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

This paper deals with the circular pattern matching (CPM) problem, which appears as an interesting problem in many biological contexts. CPM consists in finding all occurrences of the rotations of a pattern 𝒫 of length m in a text 𝒯 of length n. In this paper, we present SimpLiFiCPM (pronounced "Simplify CPM"), a simple and lightweight filter-based algorithm to solve the problem. We compare our algorithm with the state-of-the-art algorithms and the results are found to be excellent. Much of the speed of our algorithm comes from the fact that our filters are effective but extremely simple and lightweight.

/pdf/simplificpm-a-simple-and-lightweight-filter-based-algorithm-19x0y9t60e.pdf

SimpLiFiCPM: A Simple and Lightweight Filter-Based Algorithm for Circular Pattern Matching

In this paper, we present the Truncated Generalized Suffix Automaton (TGSA) and present an efficient on-line algorithm for its construction. TGSA is a novel type of finite automaton suitable for indexing DNA and RNA sequences, where the text is degenerate i.e. contains sets of characters. TGSA indexes the so called k-factors, the factors of the degenerate text with length not exceeding a given constant k. The presented algorithm works in $\mathcal{O}{(n^2)}$ time, where n is the length of the input DNA/RNA sequence. The resulting TGSA has at most linear number of states with respect to the length of the text. TGSA enables us to find the list occ(u) of all occurrences of a given pattern u in degenerate text x in time |u| + |occ(u)|.

Indexing Factors in DNA/RNA Sequences

We introduce the notion of λ-regularities in strings that consist of λ-covers and λ-seeds, and study three λ-regularities problems - the λ-cover problem, the general λ-cover problem and the λ-seed problem in this paper. λ-regularities can be viewed as generalized string regularities in the sense that a set of λ repetitive strings rather than a single repeated string are considered.

We first present a general algorithm for computing all the λ-combinations of a given string, since they serve as candidates for both λ-covers and λ-seeds. The running time of this algorithm is O(n$^2$). Relying on this result, we answer the above mentioned three problems all in O(n$^2$) time.

Algorithms for Computing the λ-regularities in Strings

Many string matching applications are based on suffix trees. Linear time sequential algorithms are available for constructing such trees. A CReW Parnllel RAM algorithm is presented here which takes 0 (logn) time with n processors, n being the length of the input string. The algorithm requires ern2) space, but only 0 (n iogn) cells need to be initialized.

/pdf/parallel-log-time-construction-of-suffix-trees-26d62jw1o0.pdf

Parallel Log-time Construction of Suffix Trees

This paper shows a simple algorithm for solving the single function coarsest partition problem on the CRCW PRAM model of parallel computation using O(n) processors in O(log n) time with O(n1+e) space.

Costas S. Iliopoulos

Papers

SimpLiFiCPM: A Simple and Lightweight Filter-Based Algorithm for Circular Pattern Matching

Indexing Factors in DNA/RNA Sequences

Algorithms for Computing the λ-regularities in Strings

Parallel Log-time Construction of Suffix Trees

A simple parallel algorithm for the single function coarsest partition problem