Enumerating Abelian Returns to Prefixes of Sturmian Words

We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian returns in Sturmian words. We determine the cardinality of the set $\mathcal{APR}_u$ of abelian returns of all prefixes of a Sturmian word $u$ in terms of the coefficients of the continued fraction of the slope, dependingly on the intercept. We provide a simple algorithm for finding the set $\mathcal{APR}_u$ and we determine it for the characteristic Sturmian words.Comment: 19page

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Cyclotomic valuation of qq-Pochhammer symbols and qq-integrality of basic hypergeometric series

We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol step functions. This provides suitable $q$-analogs of two results proved by Christol: a formula for the $p$-adic valuation of Pochhammer symbols and a criterion for the $N$-integrality of hypergeometric series

The Λp\bf{\Lambda p} interaction studied via femtoscopy in p + Nb reactions at sNN=3.18 GeV\mathbf{\sqrt{s_{NN}}=3.18} ~\mathrm{\bf{GeV}}

We report on the first measurement of $p\Lambda$ and $pp$ correlations via the femtoscopy method in p+Nb reactions at $\mathrm{\sqrt{s_{NN}}=3.18} ~\mathrm{GeV}$, studied with the High Acceptance Di-Electron Spectrometer (HADES). By comparing the experimental correlation function to model calculations, a source size for $pp$ pairs of $r_{0,pp}=2.02 \pm 0.01(\mathrm{stat})^{+0.11}_{-0.12} (\mathrm{sys}) ~\mathrm{fm}$ and a slightly smaller value for $p\Lambda$ of $r_{0,\Lambda p}=1.62 \pm 0.02(\mathrm{stat})^{+0.19}_{-0.08}(\mathrm{sys}) ~\mathrm{fm}$ is extracted. Using the geometrical extent of the particle emitting region, determined experimentally with $pp$ correlations as reference together with a source function from a transport model, it is possible to study different sets of scattering parameters. The $p\Lambda$ correlation is proven sensitive to predicted scattering length values from chiral effective field theory. We demonstrate that the femtoscopy technique can be used as valid alternative to the analysis of scattering data to study the hyperon-nucleon interaction.Comment: 12 pages, 11 figure

Pfmrk, a MO15-related protein kinase from Plasmodium falciparum. Gene cloning, sequence, stage-specific expression and chromosome localization.

Cyclin-dependent kinases (Cdks) play a central role in the regulation of the eukaryotic cell cycle. A novel gene encoding a Cdk-like protein, Pfmrk, has been isolated from the human malaria parasite Plasmodium falciparum. The gene has no introns and comprises an open reading frame encoding a protein of 324 amino acids with a predicted molecular mass of 38 kDa. Database searches revealed a striking similarity to the Cdk subfamily with the highest similarity to human MO15 (Cdk7). The overall sequence of Pfmrk shares 62% similarity and 46% identity with human MO15, in comparison to the 49-58% similarity and 34-43% identity with other human Cdks. Pfmrk contains two unique inserts: one consisting of 5 amino acids just before the cyclin-binding motif and the other composed of 13 amino acids within the T-loop equivalent region. Southern blots of genomic DNA digests and chromosomal separations showed that Pfmrk is a single-copy gene conserved between several parasite strains and is located on chromosome 10. A 2500-nucleotide transcript of this gene is expressed predominantly in the sexual blood stages (gametocytes), suggesting that Pfmrk may be involved in sexual stage development

Limit theorems for self-similar tilings

We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.Comment: 36 pages; some corrections and improved exposition, especially in Section 4; references adde