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

Bi- and tri-dentate imino-based iron and cobalt pre-catalysts for ethylene oligo-/polymerization

Recent progress on the use of iron and cobalt complex pre-catalysts for ethylene reactivity is reviewed. The review is organized in terms of the denticity of the chelate ligands employed, with particular reference to the influence of the ligand frameworks and their substituents on the catalytic performance for ethylene oligomerization/polymerization catalysis. The majority of the systems bear tri-dentate ligation at the iron/cobalt centre, though it is clear that bi-dentate iron/cobalt complex pre-catalysts have also attracted significant attention. Such systems produce in most cases highly linear products ranging from oligomeric α-olefins to high molecular weight polyethylene, and as such are promising candidates for both academic and industrial considerations

Efficacy and safety of Latanoprost/Timolol fixed combinations in treatment of refractory glaucoma following vitrectomy in short period

AIM: To evaluate the efficacy and safety of Latanoprost/Timolol fixed combinations(LTFC)in treatment of refractory glaucoma following vitrectomy in short period.<p>METHODS: In the present study, 42 eyes of 38 refractory glaucoma patients who had received vitrectomy were carried out. The patients were randomly divided into two groups after a 2-week washout period for previous antiglaucoma medication. Patients in group 1 underwent a 6-week treatment with LTFC and those in group 2 were treated with Latanoprost/Timolol unfixed combinations(LTuFC)for 6 weeks. The IOP, visual field, and mRNFL were measured after the washout period as the baseline, and after 6 weeks of therapy. Eye condition and adverse reactions were observed. <p>RESULTS: The mean baseline IOPs of groups 1 and 2 were respectively 37.90±3.74mmHg and 37.57±3.23mmHg. After 6 weeks, the mean IOPs were respectively 30.10±4.90mmHg and 30.62±4.62mmHg, indicating a significant reduction from the baseline(<i>t</i>=12.16, <i>t</i>=13.78, <i>P</i><0.01). No difference was observed in the IOP reduction between LTFC and LTuFC(20.54%±7.88%, 18.23%±7.03%, <i>t</i>=0.75, <i>P</i>>0.05). IOP reduction was 24.87%(20 eyes), 17.46%(15 eyes), and 9.65%(7 eyes)respectively among those with open-angle glaucoma, with partially open-angle glaucoma, and with closed-angle glaucoma. The eye drops didn't have effects on the vision field and mRNFL(all <i>P</i>>0.05), and their main adverse reactions were eye irritation and mild hyperemia.<p>CONCLUSION: In refractory glaucoma, especially in open-angle or partially-open-angle glaucoma, LTFC, administered after vitrectomy, helps to reduce IOP with desirable safetly and tolerance

Association of Wnt1-inducible signaling pathway protein-1 with the proliferation, migration and invasion in gastric cancer cells

Wnt1-inducible signaling pathway protein-1 is a cysteine-rich protein that belongs to the CCN family, which has been implicated in mediating the occurrence and progression through distinct molecular mechanisms in several tumor types. However, the association of Wnt1-inducible signaling pathway protein-1 with gastric cancer and the related molecular mechanisms remain to be elucidated. Therefore, this study aimed to clarify the biological role of Wnt1-inducible signaling pathway protein-1 in the proliferation, migration, and invasion in gastric cancer cells and further investigated the associated molecular mechanism on these biological functions. We first detected the expression level of Wnt1-inducible signaling pathway protein-1 in gastric cancer, and the reverse transcription polymerase chain reaction have shown that Wnt1-inducible signaling pathway protein-1 expression levels were upregulated in gastric cancer tissues. The expression of Wnt1-inducible signaling pathway protein-1 in gastric cancer cell lines was also detected by quantitative real-time polymerase chain reaction and Western blotting. Furthermore, two gastric cancer cell lines with high expression of Wnt1-inducible signaling pathway protein-1 were selected to explore the biological function of Wnt1-inducible signaling pathway protein-1 in gastric cancer. Function assays indicated that knockdown of Wnt1-inducible signaling pathway protein-1 suppressed cell proliferation, migration, and invasion in BGC-823 and AGS gastric cancer cells. Further investigation of mechanisms suggested that cyclinD1 was identified as one of Wnt1-inducible signaling pathway protein-1 related genes to accelerate proliferation in gastric cancer cells. In addition, one pathway of Wnt1-inducible signaling pathway protein-1 induced migration and invasion was mainly through the enhancement of epithelial-to-mesenchymal transition progression. Taken together, our findings presented the first evidence that Wnt1-inducible signaling pathway protein-1 was upregulated in gastric cancer and acted as an oncogene by promoting proliferation, migration, and invasion in gastric cancer cells