Ricci flow on K\"ahler-Einstein manifolds

In our previous paper math.DG/0010008, we develop some new techniques in attacking the convergence problems for the K\"ahler Ricci flow. The one of main ideas is to find a set of new functionals on curvature tensors such that the Ricci flow is the gradient like flow of these functionals. We successfully find such functionals in case of Kaehler manifolds. On K\"ahler-Einstein manifold with positive scalar curvature, if the initial metric has positive bisectional curvature, we prove that these functionals have a uniform lower bound, via the effective use of Tian's inequality. Consequently, we prove the following theorem: Let $M$ be a K\"ahler-Einstein manifold with positive scalar curvature. If the initial metric has nonnegative bisectional curvature and positive at least at one point, then the K\"ahler Ricci flow will converge exponentially fast to a K\"ahler-Einstein metric with constant bisectional curvature. Such a result holds for K\"ahler-Einstein orbifolds.Comment: 49 pages. This is a revised version. Sections 4 and 5 are simplified and streamline

Strongly Coupled Inflaton

We continue to investigate properties of the strongly coupled inflaton in a setup introduced in arXiv:0807.3191 through the AdS/CFT correspondence. These properties are qualitatively different from those in conventional inflationary models. For example, in slow-roll inflation, the inflaton velocity is not determined by the shape of potential; the fine-tuning problem concerns the dual infrared geometry instead of the potential; the non-Gaussianities such as the local form can naturally become large.Comment: 12 pages; v3, minor revision, comments and reference added, JCAP versio

Rigidity theorems for submetries in positive curvature

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Network support for integrated design

A framework of network support for utilization of integrated design over the Internet has been developed. The techniques presented also applicable for Intranet/Extranet. The integrated design system was initially developed for local application in a single site. With the network support, geographically dispersed designers can collaborate a design task through out the total design process, quickly respond to clients’ requests and enhance the design argilty. In this paper, after a brief introduction of the integrated design system, the network support framework is presented, followed by description of two key techniques involved: Java Saverlet approach for remotely executing a large program and online CAD collaboration

Privacy-Preserving Outsourcing of Large-Scale Nonlinear Programming to the Cloud

The increasing massive data generated by various sources has given birth to big data analytics. Solving large-scale nonlinear programming problems (NLPs) is one important big data analytics task that has applications in many domains such as transport and logistics. However, NLPs are usually too computationally expensive for resource-constrained users. Fortunately, cloud computing provides an alternative and economical service for resource-constrained users to outsource their computation tasks to the cloud. However, one major concern with outsourcing NLPs is the leakage of user's private information contained in NLP formulations and results. Although much work has been done on privacy-preserving outsourcing of computation tasks, little attention has been paid to NLPs. In this paper, we for the first time investigate secure outsourcing of general large-scale NLPs with nonlinear constraints. A secure and efficient transformation scheme at the user side is proposed to protect user's private information; at the cloud side, generalized reduced gradient method is applied to effectively solve the transformed large-scale NLPs. The proposed protocol is implemented on a cloud computing testbed. Experimental evaluations demonstrate that significant time can be saved for users and the proposed mechanism has the potential for practical use.Comment: Ang Li and Wei Du equally contributed to this work. This work was done when Wei Du was at the University of Arkansas. 2018 EAI International Conference on Security and Privacy in Communication Networks (SecureComm