12,175 research outputs found
Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations
Asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations (SFDEs) (see e.g. Appleby and Reynolds (2008), Appleby and Rodkina (2009), Basin and Rodkina (2008), Khasminskii (1980), Mao (1995), Mao (1997), Mao (2007), Rodkina and Basin (2007), Shu, Lam, and Xu (2009), Yang, Gao, Lam, and Shi (2009), Yuan and Lygeros (2005) and Yuan and Lygeros (2006)). In general, the existing results on asymptotic stability and boundedness of SFDEs require (i) the coefficients of the SFDEs obey the local Lipschitz condition and the linear growth condition; (ii) the diffusion operator of the SFDEs acting on a C2,1-function be bounded by a polynomial with the same order as the C2,1-function. However, there are many SFDEs which do not obey the linear growth condition. Moreover, for such highly nonlinear SFDEs, the diffusion operator acting on a C2,1-function is generally bounded by a polynomial with a higher order than the C2,1-function. Hence the existing criteria on stability and boundedness for SFDEs are not applicable andwesee the necessity to develop new criteria. Our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up-bound for the diffusion operator may take a much more general form
Linguistic Geometries for Unsupervised Dimensionality Reduction
Text documents are complex high dimensional objects. To effectively visualize
such data it is important to reduce its dimensionality and visualize the low
dimensional embedding as a 2-D or 3-D scatter plot. In this paper we explore
dimensionality reduction methods that draw upon domain knowledge in order to
achieve a better low dimensional embedding and visualization of documents. We
consider the use of geometries specified manually by an expert, geometries
derived automatically from corpus statistics, and geometries computed from
linguistic resources.Comment: 13 pages, 15 figure
5G Ultra-dense networks with non-uniform Distributed Users
User distribution in ultra-dense networks (UDNs) plays a crucial role in
affecting the performance of UDNs due to the essential coupling between the
traffic and the service provided by the networks. Existing studies are mostly
based on the assumption that users are uniformly distributed in space. The
non-uniform user distribution has not been widely considered despite that it is
much closer to the real scenario. In this paper, Radiation and Absorbing model
(R&A model) is first adopted to analyze the impact of the non-uniformly
distributed users on the performance of 5G UDNs. Based on the R&A model and
queueing network theory, the stationary user density in each hot area is
investigated. Furthermore, the coverage probability, network throughput and
energy efficiency are derived based on the proposed theoretical model. Compared
with the uniformly distributed assumption, it is shown that non-uniform user
distribution has a significant impact on the performance of UDNs.Comment: 14 pages, 10 figure
Domain knowledge, uncertainty, and parameter constraints
Ph.D.Committee Chair: Guy Lebanon; Committee Member: Alex Shapiro; Committee Member: Alexander Gray; Committee Member: Chin-Hui Lee; Committee Member: Hongyuan Zh
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