“The paper identifies universal polar dual pairs of spherical codes C and D such that for a large class of potential functions h the minima of the discrete h-potential of C on the sphere occur at the points of D and vice versa.”

“The paper determines the splitting field and a set of 68 linearly independent generators for the Mordell--Weil lattice of the elliptic surface.”

“Three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances.”

“The authors obtain accurate ground-state energies for lattices up to 80 x 80 (6400 spins) and train deep Boltzmann machines for a system with 35 x 35 (1225 spins).”

“The paper introduces and analyzes a class of discrete Gaussian free fields on Hamming graphs, where interactions are determined solely by the Hamming distance between vertices.”

“The paper demonstrates the stabilization of 70 nm-radius skyrmions at room temperature and reveals how the Co and Gd sublattices influence the temperature-dependent net magnetization.”

“The paper finds a g-wave altermagnetic spin liquid as the unique ground state for the spin-3/2 model and a richer phase diagram for the spin-7/2 model, including d-wave altermagnetic spin liquids and chiral spin liquids.”

“The paper finds a robust 4Q bipartite lattice of hedgehogs and antihedgehogs which melts through a first order phase transition.”

“The authors observe that the charge diffusion constant is well described by a simple functional dependence ~ 1/V^2 universally valid both for small and large V.”

“The paper provides clear numerical evidences for anyon excitations with fractional charge and pronounced real-space density modulations, directly supporting the recently proposed anyon density-wave halo picture.”

“The paper highlights the scaling hypothesis for loop-length distributions, the emergence of critical exponents $τ=15/7$, $d_f=7/4$, and $σ=3/7$ in several universality classes.”

“The paper demonstrates the impressive performance of both quasi-continuum models in approximating the behavior of DDSWs and RWs.”

“The research investigates the potential of Hf/Zr superlattices and dipole layer engineering to enhance the performance of gate dielectrics in advanced CMOS.”

“The research focuses on the electronic band structure of hexagonal lattices.”

“The presence of defects, particularly at smaller twist angles, provides additional control of tunneling behavior, allowing complete suppression of Klein tunneling under certain conditions.”

“The research focuses on Hölder-Lipschitz functions on fundamental domains of lattices in $\mathbb{R}^{d}$.”

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“The research focuses on fractional Chern insulators with higher Chern numbers.”

“The article's abstract or key findings would be needed to provide a specific quote. Without that, a general statement about the research's focus on topological edge states and nonlinear exciton-polaritons is the best I can offer.”