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The multiscale topological learning framework, based on persistent topological Laplacians, captures complex interactions and enhances energy prediction accuracy in multi-atom systems. 

Abstract Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology. 

AI-driven drug discovery accelerates anti-addiction treatment by enhancing precision and targeting key neurochemical systems. 

Abstract Surface moisture heterogeneity degrades temperature‐humidity (‐) similarity in the atmospheric surface layer, yet the underlying physical mechanisms driving this dissimilarity remain underexplored. This study employs large‐eddy simulations coupled with a land‐surface model to investigate ‐ similarity in the convective boundary layer (CBL) over surfaces with varying scales of surface moisture heterogeneity. Results reveal that as the heterogeneity scale increases, patch‐scale thermally induced circulations develop and interact with cellular turbulent organized structures, significantly altering scalar transport and turbulence dynamics. The patch‐scale thermally induced circulations enhance horizontal advection, modify the production and transport of scalar variances, and lead to a disproportionate increase in the standard deviations of temperature () and humidity (), accompanied by a reduction in ‐ covariance (). As a result, ‐ similarity is substantially reduced throughout the CBL. Spectral analysis reveals that ‐ dissimilarity is most strongly influenced by turbulent motions at scales corresponding to patch lengths. The findings offer insights into the role of surface heterogeneity in shaping scalar similarity in the CBL, with implications for land‐atmosphere interactions and parameterization in numerical models.