As one of major challenges, cold-start problem plagues nearly all recommender systems. In particular, new items will be overlooked, impeding the development of new products online. Given limited resources, how to utilize the knowledge of recommender
systems and design efficient marketing strategy for new items is extremely important. In this paper, we convert this ticklish issue into a clear mathematical problem based on a bipartite network representation. Under the most widely used algorithm in real e-commerce recommender systems, so-called the item-based collaborative filtering, we show that to simply push new items to active users is not a good strategy. To our surprise, experiments on real recommender systems indicate that to connect new items with some less active users will statistically yield better performance, namely these new items will have more chance to appear in other users recommendation lists. Further analysis suggests that the disassortative nature of recommender systems contributes to such observation. In a word, getting in-depth understanding on recommender systems could pave the way for the owners to popularize their cold-start products with low costs.
Using a radio frequency tunnel diode oscillator technique, we measured the temperature dependence of the in-plane London penetration depth $Deltalambda_{ab}(T)$ in Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$ single crystals, down to temperatures as low as 50 mK.
A significant number of samples, with nominal Se concentration $x$=0.36, 0.40, 0.43 and 0.45 respectively, were studied and in many cases we found that $Deltalambda_{ab}(T)$ shows an upturn below 0.7 K, indicative of a paramagnetic type contribution. After subtracting the magnetic background, the low temperature behavior of penetration depth is best described by a power law with exponent $napprox2$ and with no systematic dependence on the Se concentration. Most importantly, in the limit of T$rightarrow$0, in some samples we observed a narrow region of linear temperature dependence of penetration depth, suggestive of nodes in the superconducting gap of Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$.
In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplac
es equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplaces equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplaces equation. Full-wave simulations based on the Maxwells equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena.
We propose a general method to evaluate the material parameters for arbitrary shape transformation media. By solving the original coordinates in the transformed region via Laplaces equations, we can obtain the deformation field numerically, in turn t
he material properties of the devices to be designed such as cloaks, rotators or concentrators with arbitrary shape. Devices which have non-fixed outer boundaries, such as beam guider, can also be designed by the proposed method. Examples with full wave simulation are given for illustration. In the end, wave velocity and energy change in the transformation media are discussed with help of the deformation view.
