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 availability of fully sequenced genomes and the implementation of transcriptome technologies have increased the studies investigating the expression profiles for a variety of tissues, conditions, and species. In this study, using RNA-seq data for three distinct tissues (brain, liver, and muscle), we investigate how base composition affects mammalian gene expression, an issue of prime practical and evolutionary interest.

/pdf/transcriptome-map-of-mouse-isochores-17wk9qkvkw.pdf

Transcriptome map of mouse isochores

The suffix array is one of the most prevalent data structures for string indexing; it stores the lexicographically sorted list of suffixes of a given string. Its practical advantage compared to the suffix tree is space efficiency. In Property Indexing, we are given a string x of length n and a property $\varPi $, i.e. a set of $\varPi $-valid intervals over x. A suffix-tree-like index over these valid prefixes of suffixes of x can be built in time and space $\mathcal {O}(n)$. We show here how to directly build a suffix-array-like index, the Property Suffix Array (PSA), in time and space $\mathcal {O}(n)$. We mainly draw our motivation from weighted (probabilistic) sequences: sequences of probability distributions over a given alphabet. Given a probability threshold $\frac{1}{z}$, we say that a string p of length m matches a weighted sequence X of length n at starting position i if the product of probabilities of the letters of p at positions $i,\ldots ,i+m-1$ in X is at least $\frac{1}{z}$. Our algorithm for building the PSA can be directly applied to build an $\mathcal {O}(nz)$-sized suffix-array-like index over X in time and space $\mathcal {O}(nz)$.

Property Suffix Array with Applications

In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple &#x1d4aa;(σn2) time algorithm, where n is the length of the strings and σ is the alphabet size, and a sub-quadratic running time solution for the binary string case, both having linear space requirement. Furthermore, we present a modified algorithm applying some interesting tricks and experimentally show that the resulting algorithm runs faster.

Algorithms for Longest Common Abelian Factors

In the Range Minimum Query (RMQ) problem, we are given an array $A$ of $n$ numbers and we are asked to answer queries of the following type: for indices $i$ and $j$ between $0$ and $n-1$, query $\text{RMQ}_A(i,j)$ returns the index of a minimum element in the subarray $A[i..j]$. Answering a small batch of RMQs is a core computational task in many real-world applications, in particular due to the connection with the Lowest Common Ancestor (LCA) problem. With small batch, we mean that the number $q$ of queries is $o(n)$ and we have them all at hand. It is therefore not relevant to build an $\Omega(n)$-sized data structure or spend $\Omega(n)$ time to build a more succinct one. It is well-known, among practitioners and elsewhere, that these data structures for online querying carry high constants in their pre-processing and querying time. We would thus like to answer this batch efficiently in practice. With efficiently in practice, we mean that we (ultimately) want to spend $n + \mathcal{O}(q)$ time and $\mathcal{O}(q)$ space. We write $n$ to stress that the number of operations per entry of $A$ should be a very small constant. Here we show how existing algorithms can be easily modified to satisfy these conditions. The presented experimental results highlight the practicality of this new scheme. The most significant improvement obtained is for answering a small batch of LCA queries. A library implementation of the presented algorithms is made available.

How to answer a small batch of RMQs or LCA queries in practice

This is a theoretical study of partially occluded one-dimensional images. Here, we consider “valid” images composed from a given set of objects, where some objects appearing in the image may be partially obstructed by others. A CRCW PRAM algorithm is presented here for validating a one-dimensional image x of length n over a set of k objects of equal length in O ( log log n) time with linear work, where k is a fixed integer.

Costas S. Iliopoulos

Papers

Transcriptome map of mouse isochores

Property Suffix Array with Applications

Algorithms for Longest Common Abelian Factors

How to answer a small batch of RMQs or LCA queries in practice

Optimal parallel analysis and decomposition of partially occluded strings