An iterative algorithm for parametrization of shortest length shift registers over finite rings

The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers S_1,...,S_N, thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with S_1, and constructs at each step a particular type of minimal Gr\"obner basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte

The Mechanism of Release of P-TEFb and HEXIM1 from the 7SK snRNP by Viral and Cellular Activators Includes a Conformational Change in 7SK

The positive transcription elongation factor, P-TEFb, is required for the production of mRNAs, however the majority of the factor is present in the 7SK snRNP where it is inactivated by HEXIM1. Expression of HIV-1 Tat leads to release of P-TEFb and HEXIM1 from the 7SK snRNP in vivo, but the release mechanisms are unclear.We developed an in vitro P-TEFb release assay in which the 7SK snRNP immunoprecipitated from HeLa cell lysates using antibodies to LARP7 was incubated with potential release factors. We found that P-TEFb was directly released from the 7SK snRNP by HIV-1 Tat or the P-TEFb binding region of the cellular activator Brd4. Glycerol gradient sedimentation analysis was used to demonstrate that the same Brd4 protein transfected into HeLa cells caused the release of P-TEFb and HEXIM1 from the 7SK snRNP in vivo. Although HEXIM1 binds tightly to 7SK RNA in vitro, release of P-TEFb from the 7SK snRNP is accompanied by the loss of HEXIM1. Using a chemical modification method, we determined that concomitant with the release of HEXIM1, 7SK underwent a major conformational change that blocks re-association of HEXIM1.Given that promoter proximally paused polymerases are present on most human genes, understanding how activators recruit P-TEFb to those genes is critical. Our findings reveal that the two tested activators can extract P-TEFb from the 7SK snRNP. Importantly, we found that after P-TEFb is extracted a dramatic conformational change occurred in 7SK concomitant with the ejection of HEXIM1. Based on our findings, we hypothesize that reincorporation of HEXIM1 into the 7SK snRNP is likely the regulated step of reassembly of the 7SK snRNP containing P-TEFb

The Parker problem:existence of smooth force-free fields and coronal heating

Parker (Astrophys J 174:499, 1972) put forward a hypothesis regarding the fundamental nature of equilibrium magnetic fields in astrophysical plasmas. He proposed that if an equilibrium magnetic field is subjected to an arbitrary, small perturbation, then—under ideal plasma dynamics—the resulting magnetic field will in general not relax towards a smooth equilibrium, but rather, towards a state containing tangential magnetic field discontinuities. Even at astrophysical plasma parameters, as the singular state is approached dissipation must eventually become important, leading to the onset of rapid magnetic reconnection and energy dissipation. This topological dissipation mechanism remains a matter of debate, and is a key ingredient in the nanoflare model for coronal heating. We review the various theoretical and computational approaches that have sought to prove or disprove Parker’s hypothesis. We describe the hypothesis in the context of coronal heating, and discuss different approaches that have been taken to investigating whether braiding of magnetic field lines is responsible for maintaining the observed coronal temperatures. We discuss the many advances that have been made, and highlight outstanding open questions.</p

Synthesis of Thiazolidine-2-thiones via One-Pot A3-coupling / Carbon Disulfide Incorporation Process

© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim A copper-catalyzed two-step one-pot procedure for the synthesis of thiazolidine-2-thiones has been developed. The process involves a three-component coupling of an alkyne, an aldehyde, and an amine (A3-coupling) followed by trapping the resulting propargylamine with carbon disulfide and subsequent cyclization.status: publishe