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

Game saturation of intersecting families

We consider the following combinatorial game: two players, Fast and Slow, claim $k$-element subsets of $[n]=\{1,2,...,n\}$ alternately, one at each turn, such that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed $k$-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone the game's end as long as possible. The game saturation number is the score of the game when both players play according to an optimal strategy. To be precise we have to distinguish two cases depending on which player takes the first move. Let $gsat_F(\mathbb{I}_{n,k})$ and $gsat_S(\mathbb{I}_{n,k})$ denote the score of the saturation game when both players play according to an optimal strategy and the game starts with Fast's or Slow's move, respectively. We prove that $\Omega_k(n^{k/3-5}) \le gsat_F(\mathbb{I}_{n,k}),gsat_S(\mathbb{I}_{n,k}) \le O_k(n^{k-\sqrt{k}/2})$ holds

Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

A pedagogical example: a family of stochastic cellular automata that plays Alesia

International audienceAlesia is a two-player zero-sum game which is quite similar to the rock-paper-scissors game: the two players simultaneously move and do not know what the opponent plays at given round. The simultaneity of the moves implies that there is no deterministic good strategy in this game, otherwise one would anticipate the moves of the opponent and easily win the game. We explore how to build a family of one-dimensional stochastic cellular automata to play this game. The rules are built in an iterative way by progressively increasing the complexity of the transitions. We show the possibility to construct a family of rules with interesting results, including a good performance when confronted to the Nash-equilibrium strategy

Efficient Enumeration of Non-Equivalent Squares in Partial Words with Few Holes

International audienceA partial word is a word with holes (also called don't cares: special symbols which match any symbol). A p-square is a partial word matching at least one standard square without holes (called a full square). Two p-squares are called equivalent if they match the same sets of full squares. Denote by psquares(T) the number of non-equivalent p-squares which are subwords of a partial word T. Let PSQUARES k (n) be the maximum value of psquares(T) over all partial words of length n with k holes. We show asympthotically tight bounds: c1 · min(nk 2 , n 2) ≤ PSQUARES k (n) ≤ c2 · min(nk 2 , n 2) for some constants c1, c2 > 0. We also present an algorithm that computes psquares(T) in O(nk 3) time for a partial word T of length n with k holes. In particular, our algorithm runs in linear time for k = O(1) and its time complexity near-matches the maximum number of non-equivalent p-squares

Current tidal power technologies and their suitability for applications in coastal and marine areas

A considerable body of research is currently being performed to quantify available tidal energy resources and to develop efficient devices with which to harness them. This work is naturally focussed on maximising power generation from the most promising sites, and a review of the literature suggests that the potential for smaller scale, local tidal power generation from shallow near-shore sites has not yet been investigated. If such generation is feasible, it could have the potential to provide sustainable electricity for nearby coastal homes and communities as part of a distributed generation strategy, and would benefit from easier installation and maintenance, lower cabling and infrastructure requirements and reduced capital costs when compared with larger scale projects. This article reviews tidal barrages and lagoons, tidal turbines, oscillating hydrofoils and tidal kites to assess their suitability for small-scale electricity generation in shallow waters. This is achieved by discussing the power density, scalability, durability, maintainability, economic potential and environmental impacts of each concept. The performance of each technology in each criterion is scored against axial-flow turbines, allowing for them to be ranked according to their overall suitability. The review suggests that tidal kites and range devices are not suitable for small-scale shallow water applications due to depth and size requirements respectively. Cross-flow turbines appear to be the most suitable technology, as they have high power densities and a maximum size that is not constrained by water depth

BMP Signaling Modulates Hepcidin Expression in Zebrafish Embryos Independent of Hemojuvelin

Hemojuvelin (Hjv), a member of the repulsive-guidance molecule (RGM) family, upregulates transcription of the iron regulatory hormone hepcidin by activating the bone morphogenetic protein (BMP) signaling pathway in mammalian cells. Mammalian models have identified furin, neogenin, and matriptase-2 as modifiers of Hjv's function. Using the zebrafish model, we evaluated the effects of hjv and its interacting proteins on hepcidin expression during embryonic development. We found that hjv is strongly expressed in the notochord and somites of the zebrafish embryo and that morpholino knockdown of hjv impaired the development of these structures. Knockdown of hjv or other hjv-related genes, including zebrafish orthologs of furin or neogenin, however, failed to decrease hepcidin expression relative to liver size. In contrast, overexpression of bmp2b or knockdown of matriptase-2 enhanced the intensity and extent of hepcidin expression in zebrafish embryos, but this occurred in an hjv-independent manner. Furthermore, we demonstrated that zebrafish hjv can activate the human hepcidin promoter and enhance BMP responsive gene expression in vitro, but is expressed at low levels in the zebrafish embryonic liver. Taken together, these data support an alternative mechanism for hepcidin regulation during zebrafish embryonic development, which is independent of hjv

Production of phi mesons at mid-rapidity in sqrt(s_NN) = 200 GeV Au+Au collisions at RHIC

We present the first results of meson production in the K^+K^- decay channel from Au+Au collisions at sqrt(s_NN) = 200 GeV as measured at mid-rapidity by the PHENIX detector at RHIC. Precision resonance centroid and width values are extracted as a function of collision centrality. No significant variation from the PDG accepted values is observed. The transverse mass spectra are fitted with a linear exponential function for which the derived inverse slope parameter is seen to be constant as a function of centrality. These data are also fitted by a hydrodynamic model with the result that the freeze-out temperature and the expansion velocity values are consistent with the values previously derived from fitting single hadron inclusive data. As a function of transverse momentum the collisions scaled peripheral.to.central yield ratio RCP for the is comparable to that of pions rather than that of protons. This result lends support to theoretical models which distinguish between baryons and mesons instead of particle mass for explaining the anomalous proton yield.Comment: 326 authors, 24 pages text, 23 figures, 6 tables, RevTeX 4. To be submitted to Physical Review C as a regular article. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm