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 approximate string-matching problem with Hamming distance. The approximate string-matching with k-mismatches problem is to find all locations at which a query of length m matches a factor of a text of length n with k or fewer mismatches. The approximate string-matching algorithms have both pleasing theoretical features, as well as direct applications, especially in computational biology. We consider a generalisation of this problem, the fixed-length approximate string-matching with k-mismatches problem: given a text t, a pattern x and an integer l, search for all the occurrences in t of all factors of x of length l with k or fewer mismatches with a factor of t. We present a practical parallel algorithm of comparable simplicity that requires only time, where w is the word size of the machine (e.g. 32 or 64 in practice) and p the number of processors. Thus the algorithm’s performance is independent of k and the alphabet size |Σ|. The proposed parallel algorithm makes use of message-passing parallelism model, and word-level parallelism for efficient approximate string-matching.

https://hal-upec-upem.archives-ouvertes.fr/hal-00741966/document

A parallel algorithm for fixed-length approximate string-matching with k -mismatches

We propose a new algorithm for computing the longest prefix of each suffix of a given string of length n over a constant-sized alphabet of size \(\sigma \) that occurs elsewhere in the string with Hamming distance at most k. Specifically, we show that the proposed algorithm requires time \(\mathcal {O}(n (\sigma R)^k \log \log n (\log k+ \log \log n))\) on average, where \(R=\lceil (k+2) (\log _{\sigma } n+1) \rceil \), and space \(\mathcal {O}(n)\). This improves upon the state-of-the-art average-case time complexity for the case when \(k=1\) [23] by a factor of \(\log n / \log ^3 \log n\). In addition, we show how the proposed technique can be adapted and applied in order to compute the longest previous factors under the Hamming distance model within the same complexities. In terms of real-world applications, we show that our technique can be directly applied to the problem of genome mappability.

Longest Common Prefixes with k-Mismatches and Applications

Fibonacci strings turn out to constitute worst cases for a number of computer algorithms which find generic patterns in strings. Examples of such patterns are repetitions, Abelian squares, and "covers". In particular, we characterize in this paper the covers of a circular Fibonacci string C(F k ) and show that they are \Theta(jF k j 2 ) in number. We show also that, by making use of an appropriate encoding, these covers can be reported in \Theta(jF k j) time. By contrast, the fastest known algorithm for computing the covers of an arbitrary circular string of length n requires time O(n log n).

The covers of a circular Fibonacci string

We study the λ-seed problem of a string in this paper. Given a string x of length n and an integer λ, the λ-seed problem is to find all the sets of λ substrings of x that cover a superstring of x, assuming that each element of the set is of equal length. We present an efficient algorithm that can compute all the λ-seeds of x in O(n2) time.

Computing the λ-seeds of a string

In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied by Makinen and Navarro [Position-Restricted Substring Searching, LATIN 2006]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by Makinen and Navarro, if applied to our problem, gives sub-optimal query time and the corresponding data structure also requires more time and space.

https://hal.inria.fr/hal-01184789/document

Costas S. Iliopoulos

Papers

A parallel algorithm for fixed-length approximate string-matching with k -mismatches

Longest Common Prefixes with k-Mismatches and Applications

The covers of a circular Fibonacci string

Computing the λ-seeds of a string

Optimal Prefix and Suffix Queries on Texts