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Free, publicly-accessible full text available May 21, 2025
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Persistent homology (PH) is a method for generating topology-inspired representations of data. Empirical studies that investigate the properties of PH, such as its sensitivity to perturbations or ability to detect a feature of interest, commonly rely on training and testing an additional model on the basis of the PH representation. To gain more intrinsic insights about PH, independently of the choice of such a model, we propose a novel methodology based on the pull-back geometry that a PH encoding induces on the data manifold. The spectrum and eigenvectors of the induced metric help to identify the most and least significant information captured by PH. Furthermore, the pull-back norm of tangent vectors provides insights about the sensitivity of PH to a given perturbation, or its potential to detect a given feature of interest, and in turn its ability to solve a given classification or regression problem. Experimentally, the insights gained through our methodology align well with the existing knowledge about PH. Moreover, we show that the pull-back norm correlates with the performance on downstream tasks, and can therefore guide the choice of a suitable PH encoding.more » « lessFree, publicly-accessible full text available February 1, 2025
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Abstract The perovskite (BA)4[CuII(CuIInIII)0.5]Cl8(
1BA ; BA+=butylammonium) allows us to study the high‐pressure structural, optical, and transport properties of a mixed‐valence 2D perovskite. Compressing1BA reduces the onset energy of CuI/IIintervalence charge transfer from 1.2 eV at ambient pressure to 0.2 eV at 21 GPa. The electronic conductivity of1BA increases by 4 orders of magnitude upon compression to 20 GPa, when the activation energy for conduction decreases to 0.16 eV. In contrast, CuIIperovskites achieve similar conductivity at ≈50 GPa. The solution‐state synthesis of these perovskites is complicated, with more undesirable side products likely from the precursor mixtures containing three different metal ions. To circumvent this problem, we demonstrate an efficient mechanochemical synthesis to expand this family of halide perovskites with complex composition by simply pulverizing together powders of 2D CuIIsingle perovskites and CuIInIIIdouble perovskites. -
Abstract The perovskite (BA)4[CuII(CuIInIII)0.5]Cl8(
1BA ; BA+=butylammonium) allows us to study the high‐pressure structural, optical, and transport properties of a mixed‐valence 2D perovskite. Compressing1BA reduces the onset energy of CuI/IIintervalence charge transfer from 1.2 eV at ambient pressure to 0.2 eV at 21 GPa. The electronic conductivity of1BA increases by 4 orders of magnitude upon compression to 20 GPa, when the activation energy for conduction decreases to 0.16 eV. In contrast, CuIIperovskites achieve similar conductivity at ≈50 GPa. The solution‐state synthesis of these perovskites is complicated, with more undesirable side products likely from the precursor mixtures containing three different metal ions. To circumvent this problem, we demonstrate an efficient mechanochemical synthesis to expand this family of halide perovskites with complex composition by simply pulverizing together powders of 2D CuIIsingle perovskites and CuIInIIIdouble perovskites.