Sparsistency and agnostic inference in sparse PCA

The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? What can be said about the results of sparse PCA without assuming a sparse and unique truth? We answer these questions by investigating the properties of the recently proposed Fantope projection and selection (FPS) method in the high-dimensional setting. Our results provide general sufficient conditions for sparsistency of the FPS estimator. These conditions are weak and can hold in situations where other estimators are known to fail. On the other hand, without assuming sparsity or identifiability, we show that FPS provides a sparse, linear dimension-reducing transformation that is close to the best possible in terms of maximizing the predictive covariance.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1273 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the characteristics of emulsion chamber family events produced in low heights

The uncertainty of the primary cosmic ray composition at 10 to the 14th power -10 to the 16th power eV is well known to make the study of the nuclear interaction mechanism more difficult. Experimentally considering, if one can identify effectively the family events which are produced in low heights, then an event sample induced by primary protons might be able to be separated. It is undoubtedly very meaningful. In this paper an attempt is made to simulate the family events under the condition of mountain emulsion chamber experiments with a reasonable model. The aim is to search for the dependence of some experimentally observable quantities to the interaction height

Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit

We study a tripartite quantum system consisting of a coplanar-waveguide (CPW) resonator and a nanomechanical resonator (NAMR) connected by a flux qubit, where the flux qubit has a large detuning from both resonators. By a unitray transformation and a second-order approximation, we obtain a strong and controllable (i.e., magnetic-field-dependent) effective coupling between the NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting can be observed from the voltage-fluctuation spectrum of the CPW resonator. We further study the properties of single photon transport as inferred from the reflectance or equivalently the transmittance. We show that the reflectance and the corresponding phase shift spectra both exhibit doublet of narrow spectral features due to vacuum Rabi splitting. By tuning the external magnetic field, the reflectance and the phase shift can be varied from 0 to 1 and $-\pi$ to $\pi$, respectively. The results indicate that this hybrid quantum system can act as a quantum router.Comment: 8 pages, 6 figure