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Abstract We define the half-volume spectrum$$\{{\tilde{\omega }_p\}_{p\in \mathbb {N}}}$$ $\{{\tilde{\omega }}_p{\}}_{p\in N}$of a closed manifold$$(M^{n+1},g)$$ $(M^{n+1},g)$. This is analogous to the usual volume spectrum ofM, except that we restrict top-sweepouts whose slices each enclose half the volume ofM. We prove that the Weyl law continues to hold for the half-volume spectrum. We define an analogous half-volume spectrum$$\tilde{c}(p)$$ $\tilde{c}\left(p\right)$in the phase transition setting. Moreover, for$$3 \le n+1 \le 7$$ $3\le n+1\le 7$, we use the Allen–Cahn min-max theory to show that each$$\tilde{c}(p)$$ $\tilde{c}\left(p\right)$is achieved by a constant mean curvature surface enclosing half the volume ofMplus a (possibly empty) collection of minimal surfaces with even multiplicities. 

Abstract BackgroundMitochondrial genes and nuclear genes cooperate closely to maintain the functions of mitochondria, especially in the oxidative phosphorylation (OXPHOS) pathway. However, mitochondrial genes among arthropod lineages have dramatic evolutionary rate differences. Haplodiploid arthropods often show fast-evolving mitochondrial genes. One hypothesis predicts that the small effective population size of haplodiploid species could enhance the effect of genetic drift leading to higher substitution rates in mitochondrial and nuclear genes. Alternatively, positive selection or compensatory changes in nuclear OXPHOS genes could lead to the fast-evolving mitochondrial genes. However, due to the limited number of arthropod genomes, the rates of evolution for nuclear genes in haplodiploid species, besides hymenopterans, are largely unknown. To test these hypotheses, we used data from 76 arthropod genomes, including 5 independently evolved haplodiploid lineages, to estimate the evolutionary rates and patterns of gene family turnover of mitochondrial and nuclear genes. ResultsWe show that five haplodiploid lineages tested here have fast-evolving mitochondrial genes and fast-evolving nuclear genes related to mitochondrial functions, while nuclear genes not related to mitochondrion showed no significant evolutionary rate differences. Among hymenopterans, bees and ants show faster rates of molecular evolution in mitochondrial genes and mitochondrion-related nuclear genes than sawflies and wasps. With genome data, we also find gene family expansions and contractions in mitochondrion-related genes of bees and ants. ConclusionsOur results reject the small population size hypothesis in haplodiploid species. A combination of positive selection and compensatory changes could lead to the observed patterns in haplodiploid species. The elevated evolutionary rates in OXPHOS complex 2 genes of bees and ants suggest a unique evolutionary history of social hymenopterans. 

Strigolactone (SL) is a plant hormone required for plant development. DWARF53 (D53) functions as a transcription repressor in SL signaling. However, the role of D53 in cotton (Gossypium hirsutum, Gh) fiber development remains unclear. Here, we identify that GhD53 suppresses fiber elongation by repressing transcription of GhFAD3 genes, which control linolenic acid (C18:3) biosynthesis. Mechanistically, GhD53 interacts with SL-related transcriptional activate factor (GhSLRF) to prevent its binding on Omega-3 fatty acid desaturase gene (GhFAD3) promoters, thereby inhibiting GhFAD3 transcription. Upon SL exposure, GhD53 is degraded and leads to GhSLRF activation. This activation further promotes GhFAD3 transcription, C18:3 biosynthesis, and fiber elongation. Our findings identify the molecular mechanism of how SL controls cell elongation via D53 and offer potential strategies to improve cotton quality through SL application. 

An enhanced understanding of the mechanisms responsible for wind turbine blade leading-edge erosion (LEE) and advancing technology readiness level (TRL) solutions for monitoring its environmental drivers, reducing LEE, detecting LEE evolution, and mitigating its impact on power production are a high priority for all wind farm owners/operators and wind turbine manufacturers. Identifying and implementing solutions has the potential to continue historical trends toward lower Levelized Cost of Energy (LCoE) from wind turbines by reducing both energy yield losses and operations and maintenance costs associated with LEE. Here, we present results from the first Phenomena Identification and Ranking Tables (PIRT) assessment for wind turbine blade LEE. We document the LEE-relevant phenomena/processes that are deemed by this expert judgment assessment tool to be the highest priorities for research investment within four themes: atmospheric drivers, damage detection and quantification, material response, and aerodynamic implications. The highest priority issues, in terms of importance to LEE but where expert judgment indicates that there is a lack of fundamental knowledge, and/or implementation in measurement, and modeling is incomplete include the accurate quantification of hydrometeor size distribution (HSD) and phase, the translation of water impingement to material loss/stress, the representation of operating conditions within rain erosion testers, the quantification of damage and surface roughness progression through time, and the aerodynamic losses as a function of damage morphology. We discuss and summarize examples of research endeavors that are currently being undertaken and/or could be initiated to reduce uncertainty in the identified high-priority research areas and thus enhance the TRLs of solutions to mitigate/reduce LEE. 

A total of 14 extensometers were installed in Houston-Galveston Region, Texas, USA, at 12 locations to record compaction. The earliest extensometer began to record compaction in 1973. Records from three of the extensometers installed at Baytown (Shallow and Deep) and Pasadena exhibit anomalous subsidence from 2009 to 2017. The maximum compaction occurred around 2014 with Baytown Shallow recording 164 mm, Baytown Deep 72 mm, and Pasadena 135 mm. The anomalous subsidence exhibits features not related to primary consolidation subsidence (PCS) and secondary consolidation subsidence (SCS) of the Gulf Coast Aquifer System (GCAS). Groundwater level records at the extensometer locations indicate that the anomalous subsidence is not related to groundwater exploitation and creep of the GCAS in this region. Analysis of compaction data for the three sites indicates that the subsidence is partially elastic. Salt dome growth/evolution resulting in activation/reactivation of subsurface and surface faults is proposed as the mechanism responsible for the anomalous subsidence. 

Abstract A range of multi‐year observational data sets are used to characterize the hydroclimate of the Dallas Fort‐Worth area (DFW) and to investigate the impact of urban land cover on daily accumulated precipitation, RADAR composite reflectivity (cREF), and cloud top height (CTH) during the warm season. Analyses of observational data indicate rainfall rates (RR) in a 45° annulus sector 50–100 km downwind of the city are enhanced relative to an upwind area of comparable size. Enhancement of mean precipitation intensity in this annulus sector is not observed on days with spatially averaged RR > 6 mm/day. Under some flow directions, the probability of cREF >30 dBZ, occurrence of hail, and the probability of CTH >10,000 geopotential meters are also enhanced up to 200 km downwind of DFW. Two deep convection events that passed over DFW are simulated with the Weather Research and Forecasting model using a range of microphysical schemes and evaluated using RADAR observations. Model configurations that exhibit the highest fidelity in these control simulations are used in a series of perturbation experiments where the areal extent of the city is varied between zero (replacement with grassland) and eight times its current size. These perturbation experiments indicate a non‐linear response of Mesoscale Convective System properties to the urban areal extent and a very strong sensitivity to the microphysical scheme used. The impact on precipitation from the urban area, even when it is expanded to eight‐times the current extent, is much less marked for deep convection with stronger synoptic forcing.