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1. Broadband continuous supersymmetric transformation: a new paradigm for transformation optics

   https://doi.org/10.1186/s43593-022-00023-1  

   Yim, Jieun; Chandra, Nitish; Feng, Xilin; Gao, Zihe; Wu, Shuang; Wu, Tianwei; Zhao, Haoqi; Litchinitser, Natalia M.; Feng, Liang (December 2022, eLight)

   Abstract Transformation optics has formulated a versatile framework to mold the flow of light and tailor its spatial characteristics at will. Despite its huge success in bringing scientific fiction (such as invisibility cloaking) into reality, the coordinate transformation often yields extreme material parameters unfeasible even with metamaterials. Here, we demonstrate a new transformation paradigm based upon the invariance of the eigenspectra of the Hamiltonian of a physical system, enabled by supersymmetry. By creating a gradient-index metamaterial to control the local index variation in a family of isospectral optical potentials, we demonstrate broadband continuous supersymmetric transformation in optics, on a silicon chip, to simultaneously transform the transverse spatial characteristics of multiple optical states for arbitrary steering and switching of light flows. Through a novel synergy of symmetry physics and metamaterials, our work provides an adaptable strategy to conveniently tame the flow of light with full exploitation of its spatial degree of freedom. 

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2. Learning Transformation Synchronization

   Huang, Xiangru; Liang, Zhenxiao; Zhou, Xiaowei; Xie, Yao; Guibas, Leonidas J.; Huang, Qixing (January 2019, Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition)
3. AdaTransform: Adaptive Data Transformation

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   Tang, Zhiqiang; Peng, Xi; Li, Tingfeng; Zhu, Yizhe; Metaxas, Dimitris (October 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV))
4. Infinitely Deep Graph Transformation Networks

   https://doi.org/10.1109/ICDM58522.2023.00087  

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5. Affine-transformation invariant clustering models

   https://doi.org/10.1186/s40488-020-00111-y  

   Huang, Hsin-Hsiung; Yang, Jie (December 2020, Journal of Statistical Distributions and Applications)

   null (Ed.)

   Abstract We develop a cluster process which is invariant with respect to unknown affine transformations of the feature space without knowing the number of clusters in advance. Specifically, our proposed method can identify clusters invariant under (I) orthogonal transformations, (II) scaling-coordinate orthogonal transformations, and (III) arbitrary nonsingular linear transformations corresponding to models I, II, and III, respectively and represent clusters with the proposed heatmap of the similarity matrix. The proposed Metropolis-Hasting algorithm leads to an irreducible and aperiodic Markov chain, which is also efficient at identifying clusters reasonably well for various applications. Both the synthetic and real data examples show that the proposed method could be widely applied in many fields, especially for finding the number of clusters and identifying clusters of samples of interest in aerial photography and genomic data. 

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