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Search Results: 1 - 10 of 81970 matches for " Tie Liu "
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Application of Markov Chains to Analyze and Predict the Time Series
Tie Liu
Modern Applied Science , 2010, DOI: 10.5539/mas.v4n5p162
Abstract: Markov chains are usually used in modeling many practical problems. They are also effective in modeling time series. In this paper, we apply the Markov chains model to analyze and predict the time series. Some series can be expressed by a first-order discrete-time Markov chain and others must be expressed by a higher-order Markov chain model. Numerical examples are given. The results show that the performance and effectiveness of the Markov chain model to predict the time series is very well.
Reliable Network Design Problem under Node Failure with Benders Decomposition  [PDF]
Tie Liu, Wenguo Yang, Jun Huang
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.52026

The design of telecommunication network with capacity constraints of links, routers and ports of routers is considered in this paper. Specially, we limit each demand flow traversed through a pre-specified maximal number of links (called hops) under node failure scenarios in IP layer network. Such a design must be the most cost-effective and ensure that feasible flows continue to exist even when any relay node of the network fails. We propose a reliable mixed-integer programming (MIP) model with multi-scenario constraints to optimally design a minimum-cost survivable IP network that continues to support a good communication under any node failure scenario. Then we transform the MIP model into many single scenario models, that is, simplified MIPs, nonlinear programming (NLP) models and MIP models under Benders decomposition Then we transform the MIP model into many single scenario models, that is, simplified MIPs, nonlinear programming (NLP) models and MIP models under Benders decomposition. Three heuristic methods are proposed to solve these models including branch-and-bound algorithm, global algorithm for NLP, and heuristic algorithm based on benders decomposition. We mainly study the application of Benders decomposition method, where dual model and bounding procedures are given for each MIP model under Benders decomposition at each scenario. The results of our computational experiments validate the effectiveness of the proposed models and algorithms.

Two Proofs of the Fisher Information Inequality via Data Processing Arguments
Tie Liu,Pramod Viswanath
Mathematics , 2006,
Abstract: Two new proofs of the Fisher information inequality (FII) using data processing inequalities for mutual information and conditional variance are presented.
An Extremal Inequality Motivated by Multiterminal Information Theoretic Problems
Tie Liu,Pramod Viswanath
Mathematics , 2006,
Abstract: We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the classical entropy-power inequality (EPI). As another corollary, this inequality sheds insight into maximizing the differential entropy of the sum of two dependent random variables.
A Note on the Secrecy Capacity of the Multi-antenna Wiretap Channel
Tie Liu,Shlomo Shamai
Mathematics , 2007,
Abstract: Recently, the secrecy capacity of the multi-antenna wiretap channel was characterized by Khisti and Wornell [1] using a Sato-like argument. This note presents an alternative characterization using a channel enhancement argument. This characterization relies on an extremal entropy inequality recently proved in the context of multi-antenna broadcast channels, and is directly built on the physical intuition regarding to the optimal transmission strategy in this communication scenario.
Private Broadcasting over Independent Parallel Channels
Ashish Khisti,Tie Liu
Mathematics , 2012,
Abstract: We study private broadcasting of two messages to two groups of receivers over independent parallel channels. One group consists of an arbitrary number of receivers interested in a common message, whereas the other group has only one receiver. Each message must be kept confidential from the receiver(s) in the other group. Each of the sub-channels is degraded, but the order of receivers on each channel can be different. While corner points of the capacity region were characterized in earlier works, we establish the capacity region and show the optimality of a superposition strategy. For the case of parallel Gaussian channels, we show that a Gaussian input distribution is optimal. We also discuss an extension of our setup to broadcasting over a block-fading channel and demonstrate significant performance gains using the proposed scheme over a baseline time-sharing scheme.
Multilevel Diversity Coding with Regeneration
Chao Tian,Tie Liu
Mathematics , 2015,
Abstract: Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage efficiency. At the same time, in such large scale distributed storage systems, nodes fail on a regular basis, and the contents stored on them need to be regenerated and stored on other healthy nodes, the efficiency of which is an important factor affecting the overall quality of service. In this work, we formulate the problem of multilevel diversity coding with regeneration to address these considerations, for which the storage vs. repair-bandwidth tradeoff is investigated. We show that the extreme point on this tradeoff corresponding to the minimum possible storage can be achieved by a simple coding scheme, where contents with different reliability requirements are encoded separately with individual regenerating codes without any mixing. On the other hand, we establish the complete storage-repair-bandwidth tradeoff for the case of four storage nodes, which reveals that codes mixing different contents can strictly improve this tradeoff over the separate coding solution.
Symmetric Two-User Gaussian Interference Channel with Common Messages
Quan Geng,Tie Liu
Computer Science , 2014,
Abstract: We consider symmetric two-user Gaussian interference channel with common messages. We derive an upper bound on the sum capacity, and show that the upper bound is tight in the low interference regime, where the optimal transmission scheme is to send no common messages and each receiver treats interference as noise. Our result shows that although the availability of common messages provides a cooperation opportunity for transmitters, in the low interference regime the presence of common messages does not help increase the sum capacity.
Establishment and Application of Cryptographic Library Model  [PDF]
Tie-Ming Liu, Lie-Hui Jiang, Jing Jing, Yuan-Yuan Zhang
Journal of Computer and Communications (JCC) , 2015, DOI: 10.4236/jcc.2015.35003

When doing reverse analysis of program’s binary codes, it is often to encounter the function of cryptographic library. In order to reduce workload, a cryptographic library model has been designed by analysts. Models use formalized approach to describe the frame of cryptology and the structure of cryptographic function, complete the mapping from cryptographic function property to its architecture, and accomplish the result presentation of data analysis and mapping at last. The model can solve two problems: the first one is to know the hierarchy of the cryptographic function in the library well; the second one is to know some kinds of information, such as related cryptology algorithm and protocol, etc. These function implements can display the result graphically. The model can find relevant knowledge for the analysts automatically and rapidly, which is helpful to the learning of the overall abstract structure of cryptology.


Liu Tie''''an,

光子学报 , 1997,
Abstract: This paper describes constitutional principle and sensitivity of temperature on the infraredmicroscope. According to the parameter of optical system and law of black -body] radiation andnoise equivalent power of the infrared detector, the formula of calculating NET is strictly inferred,which provide the important basis for the research and application of instruments in the microscopicmeasuring temperature.
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