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In this brief note, we investigate the ${\mathbb{C}\mathbb{P}}^2$-genus of knots, i.e., the least genus of a smooth, compact, orientable surface in ${\mathbb{C}\mathbb{P}}^2\setminus <\#comment/>\stackrel{˚<\#comment/>}{B^4}$bounded by a knot in $S^3$. We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the ${\mathbb{C}\mathbb{P}}^2$-genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in ${\mathbb{C}\mathbb{P}}^2\mathrm{\#<\#comment/>}{\mathbb{C}\mathbb{P}}^2$. 

Societal Impact StatementThe innumerable effects of terroir—including climate, soil, microbial environment, biotic interactions, and cultivation practice—collectively alter plant performance and production. A more direct agricultural intervention is grafting, in which genetically distinct shoot and root genotypes are surgically combined to create a chimera that alters shoot performance at a distance. Selection of location and rootstock are intentional decisions in viticulture to positively alter production outcomes. Here, we show that terroir and rootstock alter the shapes of grapevine leaves in commercial vineyards throughout the California Central Valley, documenting the profound effects of these agricultural interventions that alter plant morphology. SummaryEmbedded in a single leaf shape are the latent signatures of genetic, developmental, and environmental effects. In viticulture, choice of location and rootstock are important decisions that affect the performance and production of the shoot. We hypothesize that these effects influence plant morphology, as reflected in leaf shape.We sample 1879 leaves arising from scion and rootstock combinations from commercial vineyards in the Central Valley of California. Our design tests 20 pairwise contrasts between Cabernet Sauvignon and Chardonnay scions from San Joaquin, Merced, and Madera counties from vines grafted to Teleki 5C, 1103 Paulsen, and Freedom rootstocks.We quantify clear differences between Cabernet Sauvignon and Chardonnay leaves. However, we also detect a separate, statistically independent source of shape variance that affects both Cabernet Sauvignon and Chardonnay leaves similarly. We find that this other shape difference is associated with differences in rootstock and location.The shape difference that arises from rootstock and location affects the basal part of the leaf near the petiole, known as the petiolar sinus, and affects its closure. This shape effect is independent from previously described shape differences that arise from genetic, developmental, or size effects. 

Grapevine leaves have diverse shapes and sizes which are influenced by many factors including genetics, vine phytosanitary status, environment, leaf and vine age, and node position on the shoot. To determine the relationship between grapevine leaf shape or size and leaf canopy temperature, we examined five seedling populations grown in a vineyard in California, USA. The populations had one parent with compound leaves of the Vitis piasezkii type and a different second parent with non-compound leaves. In previous work, we had measured the shape and size of the leaves collected from these populations using 21 homologous landmarks. Here, we paired these morphological data with canopy temperature measurements made using a handheld infrared thermometer. After recording time of sampling and canopy temperature, we used a linear model between time of sampling and canopy temperature to estimate temperature residuals. Based on these residuals, we determined if the canopy temperature of each vine was cooler or warmer than expected, based on the time of sampling. We established a relationship between leaf size and canopy temperature: vines with larger leaves were cooler than expected. By contrast, leaf shape was not strongly correlated with variation in canopy temperature. Ultimately, these findings indicate that vines with larger leaves may contribute to the reduction of overall canopy temperature; however, further work is needed to determine whether this is due to variation in leaf size, differences in the openness of the canopy or other related traits. 

The methane seeps on the Pacific margin of Costa Rica support extensive animal diversity and offer insights into deep-sea biogeography. During five expeditions between 2009 and 2019, we conducted intensive faunal sampling via 63 submersible dives to 11 localities at depths of 300–3600 m. Based on these expeditions and published literature, we compiled voucher specimens, images, and 274 newly published DNA sequences to present a taxonomic inventory of macrofaunal and megafaunal diversity with a focus on invertebrates. In total 488 morphospecies were identified, representing the highest number of distinct morphospecies published from a single seep or vent region to date. Of these, 131 are described species, at least 58 are undescribed species, and the remainder include some degree of taxonomic uncertainty, likely representing additional undescribed species. Of the described species, 38 are known only from the Costa Rica seeps and their vicinity. Fifteen range extensions are also reported for species known from Mexico, the Galápagos seamounts, Chile, and the western Pacific; as well as 16 new depth records and three new seep records for species known to occur at vents or organic falls. No single evolutionary narrative explains the patterns of biodiversity at these seeps, as even morphologically indistinguishable species can show different biogeographic affinities, biogeographic ranges, or depth ranges. The value of careful molecular taxonomy and comprehensive specimen-based regional inventories is emphasized for biodiversity research and monitoring. 

