Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

The 35S U5 snRNP is generated from the activated spliceosome during In vitro splicing

Primary gene transcripts of eukaryotes contain introns, which are removed during processing by splicing machinery. Biochemical studies In vitro have identified a specific pathway in which introns are recognised and spliced out. This occurs by progressive formation of spliceosomal complexes designated as E, A, B, and C. The composition and structure of these spliceosomal conformations have been characterised in many detail. In contrast, transitions between the complexes and the intermediates of these reactions are currently less clear. We have previously isolated a novel 35S U5 snRNP from HeLa nuclear extracts. The protein composition of this particle differed from the canonical 20S U5 snRNPs but was remarkably similar to the activated B* spliceosomes. Based on this observation we have proposed a hypothesis that 35S U5 snRNPs represent a dissociation product of the spliceosome after both transesterification reactions are completed. Here we provide experimental evidence that 35S U5 snRNPs are generated from the activated B* spliceosomes during In vitro splicing

Revealing Network Connectivity From Dynamics

We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring the phase differences and the collective frequency reveals information about how the oscillators are interconnected. Sufficiently many repetitions for different driving conditions yield the entire network connectivity from measuring the dynamics only. For sparsely connected networks we obtain good predictions of the actual connectivity even for formally under-determined problems.Comment: 10 pages, 4 figure

Muons with E_th >= 1 Gev and Mass Composition in the Energy Range 10^{18}-10^{20} ev Observed by Yakutsk Eas Array

The ratio of the muon flux density to charged particle flux density at distances of 300 and 600 m from the shower axis (\rhom(300)/\rhos(300) and \rhom(600)/\rhos(600)) is measured. In addition, the energy dependence of \rhom(1000) is analysed for showers with energies above $10^{18}$ eV. A comparison between the experimental data and calculations performed with the QGSJET model is given for the cases of primary proton, iron nucleus and gamma- ray. We conclude that the showers with \E\ge3\times10^{18} eV can be formed by light nuclei with a pronounced fraction of protons and helium nuclei. It is not excluded however that a small part of showers with energies above $10^{19}$ eV could be initiated by primary gamma-rays.Comment: 19th European Cosmic Ray Symposium, Aug 30 - Sep 3 2004, Florence, Italy. 3 pages, 1 figure. Submitted for publication in International Journal of Modern Physics