Rabbit Anti-Human TENN Polyclonal antibody

This letter considers the recovery of a low-tubal-rank tensor from incomplete linear observations. It is shown that the unknown tensor Z. Rn1 xn2 xn3 of tubal-rank r can be reconstructed as a unique solution of a tractable method - tensor nuclear norm (TNN) minimization, provided that the number of Gaussian observationsm = 3r(n1 + n2 - r)n3 + 1. In this work, we examine the fundamental question of the minimal number of linear observations needed to reconstruct the tensor Z from these observations, regardless of the practicality of the reconstruction scheme. Consequently, we provide two benchmark results so that different reconstruction schemes including TNNminimization can be compared to each other. Specifically, we conclude that m = 2r(n1 + n2 - 2r)n3 and m = r(n1 + n2 - r)n3 + 1 Gaussian observations are necessary and sufficient to guarantee uniform recovery and nonuniform recovery using tensor tubalrank minimization method, respectively.

We previously reported that effective treatment of chronic low back pain (CLBP) reversed abnormal brain structure and functional MRI (fMRI) activity during cognitive task performance, particularly in the left dorsolateral prefrontal cortex (DLPFC). Here, we used resting-state fMRI to examine how chronic pain affects connectivity of brain networks supporting cognitive functioning and the effect of treatment in 14 CLBP patients and 16 healthy, pain-free controls (scans were acquired at baseline for all subjects and at 6-months post-treatment for patients and a matched time-point for 10 controls). The main networks activated during cognitive task performance, task-positive network (TPN) and task-negative network (TNN) (aka default mode) network, were identified in subjects' task fMRI data and used to define matching networks in resting-state data. The connectivity of these cognitive resting-state networks was compared between groups, and before and after treatment. Our findings converged on the bilateral insula (INS) as the region of aberrant cognitive resting-state connectivity in patients pretreatment versus controls. These findings were complemented by an independent, data-driven approach showing altered global connectivity of the INS. Detailed investigation of the INS confirmed reduced connectivity to widespread TPN and TNN areas, which was partially restored post-treatment. Furthermore, analysis of diffusion-tensor imaging (DTI) data revealed structural changes in white matter supporting these findings. The left DLPFC also showed aberrant connectivity that was restored post-treatment. Altogether, our findings implicate the bilateral INS and left DLPFC as key nodes of disrupted cognition-related intrinsic connectivity in CLBP, and the resulting imbalance between TPN and TNN function is partially restored with treatment. Hum Brain Mapp 36:2075-2092, 2015. (c) 2015 Wiley Periodicals, Inc.