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We define a link lattice complex for plumbed links, generalizing constructions of Ozsváth, Stipsicz and Szabó, and of Gorsky and Némethi. We prove that for all plumbed links in rational homology 3-spheres, the link lattice complex is homotopy equivalent to the link Floer complex as anA_{\infty}-module. Additionally, we prove that the link Floer complex of a plumbed L-space link is a free resolution of its homology. As a consequence, we give an algorithm to compute the link Floer complexes of plumbed L-space links, in particular of algebraic links, from their multivariable Alexander polynomial. 

Plant genomes are littered with transposable elements (TEs). Because TEs are potentially highly mutagenic, host organisms have evolved a set of defense mechanisms to recognize and epigenetically silence them. Although the maintenance of TE silencing is well studied, our understanding of the initiation of TE silencing is limited, but it clearly involves small RNAs and DNA methylation. Once TEs are silent, the silent state can be maintained to subsequent generations. However, under some circumstances, such inheritance is unstable, leading to the escape of TEs to the silencing machinery, resulting in the transcriptional activation of TEs. Epigenetic control of TEs has been found to be closely linked to many other epigenetic phenomena, such as genomic imprinting, and is known to contribute to regulation of genes, especially those near TEs. Here we review and discuss the current models of TE silencing, its unstable inheritance after hybridization, and the effects of epigenetic regulation of TEs on genomic imprinting. 

Abstract Trans-chromosomal interactions resulting in changes in DNA methylation during hybridization have been observed in several plant species. However, little is known about the causes or consequences of these interactions. Here, we compared DNA methylomes of F1 hybrids that are mutant for a small RNA biogenesis gene, Mop1 (Mediator of paramutation1), with that of their parents, wild-type siblings, and backcrossed progeny in maize (Zea mays). Our data show that hybridization triggers global changes in both trans-chromosomal methylation (TCM) and trans-chromosomal demethylation (TCdM), most of which involved changes in CHH methylation. In more than 60% of these TCM differentially methylated regions (DMRs) in which small RNAs are available, no significant changes in the quantity of small RNAs were observed. Methylation at the CHH TCM DMRs was largely lost in the mop1 mutant, although the effects of this mutant varied depending on the location of these DMRs. Interestingly, an increase in CHH at TCM DMRs was associated with enhanced expression of a subset of highly expressed genes and suppressed expression of a small number of lowly expressed genes. Examination of the methylation levels in backcrossed plants demonstrates that both TCM and TCdM can be maintained in the subsequent generation, but that TCdM is more stable than TCM. Surprisingly, although increased CHH methylation in most TCM DMRs in F1 plants required Mop1, initiation of a new epigenetic state of these DMRs did not require a functional copy of this gene, suggesting that initiation of these changes is independent of RNA-directed DNA methylation. 

Abstract We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group$$\Gamma <{\operatorname{\mathrm{Isom}}}^+(\mathbb H^{n+1})$$, each full rank cusp corresponds to a cohomology class in$$H^{n}(\Gamma , V)$$, whereVis either the trivial coefficient or the adjoint representation. Moreover, by computing the intertwining operator, we show that different cusps give rise to linearly independent classes. 

Abstract We show convergence of small eigenvalues for geometrically finite hyperbolicn-manifolds under strong limits. For a class of convergent convex sets in a strongly convergent sequence of Kleinian groups, we use the spectral gap of the limit manifold and the exponentially mixing property of the geodesic flow along the strongly convergent sequence to find asymptotically uniform counting formulas for the number of orthogeodesics between the convex sets. In particular, this provides asymptotically uniform counting formulas (with respect to length) for orthogeodesics between converging Margulis tubes, geodesic loops based at converging basepoints, and primitive closed geodesics. 

Agriculture’s global environmental impacts are widely expected to continue expanding, driven by population and economic growth and dietary changes. This Review highlights climate change as an additional amplifier of agriculture’s environmental impacts, by reducing agricultural productivity, reducing the efficacy of agrochemicals, increasing soil erosion, accelerating the growth and expanding the range of crop diseases and pests, and increasing land clearing. We identify multiple pathways through which climate change intensifies agricultural greenhouse gas emissions, creating a potentially powerful climate change–reinforcing feedback loop. The challenges raised by climate change underscore the urgent need to transition to sustainable, climate-resilient agricultural systems. This requires investments that both accelerate adoption of proven solutions that provide multiple benefits, and that discover and scale new beneficial processes and food products. 

Abstract We establish some new relationships between Milnor invariants and Heegaard Floer homology. This includes a formula for the Milnor triple linking number from the link Floer complex, detection results for the Whitehead link and Borromean rings, and a structural property of the $$d$$-invariants of surgeries on certain algebraically split links.