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1. Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment

   https://doi.org/10.1098/rsta.2021.0033  

   Drivas, Theodore D. (June 2022, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon—anomalous dissipation—is sometimes called the ‘zeroth law of turbulence’ as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions S p ( ℓ ) := ⟨ | δ ℓ u | p ⟩ exhibit persistent power-law scaling in the inertial range, namely S p ( ℓ ) ∼ | ℓ | ζ p for exponents ζ p > 0 over an ever increasing (with Reynolds) range of scales. This behaviour indicates that the velocity field retains some fractional differentiability uniformly in the Reynolds number. The Kolmogorov 1941 theory of turbulence predicts that ζ p = p / 3 for all p and Onsager’s 1949 theory establishes the requirement that ζ p ≤ p / 3 for p ≥   3 for consistency with the zeroth law. Empirically, ζ 2 ⪆ 2 / 3 and ζ 3 ⪅ 1 , suggesting that turbulent Navier–Stokes solutions approximate dissipative weak solutions of the Euler equations possessing (nearly) the minimal degree of singularity required to sustain anomalous dissipation. In this note, we adopt an experimentally supported hypothesis on the anti-alignment of velocity increments with their separation vectors and demonstrate that the inertial dissipation provides a regularization mechanism via the Kolmogorov 4/5-law. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’. 

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2. Natural selection favours a larger eye in response to increased competition in natural populations of a vertebrate

   https://doi.org/10.1111/1365-2435.13334  

   Beston, Shannon M.; Walsh, Matthew R.; Higham, ed., Timothy (April 2019, Functional Ecology)

   Abstract Eye size varies notably across taxa. Much work suggests that this variation is driven by contrasting ecological selective pressures. However, evaluations of the relationship between ecological factors and shifts in eye size have largely occurred at the macroevolutionary scale. Experimental tests in nature are conspicuously absent.Trinidadian killifish,Rivulus hartii, are found across fish communities that differ in predation intensity. We recently showed that increased predation is associated with the evolution of a smaller eye. Here, we test how divergent predatory regimes alter the trajectory of eye size evolution using comparative mark–recapture experiments in multiple streams.We found that increases in eye size are associated with enhanced survival, irrespective of predation intensity. More importantly, eye size is associated with enhanced growth in communities that lack predators, while this trend is absent when predators are present.Such results argue that increased competition for food in sites that lack predators is the key driver of eye size evolution. Aplain language summaryis available for this article. 

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3. The pentagram map, Poncelet polygons, and commuting difference operators

   https://doi.org/10.1112/S0010437X22007345  

   Izosimov, Anton (May 2022, Compositio Mathematica)

   The pentagram map takes a planar polygon $$P$$ to a polygon $P'$ whose vertices are the intersection points of consecutive shortest diagonals of $$P$$ . This map is known to interact nicely with Poncelet polygons, that is, polygons which are simultaneously inscribed in a conic and circumscribed about a conic. A theorem of Schwartz states that if $$P$$ is a Poncelet polygon, then the image of $$P$$ under the pentagram map is projectively equivalent to $$P$$ . In the present paper, we show that in the convex case this property characterizes Poncelet polygons: if a convex polygon is projectively equivalent to its pentagram image, then it is Poncelet. The proof is based on the theory of commuting difference operators, as well as on properties of real elliptic curves and theta functions. 

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4. An emerging fungal disease is spreading across the globe and affecting the blueberry industry

   https://doi.org/10.1111/nph.20351  

   Bradshaw, Michael; Ivors, Kelly; Broome, Janet_C; Carbone, Ignazio; Braun, Uwe; Yang, Shirley; Meng, Emma; Warres, Brooke; Cline, William_O; Moparthi, Swarnalatha; et al (January 2025, New Phytologist)

   Summary Powdery mildew is an economically important disease caused byc. 1000 different fungal species.Erysiphe vacciniiis an emerging powdery mildew species that is impacting the blueberry industry. Once confined to North America,E. vacciniiis now spreading rapidly across major blueberry‐growing regions, including China, Morocco, Mexico, and the USA, threatening millions in losses.This study documents its recent global spread by analyzing both herbarium specimens, some over 150‐yr‐old, and fresh samples collected world‐wide.Our findings were integrated into a ‘living phylogeny’ via T‐BAS to simplify pathogen identification and enable rapid responses to new outbreaks. We identified 50 haplotypes, two primary introductions world‐wide, and revealed a shift from a generalist to a specialist pathogen.This research provides insights into the complexities of host specialization and highlights the need to address this emerging global threat to blueberry production. 

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5. A Compositional Theory of Linearizability

   https://doi.org/10.1145/3571231  

   Oliveira_Vale, Arthur; Shao, Zhong; Chen, Yixuan (January 2023, Proceedings of the ACM on Programming Languages)

   Compositionality is at the core of programming languages research and has become an important goal toward scalable verification of large systems. Despite that, there is no compositional account of linearizability, the gold standard of correctness for concurrent objects. In this paper, we develop a compositional semantics for linearizable concurrent objects. We start by showcasing a common issue, which is independent of linearizability, in the construction of compositional models of concurrent computation: interaction with the neutral element for composition can lead to emergent behaviors, a hindrance to compositionality. Category theory provides a solution for the issue in the form of the Karoubi envelope. Surprisingly, and this is the main discovery of our work, this abstract construction is deeply related to linearizability and leads to a novel formulation of it. Notably, this new formulation neither relies on atomicity nor directly upon happens-before ordering and is only possible because of compositionality, revealing that linearizability and compositionality are intrinsically related to each other. We use this new, and compositional, understanding of linearizability to revisit much of the theory of linearizability, providing novel, simple, algebraic proofs of the locality property and of an analogue of the equivalence with observational refinement. We show our techniques can be used in practice by connecting our semantics with a simple program logic that is nonetheless sound concerning this generalized linearizability. 

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