Analysis of Nuclear Norm Regularization for Full-rank Matrix Completion

In this paper, we provide a theoretical analysis of the nuclear-norm regularized least squares for full-rank matrix completion. Although similar formulations have been examined by previous studies, their results are unsatisfactory because only additive upper bounds are provided. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of the unknown matrix. Our relative upper bound is tighter than previous additive bounds of other methods if the mass of the target matrix is concentrated on its top eigenspaces, and also implies perfect recovery if it is low-rank. The analysis is built upon the optimality condition of the regularized formulation and existing guarantees for low-rank matrix completion. To the best of our knowledge, this is first time such a relative bound is proved for the regularized formulation of matrix completion

Eight-potential-well order-disorder ferroelectric model and effects of random fields

An eight-potential-well order-disorder ferroelectric model was presented and the phase transition was studied under the mean-field approximation. It was shown that the two-body interactions are able to account for the first-order and the second order phase transitions. With increasing the random fields in the system, a first-order phase transition is transformed into a second-order phase transition, and furthermore, a second-order phase transition is inhibited. However, proper random fields can promote the spontaneous appearance of a first-order phase transition by increasing the overcooled temperature. The connections of the model with relaxors were discussed.Comment: 8 pages, 5 figures. Submitted to Applied Physics Letter

Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.Comment: 11 pages, 4 figure

Protein tyrosine phosphatases as potential therapeutic targets

Protein tyrosine phosphorylation is a key regulatory process in virtually all aspects of cellular functions. Dysregulation of protein tyrosine phosphorylation is a major cause of human diseases, such as cancers, diabetes, autoimmune disorders, and neurological diseases. Indeed, protein tyrosine phosphorylation-mediated signaling events offer ample therapeutic targets, and drug discovery efforts to date have brought over two dozen kinase inhibitors to the clinic. Accordingly, protein tyrosine phosphatases (PTPs) are considered next-generation drug targets. For instance, PTP1B is a well-known targets of type 2 diabetes and obesity, and recent studies indicate that it is also a promising target for breast cancer. SHP2 is a bona-fide oncoprotein, mutations of which cause juvenile myelomonocytic leukemia, acute myeloid leukemia, and solid tumors. In addition, LYP is strongly associated with type 1 diabetes and many other autoimmune diseases. This review summarizes recent findings on several highly recognized PTP family drug targets, including PTP1B, Src homology phosphotyrosyl phosphatase 2(SHP2), lymphoid-specific tyrosine phosphatase (LYP), CD45, Fas associated phosphatase-1 (FAP-1), striatal enriched tyrosine phosphatases (STEP), mitogen-activated protein kinase/dual-specificity phosphatase 1 (MKP-1), phosphatases of regenerating liver-1 (PRL), low molecular weight PTPs (LMWPTP), and CDC25. Given that there are over 100 family members, we hope this review will serve as a road map for innovative drug discovery targeting PTPs

Functional examination of novel kisspeptin phosphinic peptides

Kisspeptins acting on their cognate G protein-coupled receptor, kisspeptin receptor, play important roles in the suppression of cancer cell metastasis and regulation of the reproductive system, and therefore are important for therapeutic intervention. All native functional human kisspeptins (kisspeptin-54, kisspsptin-14 and kisspeptin-13) share the 10 amino acids of kisspeptin-10 at their C-terminus (45–54). However, they are inactivated rapidly by matrix metalloproteinases (MMPs) through the cleavage of the peptide bond between glycine51 and leucine52, which limits their clinical applications. Development of MMP-resistant analogues of kisspeptins may provide better therapeutic outputs. In the present study, two kisspeptin phosphinic peptides were designed and synthesized, and their ability to induce phosphorylation of ERK1/2 through kisspeptin receptor and their inhibition on MMP-2 and MMP-9 whose activity correlates with cancer metastasis were assessed. The results showed that one analogue, phosphinic kisspeptin R isomer (PKPR), exhibited kisspeptin receptor-agonistic activity and also inhibitory activity on MMP-2, indicating that PKPR may serve as a lead for the further development of kisspeptin analogues for therapeutic purpose