Strong completeness for a class of stochastic differential equations with irregular coefficients

We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\cdot)$ belongs to the Sobolev space W_{\loc}^{1,p}. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained

Strongly interacting matter from holographic QCD model

We introduce the 5-dimension dynamical holographic QCD model, which is constructed in the graviton-dilaton-scalar framework with the dilaton background field $\Phi$ and the scalar field $X$ responsible for the gluodynamics and chiral dynamics, respectively. We review our results on the hadron spectra including the glueball and light meson spectra, QCD phase transitions and transport properties in the framework of the dynamical holographic QCD model.Comment: 8 pages, 8 figures, proceedings for QCD@Work2016, June 27-30,2014, Martina Franca, Italy. arXiv admin note: text overlap with arXiv:1409.843

Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models

Criticality of chiral phase transition at finite temperature is investigated in a soft-wall AdS/QCD model with $SU_L(N_f)\times SU_R(N_f)$ symmetry, especially for $N_f=2,3$ and $N_f=2+1$. It is shown that in quark mass plane($m_{u/d}-m_s$) chiral phase transition is second order at a certain critical line, by which the whole plane is divided into first order and crossover regions. The critical exponents $\beta$ and $\delta$, describing critical behavior of chiral condensate along temperature axis and light quark mass axis, are extracted both numerically and analytically. The model gives the critical exponents of the values $\beta=\frac{1}{2}, \delta=3$ and $\beta=\frac{1}{3}, \delta=3$ for $N_f=2$ and $N_f=3$ respectively. For $N_f=2+1$, in small strange quark mass($m_s$) region, the phase transitions for strange quark and $u/d$ quarks are strongly coupled, and the critical exponents are $\beta=\frac{1}{3},\delta=3$; when $m_s$ is larger than $m_{s,t}=0.290\rm{GeV}$, the dynamics of light flavors($u,d$) and strange quarks decoupled and the critical exponents for $\bar{u}u$ and $\bar{d}d$ becomes $\beta=\frac{1}{2},\delta=3$, exactly the same as $N_f=2$ result and the mean field result of 3D Ising model; between the two segments, there is a tri-critical point at $m_{s,t}=0.290\rm{GeV}$, at which $\beta=0.250,\delta=4.975$. In some sense, the current results is still at mean field level, and we also showed the possibility to go beyond mean field approximation by including the higher power of scalar potential and the temperature dependence of dilaton field, which might be reasonable in a full back-reaction model. The current study might also provide reasonable constraints on constructing a realistic holographic QCD model, which could describe both chiral dynamics and glue-dynamics correctly.Comment: 32 pages, 11 figures, regular articl

Physical Layer Service Integration in 5G: Potentials and Challenges

High transmission rate and secure communication have been identified as the key targets that need to be effectively addressed by fifth generation (5G) wireless systems. In this context, the concept of physical-layer security becomes attractive, as it can establish perfect security using only the characteristics of wireless medium. Nonetheless, to further increase the spectral efficiency, an emerging concept, termed physical-layer service integration (PHY-SI), has been recognized as an effective means. Its basic idea is to combine multiple coexisting services, i.e., multicast/broadcast service and confidential service, into one integral service for one-time transmission at the transmitter side. This article first provides a tutorial on typical PHY-SI models. Furthermore, we propose some state-of-the-art solutions to improve the overall performance of PHY-SI in certain important communication scenarios. In particular, we highlight the extension of several concepts borrowed from conventional single-service communications, such as artificial noise (AN), eigenmode transmission etc., to the scenario of PHY-SI. These techniques are shown to be effective in the design of reliable and robust PHY-SI schemes. Finally, several potential research directions are identified for future work.Comment: 12 pages, 7 figure

Artificial Noise-Aided Biobjective Transmitter Optimization for Service Integration in Multi-User MIMO Gaussian Broadcast Channel

This paper considers an artificial noise (AN)-aided transmit design for multi-user MIMO systems with integrated services. Specifically, two sorts of service messages are combined and served simultaneously: one multicast message intended for all receivers and one confidential message intended for only one receiver and required to be perfectly secure from other unauthorized receivers. Our interest lies in the joint design of input covariances of the multicast message, confidential message and artificial noise (AN), such that the achievable secrecy rate and multicast rate are simultaneously maximized. This problem is identified as a secrecy rate region maximization (SRRM) problem in the context of physical-layer service integration. Since this bi-objective optimization problem is inherently complex to solve, we put forward two different scalarization methods to convert it into a scalar optimization problem. First, we propose to prefix the multicast rate as a constant, and accordingly, the primal biobjective problem is converted into a secrecy rate maximization (SRM) problem with quality of multicast service (QoMS) constraint. By varying the constant, we can obtain different Pareto optimal points. The resulting SRM problem can be iteratively solved via a provably convergent difference-of-concave (DC) algorithm. In the second method, we aim to maximize the weighted sum of the secrecy rate and the multicast rate. Through varying the weighted vector, one can also obtain different Pareto optimal points. We show that this weighted sum rate maximization (WSRM) problem can be recast into a primal decomposable form, which is amenable to alternating optimization (AO). Then we compare these two scalarization methods in terms of their overall performance and computational complexity via theoretical analysis as well as numerical simulation, based on which new insights can be drawn.Comment: 14 pages, 5 figure