Knowledge Represent and Reconstruction by “Fundamentals of Materials Science” Classroom Teaching Mode Reform

AbstractClassroom teaching is the main form of teaching organization and activity way, and is also the main base on the classroom teaching mode reform. This article by “Fundamentals of Materials Science” as an example, generalizing the knowledge representation of three types and advantages in the classroom teaching, points out that the teacher's role in this progresss. We analyze that the feasibility and the ideal effect on rebuilding the students of materials science knowledge by the inquiry learning new knowledge, hierarchical practice and the freedom of assignments. The teachers can link of knowledge and new knowledge from participating in the generation of new knowledge; The teachers help students from standing in “the shoulders of giants” and not on “beach” by the careful design “training”; The teachers ensure that all students get interesting on learning “Fundamentals of Materials Science” by flexible free homework

Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric

This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train format and extend the preconditioned metric from the matrix case to the tensor case. The first-order and second-order quotient geometry of the manifold of fixed tensor train rank tensors under this metric is studied in detail. Algorithms, including Riemannian gradient descent, Riemannian conjugate gradient, and Riemannian Gauss-Newton, have been proposed for the tensor completion problem based on the quotient geometry. It has also been shown that the Riemannian Gauss-Newton method on the quotient geometry is equivalent to the Riemannian Gauss-Newton method on the embedded geometry with a specific retraction. Empirical evaluations on random instances as well as on function-related tensors show that the proposed algorithms are competitive with other existing algorithms in terms of recovery ability, convergence performance, and reconstruction quality.Comment: The manuscript has been adjusted in several place