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

The main way of analyzing biological sequences is by comparing and aligning them to each other. It remains difficult, however, to compare modern multi-billionbase DNA data sets. The difficulty is caused by the nonuniform (oligo)nucleotide composition of these sequences, rather than their size per se. To solve this problem, we modified the standard seed-and-extend approach (e.g., BLAST) to use adaptive seeds. Adaptive seeds are matches that are chosen based on their rareness, instead of using fixed-length matches. This method guarantees that the number of matches, and thus the running time, increases linearly, instead of quadratically, with sequence length. LAST, our open source implementation of adaptive seeds, enables fast and sensitive comparison of large sequences with arbitrarily nonuniform composition.

/pdf/adaptive-seeds-tame-genomic-sequence-comparison-58wsqwzwm9.pdf

Adaptive seeds tame genomic sequence comparison.

コンピュータ・サイエンス : ACM computing surveys

https://www.cs.usask.ca/~croy/papers/2009/RCK_SCP_Clones.pdf

Comparison and evaluation of code clone detection techniques and tools: A qualitative approach

DNA microarrays have become ubiquitous in biological and medical research. The most difficult problem that needs to be solved is the design of DNA oligonucleotides that (i) are highly specific, that is, bind only to the intended target, (ii) cover the highest possible number of genes, that is, all genes that allow such unique regions, and (iii) are computed fast. None of the existing programs meet all these criteria. We introduce a new approach with our software program BOND (Basic OligoNucleotide Design). According to Kane’s criteria for oligo design, BOND computes highly specific DNA oligonucleotides, for all the genes that admit unique probes, while running orders of magnitude faster than the existing programs. The same approach enables us to introduce also an evaluation procedure that correctly measures the quality of the oligonucleotides. Extensive comparison is performed to prove our claims. BOND is flexible, easy to use, requires no additional software, and is freely available for non-commercial use from http://www.csd.uwo.ca/~ilie/BOND/
 . We provide an improved solution to the important problem of oligonucleotide design, including a thorough evaluation of oligo design programs. We hope BOND will become a useful tool for researchers in biological and medical sciences by making the microarray procedures faster and more accurate.

/pdf/bond-basic-oligonucleotide-design-51a0l5xghk.pdf

BOND: Basic OligoNucleotide Design

Repetitive perhaps, but certainly not boring

An O(n2(n-k)) on-line algorithm for computing a minimum set of k-covers for a given string of length n is presented. A straightforward modification of the algorithms yields O(kn2(n-k)) algorithms for computing a minimum set of k-covers and k-segments for a given circular string of length n. We show further that the number of such minimum sets of k-covers may be exponential. Similar time complexity bounds hold for computing the minimum sets of k-segments and k-seeds.

William F. Smyth

Papers

BOND: Basic OligoNucleotide Design

Repetitive perhaps, but certainly not boring

On-line algorithms for k-Covering

The three squares lemma revisited

A new approach to the periodicity lemma on strings with holes