Deciding the Winner of an Arbitrary Finite Poset Game is PSPACE-Complete

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity of arbitrary finite poset games was only known to exist somewhere between NC^1 and PSPACE. We resolve this discrepancy by showing that deciding the winner of an arbitrary finite poset game is PSPACE-complete. To this end, we give an explicit reduction from Node Kayles, a PSPACE-complete game in which players vie to chose an independent set in a graph

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.Comment: To appear in the proceedings of WORDS 201

Fast Algorithm for Partial Covers in Words

A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$. In this article we introduce a new notion of $\alpha$-partial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least $\alpha$ positions in $w$. We develop a data structure of $O(n)$ size (where $n=|w|$) that can be constructed in $O(n\log n)$ time which we apply to compute all shortest $\alpha$-partial covers for a given $\alpha$. We also employ it for an $O(n\log n)$-time algorithm computing a shortest $\alpha$-partial cover for each $\alpha=1,2,\ldots,n$

A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

An improved map of conserved regulatory sites for Saccharomyces cerevisiae

BACKGROUND: The regulatory map of a genome consists of the binding sites for proteins that determine the transcription of nearby genes. An initial regulatory map for S. cerevisiae was recently published using six motif discovery programs to analyze genome-wide chromatin immunoprecipitation data for 203 transcription factors. The programs were used to identify sequence motifs that were likely to correspond to the DNA-binding specificity of the immunoprecipitated proteins. We report improved versions of two conservation-based motif discovery algorithms, PhyloCon and Converge. Using these programs, we create a refined regulatory map for S. cerevisiae by reanalyzing the same chromatin immunoprecipitation data. RESULTS: Applying the same conservative criteria that were applied in the original study, we find that PhyloCon and Converge each separately discover more known specificities than the combination of all six programs in the previous study. Combining the results of PhyloCon and Converge, we discover significant sequence motifs for 36 transcription factors that were previously missed. The new set of motifs identifies 636 more regulatory interactions than the previous one. The new network contains 28% more regulatory interactions among transcription factors, evidence of greater cross-talk between regulators. CONCLUSION: Combining two complementary computational strategies for conservation-based motif discovery improves the ability to identify the specificity of transcriptional regulators from genome-wide chromatin immunoprecipitation data. The increased sensitivity of these methods significantly expands the map of yeast regulatory sites without the need to alter any of the thresholds for statistical significance. The new map of regulatory sites reveals a more elaborate and complex view of the yeast genetic regulatory network than was observed previously

A Hadron Blind Detector for the PHENIX Experiment

A novel Hadron Blind Detector (HBD) has been developed for an upgrade of the PHENIX experiment at RHIC. The HBD will allow a precise measurement of electron-positron pairs from the decay of the light vector mesons and the low-mass pair continuum in heavy-ion collisions. The detector consists of a 50 cm long radiator filled with pure CF4 and directly coupled in a windowless configuration to a triple Gas Electron Multiplier (GEM) detector with a CsI photocathode evaporated on the top face of the first GEM foil.Comment: 4 pages, 3 figures, Quark Matter 2005 conference proceeding

Construction and Expected Performance of the Hadron Blind Detector for the PHENIX Experiment at RHIC

A new Hadron Blind Detector (HBD) for electron identification in high density hadron environment has been installed in the PHENIX detector at RHIC in the fall of 2006. The HBD will identify low momentum electron-positron pairs to reduce the combinatorial background in the $e^{+}e^{-}$ mass spectrum, mainly in the low-mass region below 1 GeV/c$^{2}$. The HBD is a windowless proximity-focusing Cherenkov detector with a radiator length of 50 cm, a CsI photocathode and three layers of Gas Electron Multipliers (GEM). The HBD uses pure CF$_{4}$ as a radiator and a detector gas. Construction details and the expected performance of the detector are described.Comment: QM2006 proceedings, 4 pages 3 figure