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The authors have derived a new algorithm for the optimal shortening of a channel impulse response in discrete multitone (DMT) transceivers. This algorithm uses eigenvalues and eigenvectors to generate the coefficients of the shortening impulse response filter (SIRF). In comparison with the previous approach, this new algorithm can calculate the optimal settings of an SIRF with arbitrary length.

The ongoing global pandemic of infection disease COVID-19 caused by the 2019 novel coronavirus (SARS-COV-2, formerly 2019-nCoV) presents critical threats to public health and the economy since it was identified in China, December 2019. The genome of SARS-CoV-2 had been sequenced and structurally annotated, yet little is known of the intrinsic organization and evolution of the genome. To this end, we present a mathematical method for the genomic spectrum, a kind of barcode, of SARS-CoV-2 and common human coronaviruses. The genomic spectrum is constructed according to the periodic distributions of nucleotides, and therefore reflects the unique characteristics of the genome. The results demonstrate that coronavirus SARS-CoV-2 exhibits dinucleotide TT islands in the non-structural proteins 3, 4, 5, and 6. Further analysis of the dinucleotide regions suggests that the dinucleotide repeats are increased during evolution and may confer the evolutionary fitness of the virus. The special dinucleotide regions in the SARS-CoV-2 genome identified in this study may become diagnostic and pharmaceutical targets in monitoring and curing the COVID-19 disease.

The emerging global infectious COVID-19 disease by novel Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) presents critical threats to global public health and the economy since it was identified in late December 2019 in China. The virus has gone through various pathways of evolution. To understand the evolution and transmission of SARS-CoV-2, genotyping of virus isolates is of great importance. This study presents an accurate method for effectively genotyping SARS-CoV-2 viruses using complete genomes. The method employs the multiple sequence alignments of the genome isolates with the SARS-CoV-2 reference genome. The single-nucleotide polymorphism (SNP) genotypes are then measured by Jaccard distances to track the relationship of virus isolates. The genotyping analysis of SARS-CoV-2 isolates from the globe reveals that specific multiple mutations are the predominated mutation type during the current epidemic. The proposed method serves an effective tool for monitoring and tracking the epidemic of pathogenic viruses in their global and local genetic variations. The genotyping analysis shows that the genes encoding the S proteins and RNA polymerase, RNA primase, and nucleoprotein, undergo frequent mutations. These mutations are critical for vaccine development in disease control.