Extended Kalman filters for nonlinear fractional-order systems perturbed by colored noises.

The fractional-order extended Kalman filter (FEKF) algorithm for a nonlinear fractional-order system perturbed by the colored noise is presented. Firstly, the first-order Taylor expansion is employed to linearize the nonlinear functions in the estimated system. Then, Grünwald-Letnikov difference (GLD) and the concept of fractional-order average derivative (FOAD) are employed to discretize nonlinear fractional-order systems perturbed by colored fractional-order process or measurement noise. An augmented system determined by the state and colored noises is presented to treat colored noises. Hence, the FEKFs using GLD and FOAD are carried out, respectively. By comparing two kinds of Kalman filters, FEKFs using FODA can gain the better effect of filtering for colored process or measurement noise to raise the estimation precision. Finally, we discuss three examples to show the validity of investigated FEKFs.

Long non-coding RNA snaR is involved in the metastasis of liver cancer possibly through TGF-ß1.

It was previously demonstrated that the long non-coding RNA (lncRNA) small NF90-associated RNA (snaR) served an oncogenic role in human colon cancer, although its roles in other types of cancer remain unknown. To investigate the potential involvement of lncRNA snaR in hepatocellular carcinoma (HCC), expression of snaR in liver biopsies and plasma of patients with HCC and healthy controls was detected by reverse transcription-quantitative polymerase chain reaction. ELISA was used to determine the protein expression levels of transforming growth factor-ß1 (TGF-ß1). A snaR expression vector was transfected into HCC cells, and the effects on cell migration and invasion were analyzed by Transwell migration and Matrigel invasion assays, respectively. The protein expression levels of TGF-ß1 in HCC cells were detected by western blotting. The expression of snaR and TGF-ß1 was significantly increased in the patients with HCC compared with the healthy controls. The plasma expression levels of snaR and TGF-ß1 were positively correlated in patients with HCC; however, not in healthy controls. snaR overexpression significantly promoted cancer cell migration and invasion, and additionally increased TGF-ß1 expression. Treatment with TGF-ß1 did not significantly affect snaR expression. A TGF-ß1 inhibitor attenuated the effects of snaR overexpression in cancer cell migration and invasion. snaR may promote the metastasis of liver cancer through TGF-ß1.