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The importance of machine learning (ML) in scientific discovery is growing. In order to prepare the next generation for a future dominated by data and artificial intelligence, we need to study how ML can improve K-12 students’ scientific discovery in STEM learning and how to assist K-12 teachers in designing ML-based scientific discovery (SD) learning activities. This study proposes research ideas and provides initial findings on the relationship between different ML components and young learners’ scientific investigation behaviors. Results show that cluster analysis is promising for supporting pattern interpretation and scientific communication behaviors. The levels of cognitive complexity are associated with different ML-powered SD and corresponding learning support is needed. The next steps include a further co-design study between K-12 STEM teachers and ML experts and a plan for collecting and analyzing data to further understand the connection between ML and SD. 

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets. 

The superτ-charm facility (STCF) is an electron–positron collider proposed by the Chinese particle physics community. It is designed to operate in a center-of-mass energy range from 2 to 7 GeV with a peak luminosity of 0.5 × 10³⁵cm⁻²·s⁻¹or higher. The STCF will produce a data sample about a factor of 100 larger than that of the presentτ-charm factory — the BEPCII, providing a unique platform for exploring the asymmetry of matter-antimatter (charge-parity violation), in-depth studies of the internal structure of hadrons and the nature of non-perturbative strong interactions, as well as searching for exotic hadrons and physics beyond the Standard Model. The STCF project in China is under development with an extensive R&D program. This document presents the physics opportunities at the STCF, describes conceptual designs of the STCF detector system, and discusses future plans for detector R&D and physics case studies.