQNNQLGGIPAEALWELPSLQSLD
4  102–124  23  LNYNKLQEFPVAIRTLGRLQELG
5  125–148  24  FHNNNIKAIPEKAFMGNPLLQTIH
6  149–172  24  FYDNPIQFVGRSAFQYLPKLHTLS
7  173–195  23  LNGAMDIQEFPDLKGTTSLEILT
8  196–219  24  LTRAGIRLLPSGMCQQLPRLRVLE
9  220–241  22  LSHNQIEELPSLHRCQKLEEIG
10  242–265  24  LQHNRIWEIGADTFSQLSSLQALD
11  266–289  24  LSWNAIRSIHPEAFSTLHSLVKLD
12  290–311  22  LTDNQLTTLPLAGLGGLMHLKL In conclusion, the algorithm presented in this paper offers the possibility to find regions of pseudo-periodic repeats in a long sequence.