An Accelerated Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization

We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an accelerated randomized proximal coordinate gradient (APCG) method for minimizing such convex composite functions. For strongly convex functions, our method achieves faster linear convergence rates than existing randomized proximal coordinate gradient methods. Without strong convexity, our method enjoys accelerated sublinear convergence rates. We show how to apply the APCG method to solve the regularized empirical risk minimization (ERM) problem, and devise efficient implementations that avoid full-dimensional vector operations. For ill-conditioned ERM problems, our method obtains improved convergence rates than the state-of-the-art stochastic dual coordinate ascent (SDCA) method

Brain activity in advantageous and disadvantageous situations: implications for reward/punishment sensitivity in different situations

OBJECTIVE: This study modeled win and lose trials in a simple gambling task to examine the effect of entire win-lose situations (WIN, LOSS, or TIE) on single win/lose trials and related neural underpinnings. METHODS: The behavior responses and brain activities of 17 participants were recorded by an MRI scanner while they performed a gambling task. Different conditions were compared to determine the effect of the task on the behavior and brain activity of the participants. Correlations between brain activity and behavior were calculated to support the imaging results. RESULTS: In win trials, LOSS caused less intense posterior cingulate activity than TIE. In lose trials, LOSS caused more intense activity in the right superior temporal gyrus, bilateral superior frontal gyrus, bilateral anterior cingulate, bilateral insula cortex, and left orbitofrontal cortex than WIN and TIE. CONCLUSIONS: The experiences of the participants in win trials showed great similarity among different win-lose situations. However, the brain activity and behavior responses of the participants in lose trials indicated that they experienced stronger negative emotion in LOSS. The participants also showed an increased desire to win in LOSS than in WIN or TIE conditions

Large Magnetoresistance over an Extended Temperature Regime in Monophosphides of Tantalum and Niobium

We report extremely large magnetoresistance (MR) in an extended temperature regime from 1.5 K to 300 K in non-magnetic binary compounds TaP and NbP. TaP exhibits linear MR around $1.8\times 10^4$ at 2 K in a magnetic field of 9 Tesla, which further follows its linearity up to $1.4\times 10^5$ in a magnetic field of 56 Tesla at 1.5 K. At room temperature the MR for TaP and NbP follows a power law of the exponent about $1.5$ with the values larger than $300\%$ in a magnetic field of 9 Tesla. Such large MR in a wide temperature regime is not likely only due to a resonance of the electron-hole balance, but indicates a complicated mechanism underneath.Comment: 13 pages, 4 figures; submitted in May 20, 2015; accepted for publicatio