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We present family of automatic sequences that define algebraic continued fractions in characteristic 2. This family is constructed from ultimately period words and contains the period-doubling sequence.

For the field of formal Laurent series over a finite field, Carlitz defined Π, an analogue of the real number π, and Goss defined analogues of Dirichlet L functions. Damamme proved the transcendence of L ( 1 , χ s ) / Π using the criteria of de Mathan. In this article we give a proof of the transcendence of L ( 1 , χ s ) / Π based on the Theorem of Christol and another property of k-automatic sequences.

Summary: Various bioinformatics protocols have been developed for trimming the number of operational taxonomic units (OTUs) in phylogenetic datasets, but they typically require significant manual intervention. Here we present TreeTuner, a semiautomated pipeline that allows both coarse and fine-scale tuning of large protein sequence phylogenetic datasets via the minimization of OTU redundancy. TreeTuner facilitates preliminary investigation of such datasets as well as more rigorous downstream analysis of specific subsets of OTUs.For complete details on the use and execution of this protocol, please refer to Maruyama et al. (2013) and Sibbald et al. (2019).

International audience; By providing fast scanning with low radiation doses, sparse-view (or sparse-projection) reconstruction has attracted much research attention in X-ray computerized tomography (CT) imaging. Recent contributions have demonstrated that the total variation (TV) constraint can lead to improved solution by regularizing the underdetermined ill-posed problem of sparse-view reconstruction. However, when the projection views are reduced below certain numbers, the performance of TV regularization tends to deteriorate with severe artifacts. In this paper, we explore the applicability of Gamma regularization for the sparse-view CT reconstruction. Experiments on simulated data and clinical data demonstrate that the Gamma regularization can lead to good performance in sparse-view reconstruction.

Text Let a w , B ( n ) denote the number of occurrences of the word w in the base B expansion of the non-negative integer n. In this article we generalize the results of Allouche and Shallit [2] by proving the existence of a finite set L w , B of pairs ( l , c l ) where l is a polynomial with integer coefficients of degree 1 and c l an integer such that: ∑ n ≥ 0 ( − 1 ) a w , B ( n ) ∑ ( l , c l ) ∈ L w , B c l f ( l ( n ) ) = { 0 if w ≠ 0 j , − 2 ⋅ ( − 1 ) a w , B ( 0 ) f ( 0 ) if w = 0 j where f is any function that verifies certain convergence conditions. After exponentiating, we recover previous results and obtain new ones such as ∏ n ≥ 1 ( 3 n + 1 3 n + 2 ) ( − 1 ) n = 2 3 , and ∏ n ≥ 1 ( 9 n + 7 9 n + 8 ) ( − 1 ) a 21 , 3 ( n ) = 8 7 3 . Video For a video summary of this paper, please visit https://youtu.be/0wXL7xPkooc .

A rotating ring-disk electrode (RRDE) method is herein described for studies of O 2 evolution on nickel hydrous oxide films, NiO x (hydr.), electrodeposited on the gold disk of a Au–Au RRDE in aqueous 1.0 M KOH. This technique relies on the quantitative detection of O 2 generated at the NiO x (hydr.) ∣ Au disk electrode during a linear potential scan, by the concentric, bare Au-ring electrode, which can then be used to determine contributions to the disk current ( I disk ) derived solely from O 2 evolution. Subtraction of such contributions from I disk in the potential range positive to the trailing edge of the peak ascribed to the oxidation of the NiO x (hydr.) film revealed a constant, positive current when the voltage was scanned in the positive direction, and a constant, negative current, albeit of smaller magnitude, in the subsequent scan in the negative direction. This observation suggests that once account is made for O 2 evolution, the NiO x (hydr.) ∣ Au-electrolyte interface in that potential range (0.5–0.65 V vs. Hg ∣ HgO,OH − ), behaves as a (pseudo) capacitor, a model that was further confirmed by monitoring the current as a function of the scan rate. The actual values of this pseudocapacitance were found to be on the order of ca. 80 kF mol −1 Ni sites in the film (or equivalently, ca. 0.1 e − per Ni site within the potential range specified above) and, thus, very similar to those reported earlier based on current interruption-potential decay and impedance measurements for O 2 evolution on NiO x (hydr.) grown on Ni electrodes. Implications of these results to the mechanism of self-discharge of NiO x (hydr.) electrodes for alkaline secondary batteries are discussed.