Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems

We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with real-space quantum renormalization group method. As illustration examples, a one-dimensional and a two-dimensional $XY$ models are considered. It is shown that the quantum phase transitions of these spin-chain systems can be revealed by the singular behaviors of the first derivatives of renormalized trace distance and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized trace distance and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical points

Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy

We update gamma-ray burst (GRB) luminosity relations among certain spectral and light-curve features with 139 GRBs. The distance modulus of 82 GRBs at $z>1.4$ can be calibrated with the sample at $z\leq1.4$ by using the cubic spline interpolation method from the Union2.1 Type Ia supernovae (SNe Ia) set. We investigate the joint constraints on the Cardassian expansion model and dark energy with 580 Union2.1 SNe Ia sample ($z<1.4$) and 82 calibrated GRBs data ($1.4<z\leq8.2$). In $\Lambda$CDM, we find that adding 82 high-\emph{z} GRBs to 580 SNe Ia significantly improves the constrain on $\Omega_{m}-\Omega_{\Lambda}$ plane. In the Cardassian expansion model, the best fit is $\Omega_{m}= 0.24_{-0.15}^{+0.15}$ and $n=0.16_{-0.52}^{+0.30}$ $(1\sigma)$, which is consistent with the $\Lambda$CDM cosmology $(n=0)$ in the $1\sigma$ confidence region. We also discuss two dark energy models in which the equation of state $w(z)$ is parametrized as $w(z)=w_{0}$ and $w(z)=w_{0}+w_{1}z/(1+z)$, respectively. Based on our analysis, we see that our Universe at higher redshift up to $z=8.2$ is consistent with the concordance model within $1\sigma$ confidence level.Comment: 17 pages, 6 figures, 2 tables; accepted for publication in Advances in Astronomy, special issue on Gamma-Ray Burst in Swift and Fermi Era. arXiv admin note: text overlap with arXiv:0802.4262, arXiv:0706.0938 by other author

Beyond Keywords and Relevance: A Personalized Ad Retrieval Framework in E-Commerce Sponsored Search

On most sponsored search platforms, advertisers bid on some keywords for their advertisements (ads). Given a search request, ad retrieval module rewrites the query into bidding keywords, and uses these keywords as keys to select Top N ads through inverted indexes. In this way, an ad will not be retrieved even if queries are related when the advertiser does not bid on corresponding keywords. Moreover, most ad retrieval approaches regard rewriting and ad-selecting as two separated tasks, and focus on boosting relevance between search queries and ads. Recently, in e-commerce sponsored search more and more personalized information has been introduced, such as user profiles, long-time and real-time clicks. Personalized information makes ad retrieval able to employ more elements (e.g. real-time clicks) as search signals and retrieval keys, however it makes ad retrieval more difficult to measure ads retrieved through different signals. To address these problems, we propose a novel ad retrieval framework beyond keywords and relevance in e-commerce sponsored search. Firstly, we employ historical ad click data to initialize a hierarchical network representing signals, keys and ads, in which personalized information is introduced. Then we train a model on top of the hierarchical network by learning the weights of edges. Finally we select the best edges according to the model, boosting RPM/CTR. Experimental results on our e-commerce platform demonstrate that our ad retrieval framework achieves good performance