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.

Identification Word Spacing of Erroneous Sentences on Indonesian Scientific

Scientific writings in Indonesian language must the rules of the General Guide to the Reformed Indonesian Spelling especially in terms of word spacing. good word spacing is proportional to the width of the typeface. generally use the align right facility in order to have article look neat in typing, but causes space from word to word over space. Additionally, according to the General Guide book for the updated Indonesian spelling, there are rules that use the distance of words with punctuation after and before punctuation. This research is intended to make for detecting applications using word spacing of the Regular Expression String algorithm and to comment on articles based on principles that are in accordance with the General Guidelines for Indonesian Reformed Spelling.

On the Taut String Interpretation and Other Properties of the Rudin–Osher–Fatemi Model in One Dimension

We study the one-dimensional version of the Rudin–Osher–Fatemi (ROF) denoising model and some related TV-minimization problems. A new proof of the equivalence between the ROF model and the so-called taut string algorithm is presented, and a fundamental estimate on the denoised signal in terms of the corrupted signal is derived. Based on duality and the projection theorem in Hilbert space, the proof of the taut string interpretation is strictly elementary with the existence and uniqueness of solutions (in the continuous setting) to both models following as by-products. The standard convergence properties of the denoised signal, as the regularizing parameter tends to zero, are recalled and efficient proofs provided. The taut string interpretation plays an essential role in the proof of the fundamental estimate. This estimate implies, among other things, the strong convergence (in the space of functions of bounded variation) of the denoised signal to the corrupted signal as the regularization parameter vanishes. It can also be used to prove semi-group properties of the denoising model. Finally, it is indicated how the methods developed can be applied to related problems such as the fused lasso model, isotonic regression and signal restoration with higher-order total variation regularization.

A Novel 2D Incompressible Viscous Inverse Design Method for Internal Flows Using Flexible String Algorithm

In this investigation, the flexible string algorithm (FSA), used before for inverse design of subsonic and supersonic ducts in compressible flows with and without normal shock, is developed and applied for inverse design of 2D incompressible viscous internal flow with and without separation. In the proposed method, the duct wall shape is changed under an algorithm based on deformation of a virtual flexible string in flow. At each modification step, the difference between current and target wall pressure distributions is applied to the string. The method is an iterative inverse design method and utilizes the analysis code for the flow field solution as a black-box. Some validation test cases and design examples are presented here, which show the robustness and flexibility of the method in handling complex geometries. In cases with separated flow pressure distribution, a unique solution for inverse design problem does not exist. The design algorithm is a physical and quick converging approach and can efficiently utilize commercial flow analysis software.