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Abstract Full-disk measurements of the solar magnetic field by the Helioseismic and Magnetic Imager (HMI) are often used for magnetic field extrapolations, but its limited spatial and spectral resolution can lead to significant errors. We compare HMI data with observations of NOAA 12104 by the Hinode Spectropolarimeter (SP) to derive a scaling curve for the magnetic field strength,B. The SP data in the Feilines at 630 nm were inverted with the SIR code. We find that the Milne–Eddington inversion of HMI underestimatesBand the line-of-sight flux, Φ, in all granulation surroundings by an average factor of 4.5 in plage and 9.2 in the quiet Sun in comparison to the SP. The deviation is inversely proportional to the magnetic fill factor,f, in the SP results. We derived a correction curve to match the HMIBwith the effective fluxBfin the SP data that scaled HMIBup by 1.3 on average. A comparison of non-force-free field extrapolations over a larger field of view without and with the correction revealed minor changes in connectivity and a proportional scaling of electric currents and Lorentz force (∝B∼ 1.3) and free energy (∝B² ∼ 2). Magnetic field extrapolations of HMI vector data with large areas of plage and quiet Sun will underestimate the photospheric magnetic field strength by a factor of 5–10 and the coronal magnetic flux by at least a factor of 2. An HMI inversion including a fill factor would mitigate the problem. 

Synopsis Evolutionary increases in genome size, cell volume, and nuclear volume have been observed across the tree of life, with positive correlations documented between all three traits. Developmental tempo slows as genomes, nuclei, and cells increase in size, yet the driving mechanisms are poorly understood. To bridge this gap, we use a mathematical model of the somitogenesis clock to link slowed developmental tempo with changes in intra-cellular gene expression kinetics induced by increasing genome size and nuclear volume. We adapt a well-known somitogenesis clock model to two model amphibian species that vary 10-fold in genome size: Xenopus laevis (3.1 Gb) and Ambystoma mexicanum (32 Gb). Based on simulations and backed by analytical derivations, we identify parameter changes originating from increased genome and nuclear size that slow gene expression kinetics. We simulate biological scenarios for which these parameter changes mathematically recapitulate slowed gene expression in A. mexicanum relative to X. laevis, and we consider scenarios for which additional alterations in gene product stability and chromatin packing are necessary. Results suggest that slowed degradation rates as well as changes induced by increasing nuclear volume and intron length, which remain relatively unexplored, are significant drivers of slowed developmental tempo. 

Abstract Understanding the mechanisms underlying the heating of the solar atmosphere is a fundamental problem in solar physics. The lower atmosphere of the Sun (i.e., photosphere and chromosphere) is composed of weakly ionized plasma. This results in anisotropic dissipation of electric currents by Coulomb and Cowling resistivities. Joule heating due to dissipation of currents perpendicular to the magnetic field by Cowling resistivity has been demonstrated to be the main mechanism for the heating of a sunspot umbral light bridge located in NOAA AR 12002 on 2014 March 13. Here, we focus on the same target region and demonstrate the importance of further constraining our Joule heating model using observational data in addition to magnetic field, namely plasma temperature calculated from the inversion of spectroscopic data obtained from the Interferometric BI-dimensional Spectrometer instrument of the ground-based Dunn Solar Telescope. As a parameter in our analysis, temperature is demonstrated to have the highest sensitivity after magnetic field. We show that the heating of the light bridge is a highly dynamic event that necessitates utilization of 3D spatially resolved observational data for temperature rather than a 1D temperature stratification based on theoretical/semiempirical solar atmosphere models. Our improved data-constrained analysis using spatially resolved temperatures shows that the entire light bridge is heated by the proposed mechanism, and yields heating rate values that are consistent with our previous study. 

Context.Erupting magnetic flux ropes (MFRs) are believed to play a crucial role in producing solar flares. However, the formation of erupting MFRs in complex coronal magnetic configurations and the role of their subsequent evolution in the flaring events are not fully understood. Aims.We perform a magnetohydrodynamic (MHD) simulation of active region NOAA 12241 to understand the formation of a rising magnetic flux rope during the onset of an M6.9 flare on 2014 December 18 around 21:41 UT (SOL2014-12- 18T21:41M6.9), which was followed by the appearance of parallel flare ribbons. Methods.The MHD simulation was initialised with an extrapolated non-force-free magnetic field generated from the photospheric vector magnetogram of the active region taken a few minutes before the flare. Results.The initial magnetic field topology displays a pre-existing sheared arcade enveloping the polarity inversion line. The simulated dynamics exhibit the movement of the oppositely directed legs of the sheared arcade field lines towards each other due to the converging Lorentz force, resulting in the onset of tether-cutting magnetic reconnection that produces an underlying flare arcade and flare ribbons. Concurrently, a magnetic flux rope above the flare arcade develops inside the sheared arcade and shows a rising motion. The flux rope is found to be formed in a torus-unstable region, thereby explaining its eruptive nature. Interestingly, the location and rise of the rope are in good agreement with the corresponding observations seen in extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Furthermore, the foot points of the simulation’s flare arcade match well with the location of the observed parallel ribbons of the flare. Conclusions.The presented simulation supports the development of the MFR by the tether-cutting magnetic reconnection inside the sheared coronal arcade during flare onset. The MFR is then found to extend along the polarity inversion line (PIL) through slip-running reconnection. The MFR’s eruptive nature is ascribed both to its formation in the torus-unstable region and also to the runaway tether-cutting reconnection. 

Context. The inverse Evershed flow (IEF) is a mass motion towards sunspots at chromospheric heights. Aims. We combined high-resolution observations of NOAA 12418 from the Dunn Solar Telescope and vector magnetic field measurements from the Helioseismic and Magnetic Imager (HMI) to determine the driver of the IEF. Methods. We derived chromospheric line-of-sight (LOS) velocities from spectra of H α and Ca  II IR. The HMI data were used in a non-force-free magnetic field extrapolation to track closed field lines near the sunspot in the active region. We determined their length and height, located their inner and outer foot points, and derived flow velocities along them. Results. The magnetic field lines related to the IEF reach on average a height of 3 megameter (Mm) over a length of 13 Mm. The inner (outer) foot points are located at 1.2 (1.9) sunspot radii. The average field strength difference Δ B between inner and outer foot points is +400 G. The temperature difference Δ T is anti-correlated with Δ B with an average value of −100 K. The pressure difference Δ p is dominated by Δ B and is primarily positive with a driving force towards the inner foot points of 1.7 kPa on average. The velocities predicted from Δ p reproduce the LOS velocities of 2–10 km s −1 with a square-root dependence. Conclusions. We find that the IEF is driven along magnetic field lines connecting network elements with the outer penumbra by a gas pressure difference that results from a difference in field strength as predicted by the classical siphon flow scenario. 

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable" layer''in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis. We also open-source the code at\url {https://github. com/idealab-isu/DSA}.