In this paper, we developed a feasible and efficient deep-learning-based framework to combine the United States (US) natality data for the last five decades, with changing variables and factors, into a consistent database. We constructed a graph based on the property and elements of databases, including variables, and conducted a graph convolutional network (GCN) to learn the embeddings of variables on the constructed graph, where the learned embeddings implied the similarity of variables. Specifically, we devised a loss function with a slack margin and a banlist mechanism (for a random walk) to learn the desired structure (two nodes sharing more information were more similar to each other.), and developed an active learning mechanism to conduct the harmonization. Toward a total of 9,321 variables from 49 databases (i.e., 783 stemmed variables, from 1970 to 2018), we applied our model iteratively together with human reviews for four rounds, then obtained 323 hyperchains of variables. During the harmonization, the first round of our model achieved recall and precision of 87.56%, 57.70%, respectively. Our harmonized graph neural network (HGNN) method provides a feasible and efficient way to connect relevant databases at a meta-level. Adapting to the database's property and characteristics, HGNN can learn patterns globally, which is powerful to discover the similarity between variables among databases. Our proposed method provides an effective way to reduce the manual effort in database harmonization and integration of fragmented data into useful databases for future research.

S-transformation is a unitary transformation accomplishing the main part of the diagonalization of the interaction Hamiltonian in strong coupling theories. For a compact symmetry group the action of the S-transformation on the integrals of motion is derived.

We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact). Our results improve and extend earlier and recent ones in the literature.

We identify a combinatorial quantity (the alternating sum of the h-vector) defined for any simple polytope as the signature of a toric variety. This quantity was introduced by R. Charney and M. Davis in their work, which in particular showed that its nonnegativity is closely related to a conjecture of H. Hopf on the Euler characteristic of a nonpositively curved manifold. We prove positive (or nonnegative) lower bounds for this quantity under geometric hypotheses on the polytope and, in particular, resolve a special case of their conjecture. These hypotheses lead to ampleness (or weaker conditions) for certain line bundles on toric divisors, and then the lower bounds follow from calculations using the Hirzebruch signature formula. Moreover, we show that under these hypotheses on the polytope, the ith L-class of the corresponding toric variety is (−1)^i times an effective class for any i .

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