There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

/pdf/a-dynamic-survey-of-graph-labeling-198znmwxtq.pdf

A Dynamic Survey of Graph Labeling

DNA sequencing with chain terminating inhibitors

The vast majority of coding variants are rare, and assessment of the contribution of rare variants to complex traits is hampered by low statistical power and limited functional data. Improved methods for predicting the pathogenicity of rare coding variants are needed to facilitate the discovery of disease variants from exome sequencing studies. We developed REVEL (rare exome variant ensemble learner), an ensemble method for predicting the pathogenicity of missense variants on the basis of individual tools: MutPred, FATHMM, VEST, PolyPhen, SIFT, PROVEAN, MutationAssessor, MutationTaster, LRT, GERP, SiPhy, phyloP, and phastCons. REVEL was trained with recently discovered pathogenic and rare neutral missense variants, excluding those previously used to train its constituent tools. When applied to two independent test sets, REVEL had the best overall performance (p −12 ) as compared to any individual tool and seven ensemble methods: MetaSVM, MetaLR, KGGSeq, Condel, CADD, DANN, and Eigen. Importantly, REVEL also had the best performance for distinguishing pathogenic from rare neutral variants with allele frequencies

REVEL: An Ensemble Method for Predicting the Pathogenicity of Rare Missense Variants

Standards and Guidelines for the Interpretation and Reporting of Sequence Variants in Cancer: A Joint Consensus Recommendation of the Association for Molecular Pathology, American Society of Clinical Oncology, and College of American Pathologists

A weighted sequence is a string in which a set of characters may appear at each position with respective probabilities of occurrence. Weighted sequences are able to summarize poorly defined short sequences, as well as the profiles of protein families and complete chromosome sequences. Thus it is of biological and theoretical significance to design powerful algorithms on weighted sequences. A common task is to identify repetitive motifs in weighted sequences, with presence probability not less than a given threshold. We define two types of repeats in weighted sequences, called the loose repeats and the strict repeats, respectively, and then attempt to locate these repeats. Using an iterative partitioning technique, we present algorithms for computing all the loose repeats and strict repeats of every length, respectively. Each solution costs O(n2)time.

Loose and strict repeats in weighted sequences of proteins.

A molecular sequence "model" is a (structured) sequence of distinct or identical strings separated by gaps; here we design and analyze efficient algorithms for variations of the "Model Matching" and "Model Identification" problems.

Identifying Occurrences of Maximal Pairs in Multiple Strings

A string S[1, n] is a power (or repetition or tandem repeat) of order k and period n/k, if it can be decomposed into k consecutive identical blocks each n/k letters in length. Powers and periods are fundamental structures in the study of strings and algorithms to compute them efficiently have been widely studied. Recently, Fici et al. (Proc. ICALP 2016) introduced an antipower of order k to be a string composed of k distinct blocks of the same length, n/k, called the antiperiod. Antipowers are a natural converse to powers, and are objects of combinatorial interest in their own right. In this paper, we describe efficient algorithm for computing the smallest antiperiod t of a string S of length n in O(n log∗ t) time. We also describe an algorithm to compute all the antiperiods of S that runs in O(n log n) time.

https://drops.dagstuhl.de/opus/volltexte/2019/10503/pdf/LIPIcs-CPM-2019-32.pdf/

Computing the Antiperiod(s) of a String

https://www.mimuw.edu.pl/~rytter/MYPAPERS/psc2010.pdf

New simple efficient algorithms computing powers and runs in strings

A fundamental problem in music is to classify songs according to their rhythm. A rhythm is represented by a sequence of “Quick” (Q) and “Slow” (S) symbols, which correspond to the (relative) duration of notes, such that S = 2Q. In this paper, we present an efficient algorithm for locating the maximum-length substring of a music text t that can be covered by a given rhythm r.

/pdf/identifying-rhythms-in-musical-texts-4619jaa293.pdf

Costas S. Iliopoulos

Papers

Loose and strict repeats in weighted sequences of proteins.

Identifying Occurrences of Maximal Pairs in Multiple Strings

Computing the Antiperiod(s) of a String

New simple efficient algorithms computing powers and runs in strings

Identifying rhythms in musical texts