1,258 research outputs found

    Families of finite coverings of the Riemann sphere

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    Synergistic role of fission yeast Alp16GCP6 and Mzt1MOZART1 in γ-tubulin complex recruitment to mitotic spindle pole bodies and spindle assembly

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    In fission yeast, γ-tubulin ring complex (γTuRC)–specific components Gfh1GCP4, Mod21GCP5, and Alp16GCP6 are nonessential for cell growth. Of these deletion mutants, only alp16Δ shows synthetic lethality with temperature-sensitive mutants of Mzt1MOZART1, a component of the γTuRC required for recruitment of the complex to microtubule-organizing centers. γ-Tubulin small complex levels at mitotic spindle pole bodies (SPBs, the centrosome equivalent in fungi) and microtubule levels for preanaphase spindles are significantly reduced in alp16Δ cells but not in gfh1Δ or mod21Δ cells. Furthermore, alp16Δ cells often form monopolar spindles and frequently lose a minichromosome when the spindle assembly checkpoint is inactivated. Alp16GCP6 promotes Mzt1-dependent γTuRC recruitment to mitotic SPBs and enhances spindle microtubule assembly in a manner dependent on its expression levels. Gfh1GCP4 and Mod21GCP5 are not required for Alp16GCP6-dependent γTuRC recruitment. Mzt1 has an additional role in the activation of the γTuRC for spindle microtubule assembly. The ratio of Mzt1 to γTuRC levels for preanaphase spindles is higher than at other stages of the cell cycle. Mzt1 overproduction enhances spindle microtubule assembly without affecting γTuRC levels at mitotic SPBs. We propose that Alp16GCP6 and Mzt1 act synergistically for efficient bipolar spindle assembly to ensure faithful chromosome segregation.This work was supported by Cancer Research UK, the Francis Crick Institute, Hiroshima University, and the Japan Society for the Promotion of Science KAKENHI Scientific Research (A) (16H02503) and Challenging Exploratory Research (16K14672) (T.T.)

    Regular semisimple Hessenberg varieties with cohomology rings generated in degree two

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    A regular semisimple Hessenberg variety Hess(S,h)\mathrm{Hess}(S,h) is a smooth subvariety of the flag variety determined by a square matrix SS with distinct eigenvalues and a Hessenberg function hh. The cohomology ring H(Hess(S,h))H^*(\mathrm{Hess}(S,h)) is independent of the choice of SS and is not explicitly described except for a few cases. In this paper, we characterize the Hessenberg function hh such that H(Hess(S,h))H^*(\mathrm{Hess}(S,h)) is generated in degree two as a ring. It turns out that such hh is what is called a (double) lollipop.Comment: 16 pages, 3 figure

    Modular law through GKM theory

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    The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled us to prove these results by showing the modular law for the geometrical objects, and this is indeed done by Precup-Sommers and Kiem-Lee. In this paper, we give elementary and simpler proofs to the modular law through GKM theory.Comment: 17 page, 5 figure

    Coronal Electron Distribution in Solar Flares: Drift-Kinetic Model

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    Using a model of particle acceleration and transport in solar flares, we investigate the height distribution of coronal electrons by focusing on the energy-dependent pitch-angle scattering. When pitch-angle scattering is not included, the peak heights of loop-top electrons are constant, regardless of their energy, owing to the continuous acceleration and compression of the electrons via shrinkage of magnetic loops. On the other hand, under pitch-angle scattering, the electron heights are energy dependent; intermediate energy electrons are at a higher altitude, whereas lower and higher energy electrons are at lower altitudes. This implies that the intermediate energy electrons are inhibited to follow the shrinking field lines to lower altitudes because pitch-angle scattering causes efficient precipitation of these electrons into the footpoint and their subsequent loss from the loop. This result is qualitatively consistent with the position of the above-the-loop-top hard X-ray (HXR) source that is located above coronal HXR loops emitted by lower energy electrons and microwaves emitted by higher energy electrons. Quantitative agreement with observations might be achieved by considering primary acceleration before the onset of loop shrinkage and additional pitch-angle scattering via wave-particle interactions.Comment: 18 pages, 6 figures, accepted by Ap
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