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

The k-covers problem (kCP) asks us to compute a minimum cardinality set of strings of given length k>1 that covers a given string. It was shown in a recent paper, by reduction to 3-SAT, that the k-covers problem is NP-complete. In this paper we introduce a new problem, that we call the Related Vertex Cover Problem (RVCP), which we show is a special case of Set Cover (SCP). We show further that kCP is equivalent to RVCP restricted to certain classes Gx.k of graphs that represent all strings x. We discuss approximate solutions of kCP, and we state a number of conjectures and open problems related to kCP and Gx.k

New complexity results for the k-covers problem

We consider a version of pattern matching useful in processing large musical data: ?-matching, which consists in finding matches which are ?-approximate in the sense of the distance measured as maximum difference between symbols. The alphabet is an interval of integers, and the distance between two symbols a, b is measured as |a - b|. We present ?-matching algorithms fast on the average providing that the pattern is "non-flat" and the alphabet interval is large. The pattern is "flat" if its structure does not vary substantially. We also consider (?, ?)- matching, where ? is a bound on the total number of errors. The algorithms, named ?-BM1, ?-BM2 and ?-BM3 can be thought as members of the generalized Boyer-Moore family of algorithms. The algorithms are fast on average. This is the first paper on the subject, previously only "occurrence heuristics" have been considered. Our heuristics are much stronger and refer to larger parts of texts (not only to single positions).

Three Heuristics for delta-Matching: delta-BM Algorithms

In the Longest Common Factor with k Mismatches (LCF_k) problem, we are given two strings X and Y of total length n, and we are asked to find a pair of maximal-length factors, one of X and the other of Y, such that their Hamming distance is at most k. Thankachan et al. [Thankachan et al. 2016] show that this problem can be solved in O(n log^k n) time and O(n) space for constant k. We consider the LCF_k(l) problem in which we assume that the sought factors have length at least l. We use difference covers to reduce the LCF_k(l) problem with l=Omega(log^{2k+2}n) to a task involving m=O(n/log^{k+1}n) synchronized factors. The latter can be solved in O(m log^{k+1}m) time, which results in a linear-time algorithm for LCF_k(l) with l=Omega(log^{2k+2}n). In general, our solution to the LCF_k(l) problem for arbitrary l takes O(n + n log^{k+1} n/sqrt{l}) time.

https://drops.dagstuhl.de/opus/volltexte/2018/8686/pdf/LIPIcs-CPM-2018-23.pdf/

Costas S. Iliopoulos

Papers

New complexity results for the k-covers problem

Three Heuristics for delta-Matching: delta-BM Algorithms

Linear-Time Algorithm for Long LCF with k Mismatches

Distributed pattern matching using finite automata

Abelian borders in binary words