Achieving Anisotropy in Metamaterials made of Dielectric Cylindrical Rods

We show that anisotropic negative effective dispersion relation can be achieved in pure dielectric rod-type metamaterials by turning from the symmetry of a square lattice to that of a rectangular one, i.e. by breaking the rotation symmetry of effective homogeneous medium. Theoretical predictions and conclusions are verified by both numerical calculations and computer based simulations. The proposed anisotropic metamaterial, is used to construct a refocusing slab-lens and a subdiffraction hyperlens. The all-dielectric origin makes it more straightforward to address loss and scaling, two major issues of metallic structures, thus facilitating future applications in both the terahertz and optical range.Comment: Accepted for AP

Criterion on remote clocks synchronization within a Heisenberg scaling accuracy

We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $\sigma$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is smaller than $\sigma$; otherwise the difference is beyond $\sigma$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $\sigma\sim{\pi}/{(\omega(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condition is not necessary.Comment: 5 pages, 1 figur

Assembly Bias of Dwarf-sized Dark Matter Haloes

Previous studies indicate that assembly bias effects are stronger for lower mass dark matter haloes. Here we make use of high resolution re-simulations of rich clusters and their surroundings from the Phoenix Project and a large volume cosmological simulation, the Millennium-II run, to quantify assembly bias effects on dwarf-sized dark matter haloes. We find that, in the regions around massive clusters, dwarf-sized haloes ([10^9,10^{11}]\ms) form earlier ($\Delta z \sim 2$ in redshift) and possess larger $V_{\rm max}$ ($\sim20$) than the field galaxies. We find that this environmental dependence is largely caused by tidal interactions between the ejected haloes and their former hosts, while other large scale effects are less important. Finally we assess the effects of assembly bias on dwarf galaxy formation with a sophisticated semi-analytical galaxy formation model. We find that the dwarf galaxies near massive clusters tend to be redder ($\Delta(u-r) = 0.5$) and have three times as much stellar mass compared to the field galaxies with the same halo mass. These features should be seen with observational data.Comment: 8 pages, 8 figures, accepted by MNRA

Self-Paced Learning: an Implicit Regularization Perspective

Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by minimizer function. Existing methods usually pursue this by artificially designing the explicit form of SPL regularizer. In this paper, we focus on the minimizer function, and study a group of new regularizer, named self-paced implicit regularizer that is deduced from robust loss function. Based on the convex conjugacy theory, the minimizer function for self-paced implicit regularizer can be directly learned from the latent loss function, while the analytic form of the regularizer can be even known. A general framework (named SPL-IR) for SPL is developed accordingly. We demonstrate that the learning procedure of SPL-IR is associated with latent robust loss functions, thus can provide some theoretical inspirations for its working mechanism. We further analyze the relation between SPL-IR and half-quadratic optimization. Finally, we implement SPL-IR to both supervised and unsupervised tasks, and experimental results corroborate our ideas and demonstrate the correctness and effectiveness of implicit regularizers.Comment: 12 pages, 3 figure