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We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics. 

As blue intensity (BI) methods are increasingly employed to generate temperature-sensitive tree-ring records around the globe, the influence of intra-site variation in elevation on climate-growth relationships for BI parameters remains largely unresolved. Here, we develop six latewood blue intensity (LWBI) chronologies along an elevational gradient for two montane conifer species, Abies concolor var. concolor (Gordon & Glend.) Lindl. Ex Hilderb and Picea engelmannii Parry ex Engelm., growing in the arid southwestern United States. In this first documented study to examine the climate response of LWBI from A. concolor, we find positive, significant (p < 0.05) correlations between the LWBI chronology from the highest elevation plot and spring–summer temperatures (April–August, r > 0.46). Moreover, the positive temperature response of A. concolor is generally stronger and more temporally stable than for P. engelmannii across varying seasonal windows. In comparing the differences in climate response across species and elevation, we document distinct clinal relationships between the temperature response of LWBI for A. concolor, where both the strength and temporal stability of the positive temperature signal increases with elevation. Meanwhile, the mid-elevation P. engelmannii demonstrate the highest climate sensitivity. As such, our findings contribute to a more comprehensive understanding of how elevation influences the type and strength of the climatic information embedded within the LWBI parameter from arid, montane conifers growing near their historical range margins. 

As individual tracking devices and year‐round genetic sampling become more accessible, research on the historically understudied nonbreeding period has exploded in the past decade. These studies are revealing tremendous inter‐ and intraspecific variation in migratory, molting, and other nonbreeding strategies, thereby informing efforts to protect bird populations throughout the entire annual cycle. However, we still have much to learn about where and when nonbreeding adaptive variation influences reproductive isolation and speciation. Previous work has demonstrated that some adaptations to conditions in different nonbreeding areas or migratory routes can fuel diversification by precluding opportunities for diverging lineages to interbreed or, in instances where lineages do interbreed, manifesting as disadvantageous phenotypes in hybrids. In this paper, we provide an overview of both established and speculative processes through which the primary nonbreeding events in the avian annual cycle (i.e. molt, migration, and overwintering) may interact to regulate gene flow between avian lineages. Although the relatively few but well‐described examples of divergence in nonbreeding phenotypes contributing to reproductive isolation suggest nonbreeding divergence is a common mode of speciation in birds, a growing number of population genetic studies reporting nonbreeding divergence in the absence of reproductive isolation seemingly suggest the opposite conclusion. We outline processes that could result in this apparent contradiction and propose general comparative frameworks to test factors that may predictably mediate the relationship between nonbreeding divergence and reproductive isolation. In the past, a shortage of nonbreeding natural history and population genetic data have impeded our ability to test these predictions in more than just a few systems. We urge evolutionary biologists to pay closer attention to conservation‐oriented studies, which are rapidly filling these knowledge gaps and presenting opportunities to better understand the true role of nonbreeding divergence in avian diversification. 

Abstract Human-induced warming is amplified in the Arctic, but its causes and consequences are not precisely known. Here, we review scientific advances facilitated by the Polar Amplification Model Intercomparison Project. Surface heat flux changes and feedbacks triggered by sea-ice loss are critical to explain the magnitude and seasonality of Arctic amplification. Tropospheric responses to Arctic sea-ice loss that are robust across models and separable from internal variability have been revealed, including local warming and moistening, equatorward shifts of the jet stream and storm track in the North Atlantic, and fewer and milder cold extremes over North America. Whilst generally small compared to simulated internal variability, the response to Arctic sea-ice loss comprises a non-negligible contribution to projected climate change. For example, Arctic sea-ice loss is essential to explain projected North Atlantic jet trends and their uncertainty. Model diversity in the simulated responses has provided pathways to observationally constrain the real-world response. 

Abstract We report the discovery of (Al,Cu)‐bearing metallic alloys in two micrometeorites found in the Project Stardust collection gathered from urban rooftop environments in Norway. Most of the alloys are the same as those found in the Khatyrka meteorite and other micrometeorites, though one has a composition that has not been reported previously. Oxygen isotope ratio measurements using secondary ion mass spectrometry show that the Project Stardust samples reported here, like all earlier examples of natural (Al,Cu)‐bearing alloys, contain material of chondritic affinity. 

Context.The well-studied active galactic nucleus (AGN) 3C 273 displays characteristics of both jetted-AGNs and Seyfert galaxies, which makes it an excellent source to study the disc-jet connection in AGNs. Aims.We aim to investigate the disc-jet scenario in 3C 273 using broad-band (0.3–78 keV) X-ray spectra fromXMM-NewtonandNuSTAR. Methods.We used simultaneousXMM-NewtonandNuSTARobservations of 3C 273 carried out between 2012 and 2024. The 0.3–78 keV X-ray spectra were first fitted with a simple power law (PL) and then with the accretion-ejection-basedJeTCAFmodel. TheJeTCAFmodel accounts for emission from the jet, which extends up to the sonic surface. In this framework, a reflection hump above 10 keV can also arise due to the bulk motion Comptonization of coronal photons by the jet. Results.We find that the simple PL did not provide a good fit, leaving significant residuals at energies below 1.5 keV. All the spectra were fitted well by theJeTCAFmodel. The weighted-averaged black hole mass of (7.77 ± 0.30) × 10⁸ M_⊙obtained from theJeTCAFmodel is comparable with the previous estimates based on reverberation mapping observations and accretion disc models. Conclusions.The 0.3–78 keV X-ray emission of 3C 273 can be fit by the accretion-ejection-based model in which the corona and the jet on top of it make significant contributions to the X-ray flux. The Doppler boosting factor estimated from the jet flux ranges from 1.6 to 2.2, consistent with the lower limit from the literature.