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1. $$\omega \rightarrow 3\pi $$ and $$\omega \pi ^{0}$$ transition form factor revisited

   https://doi.org/10.1140/epjc/s10052-020-08576-6  

   Albaladejo, M.; Danilkin, I.; Gonzàlez-Solís, S.; Winney, D.; Fernández-Ramírez, C.; Blin, A. N.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Szczepaniak, A. (December 2020, The European Physical Journal C)

   null (Ed.)

   Abstract In light of recent experimental results, we revisit the dispersive analysis of the $$\omega \rightarrow 3\pi $$ ω → 3 π decay amplitude and of the $$\omega \pi ^0$$ ω π 0 transition form factor. Within the framework of the Khuri–Treiman equations, we show that the $$\omega \rightarrow 3\pi $$ ω → 3 π Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the $$\omega \pi ^0$$ ω π 0 transition form factor obtained from our determination of the $$\omega \rightarrow 3\pi $$ ω → 3 π amplitude is consistent with the data from MAMI and NA60 experiments. 

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2. Contact surgery numbers

   https://doi.org/10.4310/JSG.2023.v21.n6.a4  

   Etnyre, John; Kegel, Marc; Onaran, Sinem (January 2023, Journal of Symplectic Geometry)

   It is known that any contact $$3$$-manifold can be obtained by rationally contact Dehn surgery along a Legendrian link $$L$$ in the standard tight contact $$3$$-sphere. We define and study various versions of contact surgery numbers, the minimal number of components of a surgery link $$L$$ describing a given contact $$3$$-manifold under consideration. In the first part of the paper, we relate contact surgery numbers to other invariants in terms of various inequalities. In particular, we show that the contact surgery number of a contact manifold is bounded from above by the topological surgery number of the underlying topological manifold plus three. In the second part, we compute contact surgery numbers of all contact structures on the $$3$$-sphere. Moreover, we completely classify the contact structures with contact surgery number one on $$S^1\times S^2$$, the Poincar\'e homology sphere and the Brieskorn sphere $$\Sigma(2,3,7)$$. We conclude that there exist infinitely many non-isotopic contact structures on each of the above manifolds which cannot be obtained by a single rational contact surgery from the standard tight contact $$3$$-sphere. We further obtain results for the $$3$$-torus and lens spaces. As one ingredient of the proofs of the above results we generalize computations of the homotopical invariants of contact structures to contact surgeries with more general surgery coefficients which might be of independent interest. 

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3. Protein interactome of 3′,5′‐cAMP reveals its role in regulating the actin cytoskeleton

   https://doi.org/10.1111/tpj.16313  

   Figueroa, Nicolás E.; Franz, Peter; Luzarowski, Marcin; Martinez‐Seidel, Federico; Moreno, Juan C.; Childs, Dorothee; Ziemblicka, Aleksandra; Sampathkumar, Arun; Andersen, Tonni Grube; Tsiavaliaris, Georgios; et al (June 2023, The Plant Journal)

   SUMMARY Identification of protein interactors is ideally suited for the functional characterization of small molecules. 3′,5′‐cAMP is an evolutionary ancient signaling metabolite largely uncharacterized in plants. To tap into the physiological roles of 3′,5′‐cAMP, we used a chemo‐proteomics approach, thermal proteome profiling (TPP), for the unbiased identification of 3′,5′‐cAMP protein targets. TPP measures shifts in the protein thermal stability upon ligand binding. Comprehensive proteomics analysis yielded a list of 51 proteins significantly altered in their thermal stability upon incubation with 3′,5′‐cAMP. The list contained metabolic enzymes, ribosomal subunits, translation initiation factors, and proteins associated with the regulation of plant growth such as CELL DIVISION CYCLE 48. To functionally validate obtained results, we focused on the role of 3′,5′‐cAMP in regulating the actin cytoskeleton suggested by the presence of actin among the 51 identified proteins. 3′,5′‐cAMP supplementation affected actin organization by inducing actin‐bundling. Consistent with these results, the increase in 3′,5′‐cAMP levels, obtained either by feeding or by chemical modulation of 3′,5′‐cAMP metabolism, was sufficient to partially rescue the short hypocotyl phenotype of theactin2 actin7mutant, severely compromised in actin level. The observed rescue was specific to 3′,5′‐cAMP, as demonstrated using a positional isomer 2′,3′‐cAMP, and true for the nanomolar 3′,5′‐cAMP concentrations reported for plant cells.In vitrocharacterization of the 3′,5′‐cAMP–actin pairing argues against a direct interaction between actin and 3′,5′‐cAMP. Alternative mechanisms by which 3′,5′‐cAMP would affect actin dynamics, such as by interfering with calcium signaling, are discussed. In summary, our work provides a specific resource, 3′,5′‐cAMP interactome, as well as functional insight into 3′,5′‐cAMP‐mediated regulation in plants. 

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4. Extension Quiver for Lie Superalgebra q(3)

   https://doi.org/10.3842/SIGMA.2020.141  

   Grantcharov, Nikolay; Serganova, Vera (December 2020, Symmetry, Integrability and Geometry: Methods and Applications)

   null (Ed.)

   We describe all blocks of the category of finite-dimensional q(3)-supermodules by providing their extension quivers. We also obtain two general results about the representation of q(n): we show that the Ext quiver of the standard block of q(n) is obtained from the principal block of q(n-1) by identifying certain vertices of the quiver and prove a virtual BGG-reciprocity for q(n). The latter result is used to compute the radical filtrations of q(3) projective covers. 

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5. On the Maximum Spread of Planar and Outerplanar Graphs

   https://doi.org/10.37236/11844  

   Li, Zelong; Linz, William; Lu, Linyuan; Wang, Zhiyu (July 2024, The Electronic Journal of Combinatorics)

   The spread of a graph $$G$$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $$G$$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $$n$$, the $$n$$-vertex outerplanar graph with maximum spread is the graph obtained by joining a vertex to a path on $n-1$ vertices. In this paper, we disprove this conjecture by showing that the extremal graph is the graph obtained by joining a vertex to a path on $$\lceil(2n-1)/3\rceil$$ vertices and $$\lfloor(n-2)/3\rfloor$$ isolated vertices. For planar graphs, we show that the extremal $$n$$-vertex planar graph attaining the maximum spread is the graph obtained by joining two nonadjacent vertices to a path on $$\lceil(2n-2)/3\rceil$$ vertices and $$\lfloor(n-4)/3\rfloor$$ isolated vertices. 

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