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1. From the ashes of VEI: Decoding explosivity, mass eruption rate and hazards in real time

   https://doi.org/10.22541/essoar.176967627.71453176/v1  

   Sahagian, Dork (January 2026, AGU)

   Ash-producing volcanic eruptions are a major natural hazard. The explosivity of these eruptions has been described for decades by a semi-quantitative “Volcanic Explosivity Index (VEI)” based on a number of interdependent factors (eruption duration, volume of ejected material, eruptive column height, tropospheric and stratospheric injection, and many qualitative descriptors), most of which could only be assessed after eruption had ceased. The utility of this semi-quantitative index has been questioned since then, yet its common usage persists. We suggest that if VEI is to be used in the future, it may as well be an index that can be determined in real time during an eruption, and one that strictly reflects eruption intensity. We find that the same value for the “traditional” Volcanic Explosivity Index of past eruptions can be estimated in real time during an eruption, based solely on eruption column height. This approach is not intended to replace the traditional VEI scale or supplant more detailed mechanistic approaches to mass eruption rate (MER); rather it can be used to provide a more immediate way of calculating the VEI and linking to MER, in real time while an eruption is taking place. As such, if the easily observed height can be measured, both MER and VEI can be estimated. This may facilitate emergency response by aviation, hazard management, and others to mitigate societal impact of hazardous eruptions. This scheme can be inverted to use volume-based VEI of ancient eruptions to roughly retrodict unobserved column height for key historic and pre-historic eruptions. Further, ash particle morphology reflects explosivity in terms of decompression rate at the vent of unobserved eruptions. With sufficiently rapid decompression, this could result in an observable bi-modal bubble size distribution. The morphology of ash particles reveals a threshold between VEI 3 and 4, above which there is sufficiently rapid decompression to trigger a second nucleation event near the vent. 

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2. Deciphering the variability of leaf phosphorus‐allocation strategies using leaf economic traits and reflectance spectroscopy across diverse forest types

   https://doi.org/10.1111/nph.70219  

   Dong, Tingting; Wu, Fengqi; Tsujii, Yuki; Townsend, Philip A; Yang, Nan; Xu, Weiying; Liu, Shuwen; Swenson, Nathan G; Lamour, Julien; Han, Wenxuan; et al (August 2025, New Phytologist)

   Summary Allocation of leaf phosphorus (P) among different functional fractions represents a crucial adaptive strategy for optimizing P use. However, it remains challenging to monitor the variability in leaf P fractions and, ultimately, to understand P‐use strategies across diverse plant communities.We explored relationships between five leaf P fractions (orthophosphate P, P_i; lipid P, P_L; nucleic acid P, P_N; metabolite P, P_M; and residual P, P_R) and 11 leaf economic traits of 58 woody species from three biomes in China, including temperate, subtropical and tropical forests. Then, we developed trait‐based models and spectral models for leaf P fractions and compared their predictive abilities.We found that plants exhibiting conservative strategies increased the proportions of P_Nand P_M, but decreased the proportions of P_iand P_L, thus enhancing photosynthetic P‐use efficiency, especially under P limitation. Spectral models outperformed trait‐based models in predicting cross‐site leaf P fractions, regardless of concentrations (R² = 0.50–0.88 vs 0.34–0.74) or proportions (R² = 0.43–0.70 vs 0.06–0.45).These findings enhance our understanding of leaf P‐allocation strategies and highlight reflectance spectroscopy as a promising alternative for characterizing large‐scale leaf P fractions and plant P‐use strategies, which could ultimately improve the physiological representation of the plant P cycle in land surface models. 

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3. The L _p chord Minkowski problem

   https://doi.org/10.1515/ans-2022-0041  

   Xi, Dongmeng; Yang, Deane; Zhang, Gaoyong; Zhao, Yiming (January 2023, Advanced Nonlinear Studies)

   Abstract Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n {{\mathbb{R}}}^{n} , in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p {L}_{p} chord measures is called the L p {L}_{p} chord Minkowski problem in the L p {L}_{p} Brunn-Minkowski theory, which includes the L p {L}_{p} Minkowski problem as a special case. This article solves the L p {L}_{p} chord Minkowski problem when p > 1 p\gt 1 and the symmetric case of 0 < p < 1 0\lt p\lt 1 . 

