Actin assembly ruptures the nuclear envelope by prying the lamina away from nuclear pores and nuclear membranes in starfish oocytes.

The nucleus of oocytes (germinal vesicle) is unusually large and its nuclear envelope (NE) is densely packed with nuclear pore complexes (NPCs) stockpiled for embryonic development. We showed that breakdown of this specialized NE is mediated by an Arp2/3-nucleated F-actin 'shell' in starfish oocytes, in contrast to microtubule-driven tearing in mammalian fibroblasts. Here, we address the mechanism of F-actin-driven NE rupture by correlated live-cell, super-resolution and electron microscopy. We show that actin is nucleated within the lamina sprouting filopodia-like spikes towards the nuclear membranes. These F-actin spikes protrude pore-free nuclear membranes, whereas the adjoining membrane stretches accumulate NPCs associated with the still-intact lamina. Packed NPCs sort into a distinct membrane network, while breaks appear in ER-like, pore-free regions. Thereby, we reveal a new function for actin-mediated membrane shaping in nuclear rupture that is likely to have implications in other contexts such as nuclear rupture observed in cancer cells

Interval structure of the Pieri formula for Grothendieck polynomials

We give a combinatorial interpretation of a Pieri formula for double Grothendieck polynomials in terms of an interval of the Bruhat order. Another description had been given by Lenart and Postnikov in terms of chain enumerations. We use Lascoux's interpretation of a product of Grothendieck polynomials as a product of two kinds of generators of the 0-Hecke algebra, or sorting operators. In this way we obtain a direct proof of the result of Lenart and Postnikov and then prove that the set of permutations occuring in the result is actually an interval of the Bruhat order.Comment: 27 page

Crystal energy functions via the charge in types A and C

The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this paper we prove that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler and can be more efficiently computed than the recursive definition of energy in terms of the combinatorial R-matrix.Comment: 25 pages; 1 figur

Closure relations during the plateau emission of Swift GRBs and the fundamental plane

The Neil Gehrels Swift observatory observe Gamma-Ray bursts (GRBs) plateaus in X-rays. We test the reliability of the closure relations through the fireball model when dealing with the GRB plateau emission. We analyze 455 X-ray lightcurves (LCs) collected by \emph{Swift} from 2005 (January) until 2019 (August) for which the redshift is both known and unknown using the phenomenological Willingale 2007 model. Using these fits, we analyze the emission mechanisms and astrophysical environments of these GRBs through the closure relations within the time interval of the plateau emission. Finally, we test the 3D fundamental plane relation (Dainotti relation) which connects the prompt peak luminosity, the time at the end of the plateau (rest-frame), and the luminosity at that time, on the GRBs with redshift, concerning groups determined by the closure relations. This allows us to check if the intrinsic scatter \sigma_{int} of any of these groups is reduced compared to previous literature. The most fulfilled environments for the electron spectral distribution, p>2, are Wind Slow Cooling (SC) and ISM Slow Cooling for cases in which the parameter q, which indicates the flatness of the plateau emission and accounts for the energy injection, is =0 and =0.5, respectively, both in the cases with known and unknown redshifts. We also find that for the sGRBs All ISM Environments with $q=0$ have the smallest \sigma_{int}=0.04 \pm 0.15 in terms of the fundamental plane relation holding a probability of occurring by chance of p=0.005. We have shown that the majority of GRBs presenting the plateau emission fulfil the closure relations, including the energy injection, with a particular preference for the Wind SC environment. The subsample of GRBs that fulfil given relations can be used as possible standard candles and can suggest a way to reduce the intrinsic scatter of these studied relationships.Comment: 44 pages, 23 figures; Accepted to the PASJ to be published soo

Current and future role of instrumentation and monitoring in the performance of transport infrastructure slopes

Instrumentation is often used to monitor the performance of engineered infrastructure slopes. This paper looks at the current role of instrumentation and monitoring, including the reasons for monitoring infrastructure slopes, the instrumentation typically installed and parameters measured. The paper then investigates recent developments in technology and considers how these may change the way that monitoring is used in the future, and tries to summarize the barriers and challenges to greater use of instrumentation in slope engineering. The challenges relate to economics of instrumentation within a wider risk management system, a better understanding of the way in which slopes perform and/or lose performance, and the complexities of managing and making decisions from greater quantities of data

Zero-one Schubert polynomials

We prove that if σ∈Sm is a pattern of w∈Sn, then we can express the Schubert polynomial w as a monomial times σ (in reindexed variables) plus a polynomial with nonnegative coefficients. This implies that the set of permutations whose Schubert polynomials have all their coefficients equal to either 0 or 1 is closed under pattern containment. Using Magyar's orthodontia, we characterize this class by a list of twelve avoided patterns. We also give other equivalent conditions on w being zero-one. In this case, the Schubert polynomial w is equal to the integer point transform of a generalized permutahedron

Asymmetric function theory

The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.Comment: 36 pages, 8 figures, 1 table. Written for the proceedings of the Schubert calculus conference in Guangzhou, Nov. 201