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1. Fast Sampling via Spectral Independence Beyond Bounded-degree Graphs

   https://doi.org/10.1145/3631354  

   Bezáková, Ivona; Galanis, Andreas; Goldberg, Leslie Ann; Štefankovič, Daniel (January 2024, ACM Transactions on Algorithms)

   Spectral independence is a recently developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimalO(nlogn)sampling algorithms on bounded-degree graphs for a large class of problems throughout the so-called uniqueness regime, including, for example, the problems of sampling independent sets, matchings, and Ising-model configurations. Our main contribution is to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. Previous methods for avoiding degree bounds rely on usingL^p-norms to analyse contraction on graphs with bounded connective constant (Sinclair, Srivastava, and Yin, FOCS’13). The non-linearity ofL^p-norms is an obstacle to applying these results to bound spectral independence. Our solution is to capture theL^p-analysis recursively by amortising over the subtrees of the recurrence used to analyse contraction. Our method generalises previous analyses that applied only to bounded-degree graphs. As a main application of our techniques, we consider the random graphG (n, d/n), where the previously known algorithms run in timen^O(logd) or applied only to larged. We refine these algorithmic bounds significantly, and develop fast nearly linear algorithms based on Glauber dynamics that apply to all constantd, throughout the uniqueness regime. 

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2. Sharp Hadamard Local Well-Posedness, Enhanced Uniqueness and Pointwise Continuation Criterion for the Incompressible Free Boundary Euler Equations

   https://doi.org/10.1007/s40818-025-00204-4  

   Ifrim, Mihaela; Pineau, Ben; Tataru, Daniel; Taylor, Mitchell A (June 2025, Annals of PDE)

   Abstract We provide a complete local well-posedness theory inH^sbased Sobolev spaces for the free boundary incompressible Euler equations with zero surface tension on a connected fluid domain. Our well-posedness theory includes: (i) Local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and the first proof of continuous dependence on the data, all in low regularity Sobolev spaces; (ii) Enhanced uniqueness: Our uniqueness result holds at the level of the Lipschitz norm of the velocity and the$$C^{1,\frac{1}{2}}$$regularity of the free surface; (iii) Stability bounds: We construct a nonlinear functional which measures, in a suitable sense, the distance between two solutions (even when defined on different domains) and we show that this distance is propagated by the flow; (iv) Energy estimates: We prove refined, essentially scale invariant energy estimates for solutions, relying on a newly constructed family of elliptic estimates; (v) Continuation criterion: We give the first proof of a sharp continuation criterion in the physically relevant pointwise norms, at the level of scaling. In essence, we show that solutions can be continued as long as the velocity is in$$L_T^1W^{1,\infty}$$and the free surface is in$$L_T^1C^{1,\frac{1}{2}}$$, which is at the same level as the Beale-Kato-Majda criterion for the boundaryless case; (vi) A novel proof of the construction of regular solutions. Our entire approach is in the Eulerian framework and can be adapted to work in more general fluid domains. 

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3. The Neumann function and the L ^p Neumann problem in chord-arc domains

   https://doi.org/10.1515/ans-2023-0171  

   Hofmann, Steve; Sparrius, Derek (February 2025, Advanced Nonlinear Studies)

   Abstract We construct the Neumann function in a 1-sided chord-arc domain (i.e., a uniform domain with an Ahlfors regular boundary), and establish size and Hölder continuity estimates up to the boundary. We then obtain a Kenig-Pipher type theorem, in whichL^psolvability of the Neumann problem is shown to yield solvability inL^qfor 1 <q<p, and in the Hardy spaceH¹, in 2-sided chord-arc domains, under suitable background hypotheses. 

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4. General and selective nickel-electrocatalyzed cross-electrophile C*( sp ² )–C( sp ² ) coupling

   https://doi.org/10.1073/pnas.2515413123  

   Xie, Wenbin; Song, Zhe; Shi, Qinqin; Sheng, Panping; Xu, Gu; Wen, Kaikai; Zhao, Lutang; Marks, Tobin J; Wang, Zhi-Xiang; Huang, Hui (March 2026, Proceedings of the National Academy of Sciences)

   Berenbaum, May R (Ed.)

   Transition metal-catalyzed cross-coupling of two similar electrophiles (XEC) to construct C(sp²)–C(sp²) bonds is a powerful emerging synthetic methodology. However, efficient and selective XEC to create heterocoupled C*(sp²)–C(sp²) linkages from equimolar reagents while suppressing competing homocoupling, presents a synthetic challenge. Here, we describe a promising approach to address this challenge via electrocatalytic synthesis. This approach utilizes renewable and readily available electricity to replace traditional redox reagents, minimizing chemical use and chemical waste generation, while controlling the reaction pathway by the applied potential. This highly selective and general electrocatalytic eXEC process to construct C*(sp²)–C(sp²) bonds is enabled by sequential and controllable eXEC oxidative addition processes, and supported mechanistically by experiment and DFT computation. Generality and efficacy are demonstrated by more than 80 examples, including important biaryl, fluorophore, and pharmaceutical products. Notably, the stoichiometric precision of eXEC enables the first synthesis of solution-processable low polydispersity conjugated opto-electronic polymers. Therefore, this report provides a conceptually attractive method to selectively create diverse and useful C*(sp²)–C(sp²) coupled molecules and macromolecules. 

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5. The Shape of FIREbox Galaxies and a Potential Tension with Low-mass Disks

   https://doi.org/10.3847/1538-4357/ae31f4  

   Klein, Courtney; Wang, Jenny D; Xia, Luke Y; Bullock, James S; Moreno, Jorge; Feldmann, Robert; Mercado, Francisco J; Faucher-Giguère, Claude-André; Stern, Jonathan; Sanchez, N Nicole; et al (February 2026, The Astrophysical Journal)

   Abstract We study the intrinsic and observable shapes of approximately 700 star-forming galaxies with stellar masses of 10⁸–10¹¹M_⊙from the FIREbox simulation atz= 0. We calculate intrinsic axis ratios using inertia tensors weighted by three morphology types: “All Stars,” “Young Stars,” and “Luminosity-weighted Stars.” Young Stars shows mass-dependent 3D configurations, with spheroidal, elongated, and disky shapes dominant at stellar masses of 10^8.5, 10^9.5, and 10^10.5M_⊙, respectively. Using the radiative transfer codeSKIRT, we construct mock images for each galaxy and show that projected short-to-long axis ratios,q, inferred from 2D Sérsic fits are most closely related to Luminosity-weighted Stars tensor shapes and least resemble the All Stars’ shapes. This suggests observed 2D shape distributions should not be compared to predictions based on 3D stellar mass shapes. Next, we construct a sample of mock images projected in random orientations and compare them to observed axis ratio distributions from the GAMA survey. At stellar masses below 10¹⁰M_⊙, we produce too few galaxies with observedq < 0.4 and none withq < 0.2, suggesting that FIREbox does not produce enough low-mass disk galaxies. At higher masses, 10¹⁰–10¹¹M_⊙, we find that the predictedqdistribution is sensitive to the dust-to-metal ratio; using our fiducial model, the distribution ofqvalues is formally consistent with observations, but there is tension with our ability to produce enough very thin systems withq < 0.2. Future observational and theoretical programs aimed at understanding disk and thin-disk fractions will provide crucial tests of galaxy formation models. 

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