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We investigate the possibilities of global versions of Chang’s Conjecture that involve singular cardinals. We show some $$\mathrm{ZFC} $$ ZFC limitations on such principles and prove relative to large cardinals that Chang’s Conjecture can consistently hold between all pairs of limit cardinals below $$\aleph _{\omega ^\omega }$$ ℵ ω ω .

Super-resolution structured illumination microscopy (SIM) has become a widely used method for biological imaging. Standard reconstruction algorithms, however, are prone to generate noise-specific artefacts that limit their applicability for lower signal-to-noise data. Here, we present a physically realistic noise model that explains the structured noise artefact and that is used to motivate new complementary reconstruction approaches. True Wiener-filtered SIM optimizes contrast given the available signal-to-noise ratio, flat-noise SIM fully overcomes the structured noise artefact while maintaining resolving power. Both methods eliminate ad-hoc user adjustable reconstruction parameters in favour of physical parameters, enhancing objectivity. The new reconstructions point to a trade-off between contrast and a natural noise appearance. This trade-off can be partly overcome by additional notch filtering, but at the expense of a decrease in signal-to-noise ratio. The benefits of the proposed approaches are demonstrated on focal adhesion and tubulin samples in 2D and 3D, and on nano-fabricated fluorescent test patterns.

Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of $$\varGamma $$ Γ -convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model features both Lagrangian and Eulerian terms. This calls for qualifying admissible three-dimensional deformations of planar domains in terms of injectivity. In addition, a careful treatment of the Maxwell system in the deformed film is required.

We study the effects of new physics in double Higgs production at future $e^+ e^-$ colliders. In the Standard Model the chiral limit ($m_e=0$) plays an important role for this process, being responsible for the smallness of the tree-level diagrams with respect to the 1-loop contributions. In our work, we consider the possibility of an enhancement due to the contribution of Standard Model dimension-six effective operators. We show that there are only two relevant operators for this process that are not yet (strongly) constrained by other data. We perform a sensitivity study on the operator coefficients for several benchmark values of energy and integrated luminosity related to the proposed linear colliders such as CLIC, ILC and FCC-ee and we derive expected 95% CL limits for each benchmark scenario., 17 pages, 8 figures, 1 table. New references added