Forecast Combination Under Heavy-Tailed Errors

Forecast combination has been proven to be a very important technique to obtain accurate predictions. In many applications, forecast errors exhibit heavy tail behaviors for various reasons. Unfortunately, to our knowledge, little has been done to deal with forecast combination for such situations. The familiar forecast combination methods such as simple average, least squares regression, or those based on variance-covariance of the forecasts, may perform very poorly. In this paper, we propose two nonparametric forecast combination methods to address the problem. One is specially proposed for the situations that the forecast errors are strongly believed to have heavy tails that can be modeled by a scaled Student's t-distribution; the other is designed for relatively more general situations when there is a lack of strong or consistent evidence on the tail behaviors of the forecast errors due to shortage of data and/or evolving data generating process. Adaptive risk bounds of both methods are developed. Simulations and a real example show superior performance of the new methods

Nucleation of membrane adhesions

Recent experimental and theoretical studies of biomimetic membrane adhesions [Bruinsma et al., Phys. Rev. E 61, 4253 (2000); Boulbitch et al., Biophys. J. 81, 2743 (2001)] suggested that adhesion mediated by receptor interactions is due to the interplay between membrane undulations and a double-well adhesion potential, and should be a first-order transition. We study the nucleation of membrane adhesion by finding the minimum-energy path on the free energy surface constructed from the bending free energy of the membrane and the double-well adhesion potential. We find a nucleation free energy barrier around 20kBT for adhesion of flexible membranes, which corresponds to fast nucleation kinetics with a time scale of the order of seconds. For cell membranes with a larger bending rigidity due to the actin network, the nucleation barrier is higher and may require active processes such as the reorganization of the cortex network to overcome this barrier. Our scaling analysis suggests that the geometry of the membrane shapes of the adhesion contact is controlled by the adhesion length that is determined by the membrane rigidity, the barrier height, and the length scale of the double-well potential, while the energetics of adhesion is determined by the depths of the adhesion potential. These results are verified by numerical calculations

Multiagent model and mean field theory of complex auction dynamics

Acknowledgements We are grateful to Ms Yinan Zhao for providing the data and to Yuzhong Chen and Cancan Zhou for discussions and suggestions. This work was supported by ARO under Grant No. W911NF-14-1-0504 and by NSFC under Grants Nos. 11275003 and 61174165. The visit of QC to Arizona State University was partially sponsored by the State Scholarship Fund of China.Peer reviewedPublisher PD