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.

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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

In the post-genomic era there has been an explosion in the amount of genomic data available and the primary research problems have moved from being able to produce interesting biological data to being able to efficiently process and store this information. In this paper we present efficient data structures and algorithms for the High Similarity Sequencing Problem. In the High Similarity Sequencing Problem we are given the sequences S 0, S 1, …, S k where S j = \(e_{j_1} I_{\sigma_1}e_{j_2} I_{\sigma_2} e_{j_3} I_{\sigma_3}, \dots,e_{j_\ell} I_{\sigma_\ell}\) and must perform pattern matching on the set of sequences. In this paper we present time and memory efficient datastructures by exploiting their extensive similarity, our solution leads to a query time of \(O(m + vk \log \ell + \frac{m occ_v v}{w} + \frac{PSC(p)m}{w})\) with a memory usage of O(N logN + vk logvk).

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Querying Highly Similar Structured Sequences via Binary Encoding and Word Level Operations

The constant advances in sequencing technology are turning whole-genome sequencing into a routine procedure, resulting in massive amounts of data that need to be processed. Tens of gigabytes of data in the form of short reads need to be mapped back to reference sequences, a few gigabases long. These high-throughput (or next-generation) technologies allow researchers to characterise a bacterial genome during a single experiment and at a moderate cost. In this paper, as most of the bacteria have a single circular chromosome, we present a simple, yet efficient, accurate and consistent algorithm, to solve the practical problem of matching millions of short reads to a genomic sequence with circular structure.

Mapping short reads to a genomic sequence with circular structure

Novel high-throughput (Deep) sequencing technologies have redefined the way genome sequencing is performed. They are able to produce millions of short sequences in a single experiment and with a much lower cost than previous methods. In this paper, we address the problem of efficiently mapping and classifying millions of short sequences to a reference genome, based on whether they occur exactly once in the genome or not, and by taking into consideration probability scores. In particular, we design algorithms for Massive Exact and Approximate Pattern Matching of short degenerate and weighted sequences, derived from Deep sequencing technologies, to a reference genome.

Algorithms for mapping short degenerate and weighted sequences to a reference genome

A combinatorial model for analyzing and interpreting an electrocardiogram (ECG) was presented in [Allali et al. '10] and [Iliopoulos & Michalakopoulos '09 and '10]. An application of the model is QRS peak detection and the resulting algorithm was shown to be space, as well as time efficient. Experimental results on the MIT-BIH Arrhythmia database were shown. In this paper, the peak detection algorithm is implemented in Java ME. The program is deployed on a mobile phone and simulators, and experimental results are discussed.

Combinatorial ECG analysis for mobile devices

Given two n-bit (cyclic) binary strings, A and B, represented on a circle (necklace instances). Let each sequence have the same number k of 1’s. We are interested in computing the cyclic swap distance between A and B, i.e., the minimum number of swaps needed to convert A into B, minimized over all rotations of B. We show that this distance may be approximated in O(n + k2) time.

Costas S. Iliopoulos

Papers

Querying Highly Similar Structured Sequences via Binary Encoding and Word Level Operations

Mapping short reads to a genomic sequence with circular structure

Algorithms for mapping short degenerate and weighted sequences to a reference genome

Combinatorial ECG analysis for mobile devices

Approximation algorithm for the cyclic swap problem