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1. Bohr sets in sumsets II: countable abelian groups

   https://doi.org/10.1017/fms.2023.49  

   Griesmer, John T.; Le, Anh N.; Lê, Thái Hoàng (July 2023, Forum of Mathematics, Sigma)

   Abstract We prove three results concerning the existence of Bohr sets in threefold sumsets. More precisely, lettingGbe a countable discrete abelian group and$$\phi _1, \phi _2, \phi _3: G \to G$$be commuting endomorphisms whose images have finite indices, we show that(1)If$$A \subset G$$has positive upper Banach density and$$\phi _1 + \phi _2 + \phi _3 = 0$$, then$$\phi _1(A) + \phi _2(A) + \phi _3(A)$$contains a Bohr set. This generalizes a theorem of Bergelson and Ruzsa in$$\mathbb {Z}$$and a recent result of the first author.(2)For any partition$$G = \bigcup _{i=1}^r A_i$$, there exists an$$i \in \{1, \ldots , r\}$$such that$$\phi _1(A_i) + \phi _2(A_i) - \phi _2(A_i)$$contains a Bohr set. This generalizes a result of the second and third authors from$$\mathbb {Z}$$to countable abelian groups.(3)If$$B, C \subset G$$have positive upper Banach density and$$G = \bigcup _{i=1}^r A_i$$is a partition,$$B + C + A_i$$contains a Bohr set for some$$i \in \{1, \ldots , r\}$$. This is a strengthening of a theorem of Bergelson, Furstenberg and Weiss. All results are quantitative in the sense that the radius and rank of the Bohr set obtained depends only on the indices$$[G:\phi _j(G)]$$, the upper Banach density ofA(in (1)), or the number of sets in the given partition (in (2) and (3)). 

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2. Fast mvSLOUCH : Multivariate Ornstein–Uhlenbeck‐based models of trait evolution on large phylogenies

   https://doi.org/10.1111/2041-210X.14376  

   Bartoszek, Krzysztof; Tredgett Clarke, John; Fuentes‐González, Jesualdo; Mitov, Venelin; Pienaar, Jason; Piwczyński, Marcin; Puchałka, Radosław; Spalik, Krzysztof; Voje, Kjetil Lysne (September 2024, Methods in Ecology and Evolution)

   Abstract ThePCMBase Rpackage is a powerful computational tool that enables efficient calculations of likelihoods for a wide range of phylogenetic Gaussian models.Taking advantage of it, we redesigned theRpackagemvSLOUCH.Here, we demonstrate how the new version of the package can be used to thoroughly examine the evolution and adaptation of traits in a large dataset of 1252 vascular plants through the use of multivariate Ornstein–Uhlenbeck processes.The results of our analysis demonstrate the ability of the modelling framework to distinguish between various alternative hypotheses regarding the evolution of functional traits in angiosperms. 

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3. Defense-Suppressive Fragments of RIN4 generated by AvrRpt2 Participate in NDR1-dependent Activation of RPS2

   https://doi.org/10.1101/2025.06.02.656948  

   Afzal, Ahmed J; Alam, Maheen; Huang, Jianhua; Agha, Moneeza Akbar; da_Cunha, Luis; Iqbal_Rai, Muneeza; Tahir, Jibran; Jamroze, Anmbreen; Jones, Jonathan_D G; Mackey, David (June 2025, bioRxiv)

   Abstract Plant nucleotide-binding, leucine-rich-repeat (NLR) immune receptors recognize pathogen effectors and activate immunity. The NLR RPS2 recognizes AvrRpt2, aPseudomonaseffector that promotes virulence by proteolytically cleaving a membrane-tethered host protein, RIN4. RIN4 cleavage by AvrRpt2 generates fragments that activate RPS2. A model for RPS2 activation by RIN4 destruction is consistent with the ectopic activity of RPS2 in plants lacking RIN4 but does not explain the link between AvrRpt2’s virulence activity and RPS2 activation. We found that non-membrane-tethered RIN4 derivatives are potent cytosolic activators of RPS2. Activation of RPS2 by these RIN4 derivatives, like AvrRpt2-induced activation, and unlike ectopic activation in the absence of RIN4, requires the defense signaling protein NDR1. Cleavage products of RIN4 produced by AvrRpt2 play contrasting roles in the activation of RPS2, with the membrane-tethered C-terminal fragment suppressing RPS2 and the non-membrane-tethered internal fragment, dependent on compatibility with the C-terminal fragment, overcoming its suppression of RPS2. HighlightsNon-membrane tethered derivatives of RIN4 activate RPS2-induced cell deathActivation of RPS2 by non-membrane-tethered derivatives of RIN4 requires NDR1AvrRpt2-induced cleavage fragments of RIN4 play contrasting roles in RPS2 activation 

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4. Positive interactions between an exotic invader and moss biocrusts vary across life stage and correspond with the effect of water pulses on soil nitrogen

   https://doi.org/10.1111/1365-2435.13831  

   Slate, Mandy L.; McLeod, Morgan Luce; Callaway, Ragan M. (June 2021, Functional Ecology)

   Abstract The size and frequency of resource pulses can affect plant interactions and increase the abundance of invasive species relative to native species. We examined resource pulses generated during the desiccation and rehydration of communities of native biological soil crust (biocrust)‐forming mosses, in the context of positive associations between biocrusts and the invasive forb,Centaurea stoebe.We surveyedCentaureaand biocrust cover and evaluated how interactions amongCentaurea, biocrusts and water pulses influenced plant biomass and soil nitrogen in a field experiment.Centaureaseedling and biocrust interactions were also compared in a greenhouse experiment to evaluate differences related to life stage.In field surveys,Centaureaand biocrusts were positively associated. Across water pulse treatments, biocrust biomass decreased whenCentaureawas removed, indicating thatCentaureafacilitated biocrusts. Biocrusts did not affect adultCentaureain the field, butCentaureaseedling biomass was greater when grown with biocrusts in the greenhouse. Water pulses did not affect plant biomass, but interactions betweenCentaureaand biocrusts corresponded with variation in the effect of water pulses on soil nitrogen which were not evident whenCentaureaor biocrusts were grown alone. Twenty‐four hours after large water pulses were added, soilwas nine times higher in plots where biocrusts andCentaureaco‐occurred compared with small water pulse plots. In these same plots, soiltended to be lower at the end of the experiment.These results highlight positive interactions between an invasive exotic forb and native moss biocrust. Water pulses influenced soil nitrogen availability when both plants co‐occurred, but did not affect plant biomass, suggesting that resource pulses and species interactions can interact to affect ecosystem processes. A freePlain Language Summarycan be found within the Supporting Information of this article. 

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5. Modules over orders, conjugacy classes of integral matrices, and abelian varieties over finite fields

   https://doi.org/10.1007/s40993-024-00584-9  

   Marseglia, Stefano (March 2025, Research in Number Theory)

   Abstract We give an algorithm to compute representatives of the conjugacy classes of semisimple square integral matrices with given minimal and characteristic polynomials. We also give an algorithm to compute the $$\mathbb {F}_q$$ $F_q$-isomorphism classes of abelian varieties over a finite field $$\mathbb {F}_q$$ $F_q$which belong to an isogeny class determined by a characteristic polynomial hof Frobenius when his ordinary, or qis prime and hhas no real roots. 

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