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1. Continuous stable regularity

   https://doi.org/10.1112/jlms.12822  

   Chavarria, Nicolas; Conant, Gabriel; Pillay, Anand (October 2023, Journal of the London Mathematical Society)

   Abstract We prove an analytic version of the stable graph regularity lemma by Malliaris and Shelah (Trans. Amer. Math. Soc.366(2014), no. 3, 1551–1585), which applies to stable functions . Our methods involve continuous model theory and, in particular, results on the structure of local Keisler measures for stable continuous formulas. Along the way, we develop some basic tools around ultraproducts of metric structures and linear functionals on continuous formulas, and we also describe several concrete families of examples of stable functions. 

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2. Slow saturable absorption for optimal operation in a soliton comb laser

   https://doi.org/10.1364/OE.454207  

   Kang, Zhe; Wang, Yinghe; Wang, Shaokang; Zheng, Zi-Wei; Zhang, Xianting; Menyuk, Curtis_R (April 2022, Optics Express)

   In this article, we study how the choice of parameters of a slow saturable absorber (SSA) affects the stable operation of a soliton fiber comb laser. We show that a shorter recovery time for the SSA does not always lead to shorter modelocked pulses. Instead, increasing the cavity gain plays a critical role in generating stable modelocked pulses with higher energy and shorter durations. We find that more stable, shorter, and more energetic output pulses can be achieved with lower saturation energies of the SSA and/or higher anomalous dispersion within the cavity. 

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3. Local duality for representations of finite group schemes

   https://doi.org/10.1112/s0010437x19007061  

   Benson, Dave; Iyengar, Srikanth B.; Krause, Henning; Pevtsova, Julia (February 2019, Compositio Mathematica)

   A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the $$\mathfrak{p}$$ -local and $$\mathfrak{p}$$ -torsion subcategories of the stable category, for each homogeneous prime ideal $$\mathfrak{p}$$ in the cohomology ring of the group scheme. 

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4. The genome of the stable fly, Stomoxys calcitrans, reveals potential mechanisms underlying reproduction, host interactions, and novel targets for pest control

   https://doi.org/10.1186/s12915-021-00975-9  

   Olafson, Pia U.; Aksoy, Serap; Attardo, Geoffrey M.; Buckmeier, Greta; Chen, Xiaoting; Coates, Craig J.; Davis, Megan; Dykema, Justin; Emrich, Scott J.; Friedrich, Markus; et al (March 2021, BMC Biology)

   Abstract BackgroundThe stable fly,Stomoxys calcitrans, is a major blood-feeding pest of livestock that has near worldwide distribution, causing an annual cost of over $2 billion for control and product loss in the USA alone. Control of these flies has been limited to increased sanitary management practices and insecticide application for suppressing larval stages. Few genetic and molecular resources are available to help in developing novel methods for controlling stable flies. ResultsThis study examines stable fly biology by utilizing a combination of high-quality genome sequencing and RNA-Seq analyses targeting multiple developmental stages and tissues. In conjunction, 1600 genes were manually curated to characterize genetic features related to stable fly reproduction, vector host interactions, host-microbe dynamics, and putative targets for control. Most notable was characterization of genes associated with reproduction and identification of expanded gene families with functional associations to vision, chemosensation, immunity, and metabolic detoxification pathways. ConclusionsThe combined sequencing, assembly, and curation of the male stable fly genome followed by RNA-Seq and downstream analyses provide insights necessary to understand the biology of this important pest. These resources and new data will provide the groundwork for expanding the tools available to control stable fly infestations. The close relationship ofStomoxysto other blood-feeding (horn flies andGlossina) and non-blood-feeding flies (house flies, medflies,Drosophila) will facilitate understanding of the evolutionary processes associated with development of blood feeding among the Cyclorrhapha. 

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5. Stable homotopy groups of spheres

   https://doi.org/10.1073/pnas.2012335117  

   Isaksen, Daniel C.; Wang, Guozhen; Xu, Zhouli (September 2020, Proceedings of the National Academy of Sciences)

   We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence. 

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