Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities

Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact confidence regions and confidence intervals for the solution of the normal map formulation, based on the asymptotic distribution of SAA solutions. The confidence regions are single ellipsoids with high probability. We also discuss the computation of simultaneous and individual confidence intervals

Search for Sub-eV Sterile Neutrinos in the Precision Multiple Baselines Reactor Antineutrino Oscillation Experiments

According to different effects on neutrino oscillations, the unitarity violation in the MNSP matrix can be classified into the direct unitarity violation and the indirect unitarity violation which are induced by the existence of the light and the heavy sterile neutrinos respectively. Of which sub-eV sterile neutrinos are of most interesting. We study in this paper the possibility of searching for sub-eV sterile neutrinos in the precision reactor antineutrino oscillation experiments with three different baselines at around 500 m, 2 km and 60 km. We find that the antineutrino survival probabilities obtained in the reactor experiments are sensitive only to the direct unitarity violation and offer very concentrated sensitivity to the two parameters $\theta^{}_{14}$ and $\Delta m^{2}_{41}$. If such light sterile neutrinos do exist, the active-sterile mixing angle $\theta^{}_{14}$ could be acquired by the combined rate analysis at all the three baselines and the mass-squared difference $\Delta m^{2}_{41}$ could be obtained by taking the Fourier transformation to the L / E spectrum. Of course, for such measurements to succeed, both high energy resolution and large statistics are essentially important.Comment: 19 RevTex pages, 7 figures. text structure rearranged, some figures deleted, more discussions and references added; to be appear in NP

A useful way to obtain the central charge of entanglement Hamiltonian -- Nested entanglement entropy

In this paper, we review how to obtain the central charge of a critical entanglement Hamiltonian through the nested entanglement entropy which was first introduced in [J. Lou et al. PRB 84, 245128 (2011)]. The critical phenomena of the entanglement Hamiltonian can be identified by the central charge obtained by the nested entanglement entropy. We review our previous studies[J. Lou et al. PRB 84, 245128 (2011), S. Tanaka et al. PRA 87, 214401 (2013)] in which we investigated certain entanglement nature of two-dimensional valence-bond-solid (VBS) state and quantum hard-square models on square and triangle ladders using the nested entanglement entropy.Comment: 5 pages, 3 figures, to appear in Interdisciplinary Information Science