T-duality to Scattering Amplitude and Wilson Loop in Non-commutative Super Yang-Mills Theory

We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed $AdS_5\times S_5$ spacetime, which corresponds to 4D $\mathcal{N}=4$ non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual $AdS_5\times S_5$ but with the constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop) solution in the TsT-deformed $AdS_5\times S_5$ spacetime, which are dual to the null polygon Wilson loop and the folded string solution respectively in the final dual geometry.Comment: 24 pages, latex, references added, published versio

Proton Cumulants and Correlation Functions in Au + Au Collisions at sNN\sqrt{s_\mathrm{NN}}=7.7-200 GeV from UrQMD Model

We studied the acceptance dependence of proton cumulants (up to fourth order) and correlation functions in 0--5\% most central Au+Au collisions at $\sqrt{s_\text{NN}}$=7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV from UrQMD model. We found that high order proton cumulants show suppressions at large acceptance. By decomposing the proton cumulants into linear combination of multi-proton correlation functions, we observed the two-proton correlation functions always show negative values due to the effects of baryon number conservations. The three and four-proton correlation functions are close to zero and show negligible acceptance dependence. We further observed that the proton cumulants and correlation functions follow similar trends and show a scaling behavior when plotting the results versus mean number of protons. The comparisons between experimental data and the UrQMD calculations show that the non-monotonic energy dependence of proton correlation functions measured by STAR experiment cannot be described by the UrQMD model. The UrQMD calculations can provide us baselines for the experimental studies of the proton cumulants and correlation functions. Finally, we propose to measure the rapidity dependence of the reduced proton correlation functions to search for the QCD critical point in heavy-ion collisions.Comment: 9 pages, 8 figures, Accepted by Physics Letters

Filtering for networked stochastic time-delay systems with sector nonlinearity

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the filtering problem for a class of discrete-time stochastic nonlinear networked control systems with network-induced incomplete measurements. The incomplete measurements include both the multiple random communication delays and random packet losses, which are modeled by a unified stochastic expression in terms of a set of indicator functions that is dependent on certain stochastic variable. The nonlinear functions are assumed to satisfy the sector nonlinearities. The purpose of the addressed filtering problem is to design a linear filter such that the filtering-error dynamics is exponentially mean-square stable. By using the linear-matrix-inequality (LMI) method and delay-dependent technique, sufficient conditions are derived which are dependent on the occurrence probability of both the random communication delays and missing measurement. The filter gain is then characterized by the solution to a set of LMIs. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures