Ic due to the underlying signal being approximately period-10. We simulatedIc due to the underlying

Ic due to the underlying signal being approximately period-10. We simulated
Ic due to the underlying signal being approximately period-10. We simulated eroded sequences by generating 100 synthetic perfectly period-10 symbolic sequences of length N = 150 and then eroding these in increments of 1 to a maximum of 50 erosion. We simulated approximately periodic symbolic sequences using a Gaussian distributed period with expected value of 10 and standard deviation s. These were then repeated for many standard deviations s ?[0.1, 3].Results of the period estimation comparison are shown in Figure 2. In this experiment, a sequence length of N = 150 was selected, this being approximately PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/27107493 the length of nucleosome associated DNA. If N is varied from 150, e.g. to 149, the advantage of the IPDFT over the DFT is not preserved, as is also noted in Epps [11], however for the purposes of this paper the IPDFT can be considered a better choice since the AZD4547 web periods it evaluates are not dependent on the sequence fragment length, while the reverse is true for the DFT. The relative advantage of the autocorrelation over the IPDFT is also not necessarily preserved when N is varied, in particular for prime values of N [11]. The greater accuracy in estimation of the dominant period by the Hybrid derives from the complementary nature of the flaws in the Fourier transform and autocorrelation measurements. When synthetic period-10 sequences are degraded instead by varying the period to produce approximate periodicity, and a similar analysis to that for Figure 2 performed, Fourier-based methods appear to generally outperform autocorrelation. This can be explained by the fact that the period was allowed to vary within each sequence fragment but with a mean of 10 bp, so that Fourier methods with a fixed 10 bp period basis function are better suited to the problem than autocorrelation, which depends on exact similarity between s[n] and s[n + 10] for the n’th sequence position index. Comparing the two panels in Figure 2, it can be noted that the Hybrid approach generally retains the betterDFT100 80 60 40 20 00IPDFTAutocorrHybridPercent CorrectPercent Erosion0.0.Standard Deviation1.1.2.2.3.Figure 2 Average accuracy of dominant period estimation for simulated sequences. Eroded (left) – sequences were period-10 synthetic sequences of length N = 150, eroded to the extent indicated on the x-axis. Approximate (right) – sequences were of length N = 150, with periods Gaussian distributed about an expected value of 10 bp.Epps et al. Biology Direct 2011, 6:21 http://www.biology-direct.com/content/6/1/Page 6 ofperiod estimate from either the autocorrelation or Fourier-based methods in each case. Reasons for this were discussed in Epps [11]. To summarise the comparison of exploratory period estimation methods for synthetic data, results show that IPDFT and Hybrid were roughly equivalent in their average accuracy for approximately periodic sequences, while the Hybrid was considerably superior on eroded synthetic sequences (Figure 2). The results of the significance measure comparison for imperfect and approximate periodicities are seen in Figure 3, for fragment lengths N = 150 each expressed in terms of the probability of an equivalent or larger periodic component at exactly period-10 (for the BWB and Chi-squared measures) or the probability of an equivalent or larger peak in the periodicity profile |XIP [p]| (for the g-statistic). All measures show the expected increasing probability with degradation to the sequence fragment periodicity, and all are monotoni.