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

Proceedings of the Prague Stringology Conference '03

In this paper, we revisit the classic and well-studied longest common subsequence (LCS) problem and study some new variants, first introduced and studied by Rahman and Iliopoulos [Algorithms for Computing Variants of the Longest Common Subsequence Problem, ISAAC 2006]. Here we define a generalization of these variants, the longest parameterized common subsequence (LPCS) problem, and show how to solve it in O(n2) and O(n+Rlog n) time. Furthermore, we show how to compute two variants of LCS, RELAG and RIFIG in O(n + R) time.

/pdf/algorithms-for-computing-the-longest-parameterized-common-1n1luqrdey.pdf

Algorithms for computing the longest parameterized common subsequence

The inference of common motifs in a set of strings is a well-known problem with many applications in biological sciences. We study a new variant of this problem that oers a solution with the added exibility in the length of the common motifs to be found. We present algorithms that allow stretching of the length of the motifs as well as elasticity in the length of gaps between the motifs. The main data structure used in these algorithms is the suffix tree.

/pdf/application-of-suffix-trees-for-the-acquisition-of-common-1s6w5zxtfe.pdf

Application of suffix trees for the acquisition of common motifs with gaps in a set of strings

Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string S is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1,... , kn-1. Our main result is an (N + M)-time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a non-empty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in S in (min{W, n2}N)-time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in S. We also show that a result, which is essentially the same as our string comparison linear-time algorithm, can be obtained by employing an automata-based approach.

/pdf/comparing-degenerate-strings-3fgebpbbl0.pdf

Comparing Degenerate Strings

The swap matching problem consists if finding a pattern in a text, while allowing for transpositions in the pattern. A new approach using a graph-theoretic model was presented in [6] by Iliopoulos et al. In this paper we present a useful application for this algorithm and provide an analysis of its running time with a naive approach through implementation.

Costas S. Iliopoulos

Papers

Proceedings of the Prague Stringology Conference '03

Algorithms for computing the longest parameterized common subsequence

Application of suffix trees for the acquisition of common motifs with gaps in a set of strings

Comparing Degenerate Strings

Implementation of a Swap Matching Algorithm Using a Graph Theoretic Model