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Coastal wetlands act as natural buffers against wave energy and storm surges. In the course of energy dissipation, vegetation stems are exposed to wave action, which may lead to stem breakage. An integral component of wave attenuation modeling involves quantifying the extent of damaged vegetation, which relies on determining the maximum drag force (FDmax) and maximum moment of drag (MDmax) experienced by vegetation stems. Existing closed-form theoretical equations for MDmax and FDmax are only valid for linear and weakly nonlinear deep water waves. To address this limitation, this study first establishes an extensive synthetic dataset encompassing 256,450 wave and vegetation scenarios. Their corresponding wave crests, wave troughs, MDmax, and FDmax, which compose the dataset, are numerically computed through an efficient algorithm capable of fast computing fully nonlinear surface gravity waves in arbitrary depth. Seven dominant wave and vegetation related dimensionless parameters that impact MDmax and FDmax are discerned and incorporated as input feature parameters into an innovative sparse regression algorithm to reveal the underlying nonlinear relationships between MDmax, FDmax and the input features. Sparse regression is a subfield of machine learning that primarily focuses on identifying a subset of relevant feature functions from a feature function library. Leveraging this synthetic dataset and the power of sparse regression, concise yet accurate closed-form equations for MDmax and FDmax are developed. The discovered equations exhibit good accuracy compared with the ground truth in the synthetic dataset, with a maximum relative error below 6.6% and a mean relative error below 1.4%. Practical applications of these equations involve assessment of the extent of damaged vegetation under wave impact and estimation of MDmax and FDmax on cylindrical structures. 

Abstract Barred galaxies exhibit boxy/peanut or X-shapes (BP/X) protruding from their disks in edge-on views. Two types of BP/X morphologies exist depending on whether the X-wings meet at the center (CX) or are off-centered (OX). Orbital studies indicate that various orbital types can generate X-shaped structures. Here we provide a classification approach that identifies the specific orbit families responsible for generating OX- and CX-shaped structures. Applying this approach to three differentN-body bar models, we show that both OX and CX structures are associated with thex1 orbit family, but OX-supporting orbits possess higher angular momentum (closer tox1 orbits) than orbits in CX structures. Consequently, as the bar slows down, the contribution of higher angular momentum OX-supporting orbits decreases and that of lower angular momentum orbits increases, resulting in an evolution of the morphology from OX to CX. If the bar does not slow down, the shape of the BP/X structure and the fractions of OX/CX-supporting orbits remain substantially unchanged. Bars that do not undergo buckling but that do slow down initially show the OX structure and are dominated by high angular momentum orbits, transitioning to a CX morphology. Bars that buckle exhibit a combination of both OX- and CX-supporting orbits immediately after the buckling but become more CX dominated as their pattern speed decreases. This study demonstrates that the evolution of BP/X morphology and orbit populations strongly depends on the evolution of the bar angular momentum. 

ABSTRACT We apply the barred Schwarzschild method developed by Tahmasebzadeh et al. (2022) to a barred S0 galaxy, NGC 4371, observed by IFU instruments from the TIMER and ATLAS3D projects. We construct the gravitational potential by combining a fixed black hole mass, a spherical dark matter halo, and stellar mass distribution deprojected from 3.6 μm S$^4$G image considering an axisymmetric disc and a triaxial bar. We independently modelled kinematic data from TIMER and ATLAS3D. Both models fit the data remarkably well. We find a consistent bar pattern speed from the two sets of models with $$\Omega _{\rm p} = 23.6 \pm 2.8 \, \mathrm{km \, s^{-1} \, kpc^{-1} }$$ and $$\Omega _{\rm p} = 22.4 \pm 3.5 \, \mathrm{km \, s^{-1} \, kpc^{-1} }$$, respectively. The dimensionless bar rotation parameter is determined to be $$\mathcal {R} \equiv R_{\rm cor}/R_{\rm bar}=1.88 \pm 0.37$$, indicating a likely slow bar in NGC 4371. Additionally, our model predicts a high amount of dark matter within the bar region ($$M_{\rm DM}/ M_{\rm total}$$\sim 0.51 \pm 0.06$$), which, aligned with the predictions of cosmological simulations, indicates that fast bars are generally found in baryon-dominated discs. Based on the best-fitting model, we further decompose the galaxy into multiple 3D orbital structures, including a BP/X bar, a classical bulge, a nuclear disc, and a main disc. The BP/X bar is not perfectly included in the input 3D density model, but BP/X-supporting orbits are picked through the fitting to the kinematic data. This is the first time a real barred galaxy has been modelled utilizing the Schwarzschild method including a 3D bar. 

Plant growth and development are acutely sensitive to high ambient temperature caused in part due to climate change. However, the mechanism of high ambient temperature signaling is not well defined. Here, we show that HECATEs (HEC1 and HEC2), two helix-loop-helix transcription factors, inhibit thermomorphogenesis. While the expression of HEC1 and HEC2 is increased and HEC2 protein is stabilized at high ambient temperature, hec1hec2 double mutant showed exaggerated thermomorphogenesis. Analyses of the four PHYTOCHROME INTERACTING FACTOR (PIF1, PIF3, PIF4 and PIF5) mutants and overexpression lines showed that they all contribute to promote thermomorphogenesis. Furthermore, genetic analysis showed that pifQ is epistatic to hec1hec2 . HECs and PIFs oppositely control the expression of many genes in response to high ambient temperature. PIFs activate the expression of HEC s in response to high ambient temperature. HEC2 in turn interacts with PIF4 both in yeast and in vivo . In the absence of HECs, PIF4 binding to its own promoter as well as the target gene promoters was enhanced, indicating that HECs control PIF4 activity via heterodimerization. Overall, these data suggest that PIF4-HEC forms an autoregulatory composite negative feedback loop that controls growth genes to modulate thermomorphogenesis.