Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle

Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate.Comment: 28 page

Measuring robustness of community structure in complex networks

The theory of community structure is a powerful tool for real networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks obtained from complex systems always contain error edges, evaluating the robustness of community structure is an urgent and important task. In this letter, we employ the critical threshold of resolution parameter in Hamiltonian function, $\gamma_C$, to measure the robustness of a network. According to spectral theory, a rigorous proof shows that the index we proposed is inversely proportional to robustness of community structure. Furthermore, by utilizing the co-evolution model, we provides a new efficient method for computing the value of $\gamma_C$. The research can be applied to broad clustering problems in network analysis and data mining due to its solid mathematical basis and experimental effects.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1303.7434 by other author

Giant Magnons and Spiky Strings on S^3 with B-field

We study solutions for a rotating string on S^3 with a background NS-NS B-field and show the existence of spiky string and giant magnon as two limiting solutions. We make a connection to the sine-Gordon model via the Polyakov worldsheet action and study the effect of B-field. In particular, we find the magnon solution can be mapped to the excitation of a fractional spin chain. We conjecture a B-deformed SYM to be the gauge theory dual to this background.Comment: 22 pages, 3 figures, more references adde

High pTp_T Parton Energy Loss from Jet Pair Correlation Observables in the PHENIX Experiment

By tuning several experimental observables, such as momentum and reaction plane, the PHENIX experiment has performed a systematic study of high $p_T$ parton energy loss in hot nuclear matter, as well as jet induced medium modifications, such as the ridge and shoulder. Baseline d+Au measurements are also studied to provide the comparison as control of cold nuclear matter effect.Comment: 4 pages, 6 figures. To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee, with minor correctio