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4. Gridded road network statistics and settlement age surfaces for core-based statistical areas in the conterminous U.S.

   https://doi.org/10.6084/m9.figshare.19593496.v1  

   Uhl, Johannes H.; Burghardt, Keith (January 2022, figshare)

   These geotiff files represent road network statistics for each core-based statistical area (CBSA) in the conterminous U.S., within grid cells of 1km x 1km. The road network statistics are based on the National transportation dataset (USGS-NTD) v2019. These statistics include: gridcell_stats_azimuthvariety_1km_all_cbsas.tif: The number of unique road angles (azimuth / orientation) in bins of 10 degrees per 1 sqkm grid cell. gridcell_stats_deadendrate_1km_all_cbsas.tif: The proportion of dead ends (nodes of degree 1) of all nodes per 1 sqkm grid cell. gridcell_stats_kmroad_1km_all_cbsas.tif: The approximate total road network length per 1 sqkm grid cell. This is based on the road segment length appended to each road segment centroid and may be biased for very long road segments. gridcell_stats_meandegree_1km_all_cbsas.tif: The average nodal degree of all nodes per 1 sqkm grid cell. gridcell_stats_meangriddedness_1km_all_cbsas.tif: The average griddedness of all nodes per 1 sqkm grid cell. gridcell_stats_nodedensity_1km_all_cbsas.tif: The number of nodes per 1 sqkm grid cell. gridcell_stats_nodesperkmroad_1km_all_cbsas.tif: The number of nodes per km road within each 1 sqkm grid cell. gridcell_stats_firstbuiltup_1km_all_cbsas.tif: The approximate settlement age per 1 sqkm grid cell. This layer is derived from the HISDAC-US First-built-up year (FBUY) layer, which is derived from Zillow's Transaction and Assessment Dataset (ZTRAX). The FBUY data is available here: Leyk, Stefan; Uhl, Johannes H., 2018, "FBUY.tar.gz", Historical settlement composite layer for the U.S. 1810 - 2015, https://doi.org/10.7910/DVN/PKJ90M/BOA5YC, Harvard Dataverse, V2  gridcell_stats_1km_all_cbsas_arcmap10.8.mxd: ESRI ArcMap 10.8 MXD file for quick visualization of the gridded surfaces. Spatial resolution: 1x1km Spatial reference: SR-ORG:7480, USA_Contiguous_Albers_Equal_Area_Conic_USGS_version Source data: USGS-NTD, HISDAC-US. File format: GeoTIFF. Spatial coverage of the road network metrics: All CBSAs in the conterminous U.S. Spatial coverage of the "first built-up year" surface: all U.S. counties that are covered by the HISDAC-US  historical settlement layers. This datasets includes around 2,700 U.S.  counties. In the remaining counties, construction year coverage in the  underlying ZTRAX data (Zillow Transaction and Assessment Dataset) is  low. See Leyk & Uhl (2018) for details. All data created by Johannes H. Uhl, University of Colorado Boulder, USA. Code available at https://github.com/johannesuhl/USRoadNetworkEvolution. References: Burghardt, K., Uhl, J., Lerman, K.,  & Leyk, S. (2022). Road   Network Evolution in the Urban and Rural  United States Since 1900.   Computers, Environment and Urban Systems. Leyk, S., & Uhl, J. H. (2018). HISDAC-US, historical settlement   data  compilation for the conterminous United States over 200 years. Scientific data, 5(1), 1-14. DOI:  https://doi.org/10.1038/sdata.2018.175  

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5. Averages Along the Primes: Improving and Sparse Bounds

   https://doi.org/10.1515/conop-2020-0003  

   Han, Rui; Krause, Ben; Lacey, Michael T.; Yang, Fan (February 2020, Concrete Operators)

   Abstract Consider averages along the prime integers ℙ given by {\mathcal{A}_N}f(x) = {N^{ - 1}}\sum\limits_{p \in \mathbb{P}:p \le N} {(\log p)f(x - p).} These averages satisfy a uniform scale-free ℓ p -improving estimate. For all 1 < p < 2, there is a constant C p so that for all integer N and functions f supported on [0, N ], there holds {N^{ - 1/p'}}{\left\| {{\mathcal{A}_N}f} \right\|_{\ell p'}} \le {C_p}{N^{ - 1/p}}{\left\| f \right\|_{\ell p}}. The maximal function 𝒜 * f = sup N |𝒜 N f | satisfies ( p , p ) sparse bounds for all 1 < p < 2. The latter are the natural variants of the scale-free bounds. As a corollary, 𝒜 * is bounded on ℓ p ( w ), for all weights w in the Muckenhoupt 𝒜 p class. No prior weighted inequalities for 𝒜 * were known. 

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