Multiagent model and mean field theory of complex auction dynamics

Acknowledgements We are grateful to Ms Yinan Zhao for providing the data and to Yuzhong Chen and Cancan Zhou for discussions and suggestions. This work was supported by ARO under Grant No. W911NF-14-1-0504 and by NSFC under Grants Nos. 11275003 and 61174165. The visit of QC to Arizona State University was partially sponsored by the State Scholarship Fund of China.Peer reviewedPublisher PD

An Examination of the Editors and Friendship of the Tang Songs and Poems in the Classification of the Categories

Zhao Mengkui’s compilation of Tang poems is one of the largest collections of Tang poems in the Southern Song Dynasty, and has served as a guide in the history of the compilation of Chinese Tang poems. Zhao Mengkui, the compiler of the “Tang Songs and Poems”, was born into a royal family of imperial examiners and had excellent family roots and profound academic training. The problem of the different records of Zhao Mengkui’s origin is due to the fact that he lived in a different place of official transfer. In his life, Zhao Mengkui had a close personal friendship with Liu Kezhuang, Li Qianwei, Lin Xiyi, and other literati. It is an important reference value for the study of the compilation of the Tang Songs and Poems

Grating-Free nth order cascaded Raman fibre lasers using highly Ge-Doped low loss fibre

Yucheng Zhao, Yahua Li, and Stuart D. Jackso

Geochemitry of the Xiong’er volcanic rocks: implications for the Paleo-Mesoproterozoic accretion of the North China Craton

This journal supplement has title: Awards Ceremony Speeches and Abstracts of the 19th Annual V.M. Goldschmidt ConferenceThe Xiong.er volcanic belt along the southern margin of the North China Craton is dominated by basaltic andesite and andesite with minor dacite and rhyolite. Geochemically, the Xiong.er volcanic rocks fall in the calc-alkaline series, with enrichments in the LILE and LREE, and negative anomalies on Nb-Ta-Ti, similar to arc-related volcanic rocks (He et al. 2008; Zhao et al. 2009). Available SHRIMP and LA-ICP-MS U-Pb zircon age data indicate that the volcanism forming the Xiong.er volcanic rocks erupted intermittently over a protracted interval from 1.78 Ga, through 1.76-1.75 Ga and 1.65 Ga, to 1.45 Ga, though a major phase of the volcanism occurred at 1.78-175 Ga (He et al. 2009). Taken together, the Xiong.er volcanic belt was most likely a Paleo-Mesoproterozoic continental magmatic arc at the southern margin of the North China Craton. Age-similar continental magmatic arcs were also present at the southeastern margin of Laurentia, southern margin of Baltica, northwestern margin of Amonzonia, and southern and eastern margins of the North Australia Craton, which are considered to represent subduction-related outbuilding on the continental margins of the supercontinent Columbia (Zhao et al. 2004).postprintThe 19th Annual Goldschmidt Conference, Davos, Switzerland, 21-26 June 2009. In Geochimica et Cosmochimica Acta, 2009, v. 73 n. 13 suppl., p. A151

The number of independent sets in a graph with small maximum degree

Let ${\rm ind}(G)$ be the number of independent sets in a graph $G$. We show that if $G$ has maximum degree at most $5$ then $${\rm ind}(G) \leq 2^{{\rm iso}(G)} \prod_{uv \in E(G)} {\rm ind}(K_{d(u),d(v)})^{\frac{1}{d(u)d(v)}}$$ (where $d(\cdot)$ is vertex degree, ${\rm iso}(G)$ is the number of isolated vertices in $G$ and $K_{a,b}$ is the complete bipartite graph with $a$ vertices in one partition class and $b$ in the other), with equality if and only if each connected component of $G$ is either a complete bipartite graph or a single vertex. This bound (for all $G$) was conjectured by Kahn. A corollary of our result is that if $G$ is $d$-regular with $1 \leq d \leq 5$ then $${\rm ind}(G) \leq \left(2^{d+1}-1\right)^\frac{|V(G)|}{2d},$$ with equality if and only if $G$ is a disjoint union of $V(G)/2d$ copies of $K_{d,d}$. This bound (for all $d$) was conjectured by Alon and Kahn and recently proved for all $d$ by the second author, without the characterization of the extreme cases. Our proof involves a reduction to a finite search. For graphs with maximum degree at most $3$ the search could be done by hand, but for the case of maximum degree $4$ or $5$, a computer is needed.Comment: Article will appear in {\em Graphs and Combinatorics

Zhao v. Atty Gen USA

USDC for the Eastern District of Pennsylvani