EERTREE: An Efficient Data Structure for Processing Palindromes in Strings

We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using this structure, we present simple and efficient solutions for a number of problems involving palindromes.Comment: 21 pages, 2 figures. Accepted to IWOCA 201

Optimal control of circuit quantum electrodynamics in one and two dimensions

Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of two qubits inside a cavity, but, more generally, to architectures based on two-dimensional arrays of cavities and qubits. For high-fidelity gate operations, simultaneous evolutions of controls and couplings in the two coupling dimensions of cavity grids are shown to be significantly faster than conventional sequential implementations. Even under experimentally realistic conditions speedups by a factor of three can be gained. The methods immediately scale to large grids and indirect gates between arbitrary pairs of qubits on the grid. They are anticipated to be paradigmatic for 2D arrays and lattices of controllable qubits.Comment: Published version

Finding Top-k Longest Palindromes in Substrings

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is one of the most important and classical problems regarding palindromic structures, that is, to compute the longest palindrome appearing in a string $T$ of length $n$. The problem can be solved in $O(n)$ time by the famous algorithm of Manacher [Journal of the ACM, 1975]. This paper generalizes the longest palindrome problem to the problem of finding top-$k$ longest palindromes in an arbitrary substring, including the input string $T$ itself. The internal top-$k$ longest palindrome query is, given a substring $T[i..j]$ of $T$ and a positive integer $k$ as a query, to compute the top-$k$ longest palindromes appearing in $T[i.. j]$. This paper proposes a linear-size data structure that can answer internal top-$k$ longest palindromes query in optimal $O(k)$ time. Also, given the input string $T$, our data structure can be constructed in $O(n\log n)$ time. For $k = 1$, the construction time is reduced to $O(n)$

Chromatic quasisymmetric functions

We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric functions. We present a conjectural refinement of Stanley's power sum basis expansion, which we prove in special cases. We describe connections between the chromatic quasisymmetric function and both the $q$-Eulerian polynomials introduced in our earlier work and, conjecturally, representations of symmetric groups on cohomology of regular semisimple Hessenberg varieties, which have been studied by Tymoczko and others. We discuss an approach, using the results and conjectures herein, to the $e$-positivity conjecture of Stanley and Stembridge for incomparability graphs of $(3+1)$-free posets.Comment: 57 pages; final version, to appear in Advances in Mat

A versatile palindromic amphipathic repeat coding sequence horizontally distributed among diverse bacterial and eucaryotic microbes

<p>Abstract</p> <p>Background</p> <p>Intragenic tandem repeats occur throughout all domains of life and impart functional and structural variability to diverse translation products. Repeat proteins confer distinctive surface phenotypes to many unicellular organisms, including those with minimal genomes such as the wall-less bacterial monoderms, <it>Mollicutes</it>. One such repeat pattern in this clade is distributed in a manner suggesting its exchange by horizontal gene transfer (HGT). Expanding genome sequence databases reveal the pattern in a widening range of bacteria, and recently among eucaryotic microbes. We examined the genomic flux and consequences of the motif by determining its distribution, predicted structural features and association with membrane-targeted proteins.</p> <p>Results</p> <p>Using a refined hidden Markov model, we document a 25-residue protein sequence motif tandemly arrayed in variable-number repeats in ORFs lacking assigned functions. It appears sporadically in unicellular microbes from disparate bacterial and eucaryotic clades, representing diverse lifestyles and ecological niches that include host parasitic, marine and extreme environments. Tracts of the repeats predict a malleable configuration of recurring domains, with conserved hydrophobic residues forming an amphipathic secondary structure in which hydrophilic residues endow extensive sequence variation. Many ORFs with these domains also have membrane-targeting sequences that predict assorted topologies; others may comprise reservoirs of sequence variants. We demonstrate expressed variants among surface lipoproteins that distinguish closely related animal pathogens belonging to a subgroup of the <it>Mollicutes</it>. DNA sequences encoding the tandem domains display dyad symmetry. Moreover, in some taxa the domains occur in ORFs selectively associated with mobile elements. These features, a punctate phylogenetic distribution, and different patterns of dispersal in genomes of related taxa, suggest that the repeat may be disseminated by HGT and intra-genomic shuffling.</p> <p>Conclusions</p> <p>We describe novel features of PARCELs (<b>P</b>alindromic <b>A</b>mphipathic <b>R</b>epeat <b>C</b>oding <b>EL</b>ements), a set of widely distributed repeat protein domains and coding sequences that were likely acquired through HGT by diverse unicellular microbes, further mobilized and diversified within genomes, and co-opted for expression in the membrane proteome of some taxa. Disseminated by multiple gene-centric vehicles, ORFs harboring these elements enhance accessory gene pools as part of the "mobilome" connecting genomes of various clades, in taxa sharing common niches.</p

The IGS-ETS in Bacillus (Insecta Phasmida): molecular characterization and the relevance of sex in ribosomal DNA evolution

<p>Abstract</p> <p>Background</p> <p>DNA encoding for ribosomal RNA (rDNA) is arranged in tandemly-repeated subunits, each containing ribosomal genes and non-coding spacers. Because tandemly-repeated, rDNA evolves under a balanced influence of selection and "concerted evolution", which homogenizes rDNA variants over the genome (through genomic turnover mechanisms) and the population (through sexuality).</p> <p>Results</p> <p>In this paper we analyzed the IGS-ETS of the automictic parthenogen <it>Bacillus atticus </it>and the bisexual <it>B. grandii</it>, two closely related stick-insect species. Both species share the same IGS-ETS structure and sequence, including a peculiar head-to-tail array of putative transcription enhancers, here named <it>Bag530</it>. Sequence variability of both IGS-ETS and <it>Bag530 </it>evidenced a neat geographic and subspecific clustering in <it>B. grandii</it>, while <it>B. atticus </it>shows a little but evident geographic structure. This was an unexpected result, since the parthenogen <it>B. atticus </it>should lack sequence fixation through sexuality. In <it>B. atticus </it>a new variant might spread in a given geographic area through colonization by an all-female clone, but we cannot discard the hypothesis that <it>B. atticus </it>was actually a bisexual taxon in that area at the time the new variant appeared. Moreover, a gene conversion event between two <it>Bag530 </it>variants of <it>B. grandii benazzii </it>and <it>B. grandii maretimi </it>suggested that rRNA might evolve according to the so-called "library hypothesis" model, through differential amplification of rDNA variants in different taxa.</p> <p>Conclusion</p> <p>On the whole, <it>Bacillus </it>rDNA evolution appears to be under a complex array of interacting mechanisms: homogenization may be achieved through genomic turnover that stabilizes DNA-binding protein interactions but, simultaneously, new sequence variants can be adopted, either by direct appearance of newly mutated repeats, or by competition among repeats, so that both DNA-binding proteins and repeat variants drive each other's evolution. All this, coupled with chromosome reshuffling due to sexuality (when present), might drive a quick fixation of new rDNA variants in the populations.</p