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Figure 9: Approximate counting update and query.

Figure 9 Approximate counting update and query.

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The real dataset can be download from NCBI via accession number (access.) provided in the descriptions. Table 1: Synthetic and real dataset used in the experiments
The real dataset can be download from NCBI via accession number (access.) provided in the descriptions. Table 1: Synthetic and real dataset used in the experiments
Figure 1: Similarities between synthetic sequences with different sizes, detected by Smash++. The parameters used are k-mer size = 14 and number of substitutions in substitution-tolerant Markov model (STMM) = 5, which are the default parameters used by Smash+-+. For the threshold, the default values of 1.5 and 1.97 are used for panels a-d and e, respectively. (a) 1.5 kb sequences; (b) 100 kb sequences. No similarity is detected for Part II of the reference because it is mutated 90%. Parts III and IV of the reference and I and II of the target are joined because there is no space between consecutive regions. (c) 5 Mb sequences; (d) 100 Mb sequences; (e) 60 kb sequences. Roughly 43% of mutation is detected.
Figure 1: Similarities between synthetic sequences with different sizes, detected by Smash++. The parameters used are k-mer size = 14 and number of substitutions in substitution-tolerant Markov model (STMM) = 5, which are the default parameters used by Smash+-+. For the threshold, the default values of 1.5 and 1.97 are used for panels a-d and e, respectively. (a) 1.5 kb sequences; (b) 100 kb sequences. No similarity is detected for Part II of the reference because it is mutated 90%. Parts III and IV of the reference and I and II of the target are joined because there is no space between consecutive regions. (c) 5 Mb sequences; (d) 100 Mb sequences; (e) 60 kb sequences. Roughly 43% of mutation is detected.
Figure 2: Similarities in a real dataset, detected by Smash++. (a) G. gallus (chicken) chr. 18 and M. gallopavo (turkey) chr. 20. The parameters were k-mer size = 14, No. substitutions in STMM = 5, threshold = 1.9, and minimum block size (m) = 500,000; i.e., regions smaller than 500,000 bp were not considered for further processing; (b) G. gallus chr. 14 and M. gallopavo chr. 16. The result is obtained by setting k = 14, No. substitutions = 5, threshold = 1.95, and m = 400,000; (c) H. sapiens (human) chr. 12 and P. troglodytes (chimpanzee) chr. 12. The parameters were k = 14, without using STMM, threshold = 1.9, and m = 100,000; (d) X. oryzae pv. oryzae PXO99A (a rice pathogen) and X. oryzae pv. oryzae MAFF 311018 (a rice pathogen). The result was obtained by setting k = 13, threshold = 1.55, and m = 10,000.
Figure 2: Similarities in a real dataset, detected by Smash++. (a) G. gallus (chicken) chr. 18 and M. gallopavo (turkey) chr. 20. The parameters were k-mer size = 14, No. substitutions in STMM = 5, threshold = 1.9, and minimum block size (m) = 500,000; i.e., regions smaller than 500,000 bp were not considered for further processing; (b) G. gallus chr. 14 and M. gallopavo chr. 16. The result is obtained by setting k = 14, No. substitutions = 5, threshold = 1.95, and m = 400,000; (c) H. sapiens (human) chr. 12 and P. troglodytes (chimpanzee) chr. 12. The parameters were k = 14, without using STMM, threshold = 1.9, and m = 100,000; (d) X. oryzae pv. oryzae PXO99A (a rice pathogen) and X. oryzae pv. oryzae MAFF 311018 (a rice pathogen). The result was obtained by setting k = 13, threshold = 1.55, and m = 10,000.
Figure 4: (a) The peak memory consumption, in gigabytes; and (b) the elapsed (wall clock) time usage, in minutes, of Smash++ obtained by running on all synthetic and real datasets described in Table 1.
Figure 4: (a) The peak memory consumption, in gigabytes; and (b) the elapsed (wall clock) time usage, in minutes, of Smash++ obtained by running on all synthetic and real datasets described in Table 1.
Figure 5: Comparison of Smash++ and Smash, in terms of (a) memory usage; and (b) time usage, running on real and synthetic data described in Table 1. To have a fai comparison, only 1 model (FCM) is used by Smash++, and also self-complexity is not computed. Diamonds indicate the mean, and bars, the ranges from minimun to maximum values.
Figure 5: Comparison of Smash++ and Smash, in terms of (a) memory usage; and (b) time usage, running on real and synthetic data described in Table 1. To have a fai comparison, only 1 model (FCM) is used by Smash++, and also self-complexity is not computed. Diamonds indicate the mean, and bars, the ranges from minimun to maximum values.
Figure 6: The schema of Smash++. The process of finding similar regions in reference and target sequences and computing the redundancy in each region includes & stages. Smash++ outputs a x.pos file that includes the positions of the similar regions, and can be then visualized, resulting in an SVG image.
Figure 6: The schema of Smash++. The process of finding similar regions in reference and target sequences and computing the redundancy in each region includes & stages. Smash++ outputs a x.pos file that includes the positions of the similar regions, and can be then visualized, resulting in an SVG image.
Figure 7: Data model used by Smash++. (a) Cooperation between finite-context models (FCMs) and substitution-tolerant Markov models (STMMs). Note that each STMM needs to be associated with an FCM. (b) Probability of an input symbol is estimated by using the probability and weight values that have been obtained from processing previous symbols.
Figure 7: Data model used by Smash++. (a) Cooperation between finite-context models (FCMs) and substitution-tolerant Markov models (STMMs). Note that each STMM needs to be associated with an FCM. (b) Probability of an input symbol is estimated by using the probability and weight values that have been obtained from processing previous symbols.
Figure 8: The data structures used by Smash+-+ to store the models in memory. (a) Table of 64-bit counters that uses up to 128 MB of memory, (b) table of 32 bit counter: that consumes at most 960 MB of memory, (c) table of 8 bit approximate counters with memory usage of up to 1 GB, and (d) Count-Min-Log sketch of 4-bit counters which consumes up to }w x dB of memory; e.g., if w = 2° and d = 4, it uses 2 GB of memory.
Figure 8: The data structures used by Smash+-+ to store the models in memory. (a) Table of 64-bit counters that uses up to 128 MB of memory, (b) table of 32 bit counter: that consumes at most 960 MB of memory, (c) table of 8 bit approximate counters with memory usage of up to 1 GB, and (d) Count-Min-Log sketch of 4-bit counters which consumes up to }w x dB of memory; e.g., if w = 2° and d = 4, it uses 2 GB of memory.
Figure 10: Count-Min-Log Sketch update and query. The Kolmogorov complexity is not computable; hence, an al- ternative is required to compute it approximately. It has been shown in the literature that a compression algorithm can be used for this purpose [44-46]. In this article, we use a reference- free compressor to approximate the complexity and, conse-
Figure 10: Count-Min-Log Sketch update and query. The Kolmogorov complexity is not computable; hence, an al- ternative is required to compute it approximately. It has been shown in the literature that a compression algorithm can be used for this purpose [44-46]. In this article, we use a reference- free compressor to approximate the complexity and, conse-
Figure 11: Finding similar regions in reference and target sequences. Smash++ first finds the regions in the target that are similar to the reference and then finds the regions in the reference that are similar to the detected target regions. This procedure is performance for both regular and inverted homologies.
Figure 11: Finding similar regions in reference and target sequences. Smash++ first finds the regions in the target that are similar to the reference and then finds the regions in the reference that are similar to the detected target regions. This procedure is performance for both regular and inverted homologies.
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