arXiv subjects

Xianming Liu

Publications and source records attributed to Xianming Liu.

167 records · Page 10Linked to original sources

arXiv2015

Capacity Regions of Families of Continuous-Time Multi-User Gaussian Channels

In this paper, we propose to use Brownian motions to model families of continuous-time multiuser Gaussian channels without bandwidth limit. It turns out that such a formulation allows parallel translation of many fundamental notions and techniques from the discrete-time setting to the continuous-time regime, which enables us to derive the capacity regions of a continuous-time white Gaussian multiple access channel with/without feedback, a continuous-time white Gaussian interference channel without feedback and a continuous-time white Gaussian broadcast channel without feedback. In theory, these capacity results give the fundamental transmission limit modulation/coding schemes can achieve for families of continuous-time Gaussian one-hop channels without bandwidth limit; in practice, the explicit capacity regions derived and capacity achieving modulation/coding scheme proposed may provide engineering insights on designing multi-user communication systems operating on an ultra-wideband regime.

cs.IT↗

arXiv2015

Decentralized Recommender Systems

This paper proposes a decentralized recommender system by formulating the popular collaborative filleting (CF) model into a decentralized matrix completion form over a set of users. In such a way, data storages and computations are fully distributed. Each user could exchange limited information with its local neighborhood, and thus it avoids the centralized fusion. Advantages of the proposed system include a protection on user privacy, as well as better scalability and robustness. We compare our proposed algorithm with several state-of-the-art algorithms on the FlickerUserFavor dataset, and demonstrate that the decentralized algorithm can gain a competitive performance to others.

cs.IR↗

arXiv2013

Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems

This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable conditions, it is proved that an exponentially tracking random invariant manifold exists, eliminating the fast motion for this coupled system. It is further shown that if the scaling parameter tends to zero, the invariant manifold tends to a slow manifold which captures long time dynamics. As examples the results are applied to a few systems of coupled parabolic-hyperbolic partial differential equations, coupled parabolic partial differential-ordinary differential equations, and coupled hyperbolic-hyperbolic partial differential equations.

math.PR↗

arXiv2013

Small noise approximation of center manifolds for stochastic dynamical systems

This paper provides a small noise approximation for local random center manifolds of a class of stochastic dynamical systems in Euclidean space. An example is presented to illustrate the method.

math.DS↗

arXiv2009

Synchronization of dissipative dynamical systems driven by non-Gaussian Levy noises

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under non- Gaussian Levy noises is considered. After discussing cocycle prop- erty, stationary orbits and random attractors, a synchronization phe- nomenon is shown to occur, when the drift terms of the coupled system satisfy certain dissipativity and integrability conditions. The synchro- nization result implies that coupled dynamical systems share a dy- namical feature in some asymptotic sense.

math.DS↗