In histopathology, pathologists examine both tissue architecture at low magnification and fine-grained morphology at high magnification. Yet, the performance of pathology foundation models across magnifications and the effect of magnification sampling during training remain poorly understood. We model magnification sampling as a multi-source domain adaptation problem and develop a simple theoretical framework that reveals systematic trade-offs between sampling strategies. We show that the widely used discrete uniform sampling of magnifications (0.25, 0.5, 1.0, 2.0 mpp) leads to degradation at intermediate magnifications. We introduce continuous magnification sampling, which removes gaps in magnification coverage while preserving performance at standard scales. Further, we derive sampling distributions that optimize representation quality across magnification scales. To evaluate these strategies, we introduce two new benchmarks (TCGA-MS, BRACS-MS) with appropriate metrics.Our experiments show that continuous sampling can improve downstream task performance at intermediate magnifications, with gains of up to 4 percentage points in balanced classification accuracy, and that optimized distributions can further improve performance. Finally, we evaluate current histopathology foundation models, finding that magnification is a primary driver of performance variation across models. Our work paves the way towards future pathology foundation models that perform reliably across magnifications.
In this paper, we consider a singular Kirchhoff double phase problem with a right-hand side that consists of a singular and superlinear reaction term. Moreover, we allow critical growth on the nonlinear Neumann boundary condition. Using an equivalent norm in our function space and very general assumptions on the data, we prove the existence of two weak solutions whereby the first solution turns out to have negative energy sign while for the second one it is positive. Our proofs are based on variational methods and minimization of the associated energy functional over certain subsets of the Nehari manifold which are characterized by the corresponding fibering function.
Locational marginal pricing (LMP) provides efficient locational dispatch and investment signals but requires a complementary congestion hedging instrument to function effectively. This paper investigates how exposure to locational price differences is managed in North American nodal electricity markets through the implementation of Financial Transmission Rights (FTRs). Drawing on insights from 15 industry experts directly involved across all major North American electricity markets, we consolidate first-hand perspectives that reveal the practical complexities of FTR design and implementation. While most interviewees view FTRs positively, their experiences uncover multiple nuanced challenges to successfully design locational hedging instruments, which are often overlooked in the academic literature. As FTR design depends on market characteristics, we apply the findings to the European electricity market and discuss implications for a possible implementation of LMP in Europe.
In seawater electrolysis, chloride corrosion and Fe leaching-related deactivation remain the main factors limiting the operational stability of NiFe-based anodes. Here, NiFe2 O4 is employed as a model catalyst to elucidate the dissolution-complexation-redeposition behavior of Fe species and their cooperative interactions with Cl- during the oxygen evolution reaction (OER). We reveal that although Fe dissolution is unavoidable, OER, a portion of the leached Fe3 + does not remain in the bulk electrolyte but rapidly coordinates with Cl- to form soluble [FeCl4 ]- complexes. These [FeCl4 ]- species are subsequently driven back to the anode surface under anodic potentials, giving rise to a dynamic dissolution-redeposition equilibrium. The redeposited Fe, stabilized through Fe-Cl interactions, generates surface-bound chloride species that repel free Cl- from the electrolyte, simultaneously suppressing chloride corrosion and enhancing catalytic activity. Benefiting from this metal-halide synergistic stabilization, NiFe2 O4 exhibits outstanding OER performance, achieving 100 mA cm-2 at a low overpotential of 248 mV and exhibiting remarkable stability, operating continuously in chloride-containing electrolyte for over 40 0 0 h with an extremely low degradation rate of 3.84 mu V h-1 . (c) 2026 Published by Elsevier Ltd on behalf of The editorial office of Journal of Materials Science & Technology.
Hetero-agglomeration of micron- and submicron-sized particles enables the formation of all-solid-state battery cathode materials with enhanced safety and energy density. This study investigates a turbulent pipe flow process for mixing lithium iron phosphate (LiFePO4, LFP), lithium indium chloride (Li3InCl6, LIC), and carbon black (CB) to form three-component hetero-agglomerates. The analysis aims to identify suitable pipe dimensions and evaluate how different mixing configurations affect agglomerate size, composition, and structure. The investigation employs a dedicated simulation framework utilizing a mesh-free representation of turbulent flow fields derived from direct numerical simulation datasets. Lagrangian particle tracking incorporates an improved discrete random walk model, while stochastic agglomerate structure simulations account for various turbulent collision mechanisms, hydrodynamic interactions, and breakup events. Prior to simulations, virtual CB aggregates were stereologically reconstructed from scanning electron microscopy images, the particle size distributions were determined using laser light diffraction, and the surface energies of all materials were determined from contact angle measurements using the Owens-Wendt-Rabel-Kaelble method. Simulations examined parallel mixing and sequential premixing configurations (LFP-CB, LIC-CB, and LFP-LIC) across various pipe diameters. For parallel mixing under experimental process conditions, an 18 mm pipe diameter proved optimal, achieving maximum particle capture in agglomerates at a downstream distance of 2.73 m. Premixing diameters were selected based on mixing length and deposition. The mixing configuration significantly influences the agglomerate composition, material-specific mixing quality measures, and the contact-pair distribution. The findings provide concrete recommendations for experimental process design regarding pipe dimensions and mixing strategies, while the influence on electrochemical properties requires further investigation.
