Erratum: Mohammad Shibli Kaysar and Mohammad Ibrahim Khan A Modified Median String Algorithm for Gene Regulatory Motif Classification Symmetry 2020, 12, 8

The authors wish to make the following corrections to their paper: [...]

A Modified Median String Algorithm for Gene Regulatory Motif Classification

Consensus string is a significant feature of a deoxyribonucleic acid (DNA) sequence. The median string is one of the most popular exact algorithms to find DNA consensus. A DNA sequence is represented using the alphabet Σ= {a, c, g, t}. The algorithm generates a set of all the 4l possible motifs or l-mers from the alphabet to search a motif of length l. Out of all possible l-mers, it finds the consensus. This algorithm guarantees to return the consensus but this is NP-complete and runtime increases with the increase in l-mer size. Using transitional probability from the Markov chain, the proposed algorithm symmetrically generates four subsets of l-mers. Each of the subsets contains a few l-mers starting with a particular letter. We used these reduced sets of l-mers instead of using 4ll-mers. The experimental result shows that the proposed algorithm produces a much lower number of l-mers and takes less time to execute. In the case of l-mer of length 7, the proposed system is 48 times faster than the median string algorithm. For l-mer of size 7, the proposed algorithm produces only 2.5% l-mer in comparison with the median string algorithm. While compared with the recently proposed voting algorithm, our proposed algorithm is found to be 4.4 times faster for a longer l-mer size like 9.

Computing the Expected Edit Distance from a String to a Probabilistic Finite-State Automaton

In a number of fields, it is necessary to compare a witness string with a distribution. One possibility is to compute the probability of the string for that distribution. Another, giving a more global view, is to compute the expected edit distance from a string randomly drawn to the witness string. This number is often used to measure the performance of a prediction, the goal then being to return the median string, or the string with smallest expected distance. To be able to measure this, computing the distance between a hypothesis and that distribution is necessary. This paper proposes two solutions for computing this value, when the distribution is defined with a probabilistic finite state automaton. The first is exact but has a cost which can be exponential in the length of the input string, whereas the second is a fully polynomial-time randomized schema.