Sea cucumbers (Holothuroidea) are a diverse clade of echinoderms found from intertidal waters to the bottom of the deepest oceanic trenches. Their reduced skeletons and limited number of phylogenetically informative traits have long obfuscated morphological classifications. Sanger-sequenced molecular datasets have also failed to constrain the position of major lineages. Noteworthy, topological uncertainty has hindered a resolution for Neoholothuriida, a highly diverse clade of Permo-Triassic age. We perform the first phylogenomic analysis of Holothuroidea, combining existing datasets with 13 novel transcriptomes. Using a highly curated dataset of 1100 orthologues, our efforts recapitulate previous results, struggling to resolve interrelationships among neoholothuriid clades. Three approaches to phylogenetic reconstruction (concatenation under both site-homogeneous and site-heterogeneous models, and coalescent-aware inference) result in alternative resolutions, all of which are recovered with strong support and across a range of datasets filtered for phylogenetic usefulness. We explore this intriguing result using gene-wise log-likelihood scores and attempt to correlate these with a large set of gene properties. While presenting novel ways of exploring and visualizing support for alternative trees, we are unable to discover significant predictors of topological preference, and our efforts fail to favour one topology. Neoholothuriid genomes seem to retain an amalgam of signals derived from multiple phylogenetic histories. 

BackgroundWhile many factors are associated with stepping activity after stroke, there is significant variability across studies. One potential reason to explain this variability is that there are certain characteristics that arenecessaryto achieve greater stepping activity that differ from others thatmayneed to be targeted to improve stepping activity. ObjectiveUsing two step thresholds (2500 steps/day, corresponding to home vs. community ambulation and 5500 steps/day, corresponding to achieving physical activity guidelines through walking), we applied 3 different algorithms to determine which predictors are most important to achieve these thresholds. MethodsWe analyzed data from 268 participants with stroke that included 25 demographic, performance-based and self-report variables. Step 1 of our analysis involved dimensionality reduction using lasso regularization. Step 2 applied drop column feature importance to compute the mean importance of each variable. We then assessed which predictors were important to all 3 mathematically unique algorithms. ResultsThe number of relevant predictors was reduced from 25 to 7 for home vs. community and from 25 to 16 for aerobic thresholds. Drop column feature importance revealed that 6 Minute Walk Test and speed modulation were the only variables found to be important to all 3 algorithms (primary characteristics)for each respective threshold. Other variables related to readiness to change activity behavior and physical health, among others, were found to be important to one or two algorithms (ancillary characteristics). ConclusionsAddressing physical capacity isnecessary but not sufficientto achieve important step thresholds, asancillary characteristics, such as readiness to change activity behavior and physical health may also need to be targeted. This delineation may explain heterogeneity across studies examining predictors of stepping activity in stroke. 

Abstract The trace of the $$n$$ -framed surgery on a knot in $$S^{3}$$ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded $$2$$ -sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable $$3$$ -dimensional knot invariants. For each $$n$$ , this provides conditions that imply a knot is topologically $$n$$ -shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice. 

Abstract Pouched lamprey (Geotria australis) or kanakana/piharau is a culturally and ecologically significant jawless fish that is distributed throughout Aotearoa New Zealand. Despite its importance, much remains unknown about historical relationships and gene flow between populations of this enigmatic species within New Zealand. To help inform management, we assembled a draft Geotria australis genome and completed the first comprehensive population genomics analysis of pouched lamprey within New Zealand using targeted gene sequencing (Cyt-b and COI) and restriction site-associated DNA sequencing (RADSeq) methods. Employing 16,000 genome-wide single nucleotide polymorphisms (SNPs) derived from RADSeq (n=186) and sequence data from Cyt-b (766 bp, n=94) and COI (589 bp, n=20), we reveal low levels of structure across 10 sampling locations spanning the species range within New Zealand. F-statistics, outlier analyses, and STRUCTURE suggest a single panmictic population, and Mantel and EEMS tests reveal no significant isolation by distance. This implies either ongoing gene flow among populations or recent shared ancestry among New Zealand pouched lamprey. We can now use the information gained from these genetic tools to assist managers with monitoring effective population size, managing potential diseases, and conservation measures such as artificial propagation programs. We further demonstrate the general utility of these genetic tools for acquiring information about elusive species.