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Generalizing the continuous rank function of Barja-Pardini-Stoppino, in this paper we consider cohomological rank functions of Q-twisted (complexes of) coherent sheaves on abelian varieties. They satisfy a natural transformation formula with respect to the Fourier-Mukai-Poincaré transform, which has several consequences. In many concrete geometric contexts these functions provide useful invariants. We illustrate this with two different applications, the first one to GVsubschemes and the second one to multiplication maps of global sections of ample line bundles on abelian varieties.

Chiral magnets endowed with topological spin textures are expected to have promising applications in next‐generation magnetic memories. In contrast to the well‐studied 2D or 3D magnetic skyrmions, the authors report the discovery of 1D nontrivial magnetic solitons in a transition metal dichalcogenide 2H‐TaS2 via precise intercalation of Cr elements. In the synthetic Cr1/3TaS2 (CTS) single crystal, the coupling of the strong spin–orbit interaction from TaS2 and the chiral arrangement of the magnetic Cr ions evoke a robust Dzyaloshinskii–Moriya interaction. A magnetic helix having a short spatial period of ≈25 nm is observed in CTS via Lorentz transmission electron microscopy. In a magnetic field perpendicular to the helical axis, the helical spin structure transforms into a chiral soliton lattice (CSL) with the spin structure evolution being consistent with the chiral sine‐Gordon theory, which opens promising perspectives for the application of CSL to fast‐speed nonvolatile magnetic memories. This work introduces a new paradigm to soliton physics and provides an effective strategy for seeking novel 2D magnets.

Salinity is among the environmental factors that affect plant growth and development and constrain agricultural productivity. Salinity stress triggers increases in cytosolic free Ca2+ concentration ([Ca2+]i) via Ca2+ influx across the plasma membrane. Salinity stress, as well as other stresses, induces the production of reactive oxygen species (ROS). It is well established that ROS also triggers increases in [Ca2+]i. However, the relationship and interaction between salinity stress-induced [Ca2+]i increases and ROS-induced [Ca2+]i increases remain poorly understood. Using an aequorin-based Ca2+ imaging assay we have analyzed [Ca2+]i changes in response to NaCl and H2O2 treatments in Arabidopsis thaliana. We found that NaCl and H2O2 together induced larger increases in [Ca2+]i in Arabidopsis seedlings than either NaCl or H2O2 alone, suggesting an additive effect on [Ca2+]i increases. Following a pre-treatment with either NaCl or H2O2, the subsequent elevation of [Ca2+]i in response to a second treatment with either NaCl or H2O2 was significantly reduced. Furthermore, the NaCl pre-treatment suppressed the elevation of [Ca2+]i seen with a second NaCl treatment more than that seen with a second treatment of H2O2. A similar response was seen when the initial treatment was with H2O2; subsequent addition of H2O2 led to less of an increase in [Ca2+]i than did addition of NaCl. These results imply that NaCl-gated Ca2+ channels and H2O2-gated Ca2+ channels may differ, and also suggest that NaCl- and H2O2-evoked [Ca2+]i may reduce the potency of both NaCl and H2O2 in triggering [Ca2+]i increases, highlighting a feedback mechanism. Alternatively, NaCl and H2O2 may activate the same Ca2+ permeable channel, which is expressed in different types of cells and/or activated via different signaling pathways.

To survive, plants must respond rapidly and effectively to various stress factors, including biotic and abiotic stresses. Salinity stress triggers the increase of cytosolic free Ca2+ concentration ([Ca2+]i) via Ca2+ influx across the plasma membrane, as well as bacterial flg22 and plant endogenous peptide Pep1. However, the interaction between abiotic stress-induced [Ca2+]i increases and biotic stress-induced [Ca2+]i increases is still not clear. Employing an aequorin-based Ca2+ imaging assay, in this work, we investigated the [Ca2+]i changes in response to flg22, Pep1, and NaCl treatments in Arabidopsis thaliana. We observed an additive effect on the [Ca2+]i increase which induced by flg22, Pep1, and NaCl. Our results indicate that biotic and abiotic stresses may activate different Ca2+ permeable channels. Further, calcium signal induced by biotic and abiotic stresses was independent in terms of spatial and temporal patterning.

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HighlightBased on the aequorin system, we describe the establishment of a calcium reporter line in rice and test the responses of the reporter towards salt and oxidative stress.