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5 results on '"High order Markov chain"'

1. A survey on the spectral theory of nonnegative tensors.

Author

Chang, Kungching, Qi, Liqun, and Zhang, Tan

Subjects
*SPECTRAL theory, *NONNEGATIVE matrices, *TENSOR algebra, *EIGENVALUES, *HYPERGRAPHS, *QUANTUM entanglement, *QUANTUM theory, *MARKOV processes
Abstract

SUMMARY This is a survey paper on the recent development of the spectral theory of nonnegative tensors and its applications. After a brief review of the basic definitions on tensors, the H-eigenvalue problem and the Z-eigenvalue problem for tensors are studied separately. To the H-eigenvalue problem for nonnegative tensors, the whole Perron-Frobenius theory for nonnegative matrices is completely extended, while to the Z-eigenvalue problem, there are many distinctions and are studied carefully in details. Numerical methods are also discussed. Three kinds of applications are studied: higher order Markov chains, spectral theory of hypergraphs, and the quantum entanglement. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2013
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2. Modelling precipitation in Sweden using multiple step markov chains and a composite model

Author

Lennartsson, Jan, Baxevani, Anastassia, and Chen, Deliang

Subjects
*METEOROLOGICAL precipitation, *MARKOV processes, *COPULA functions, *PARETO principle, *MATHEMATICAL models, *PROBABILITY theory, *STOCHASTIC processes
Abstract

Summary: In this paper, we propose a new method for modelling precipitation in Sweden. We consider a chain dependent stochastic model that consists of a component that models the probability of occurrence of precipitation at a weather station and a component that models the amount of precipitation at the station when precipitation does occur. For the first component, we show that for most of the weather stations in Sweden a Markov chain of an order higher than one is required. For the second component, which is a Gaussian process with transformed marginals, we use a composite of the empirical distribution of the amount of precipitation below a given threshold and the generalized Pareto distribution for the excesses in the amount of precipitation above the given threshold. The derived models are then used to compute different weather indices. The distribution of the modelled indices and the empirical ones show good agreement, which supports the choice of the model. [Copyright &y& Elsevier]

Published
2008
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3. A new statistical method for detecting network anomalies

Author

Callegari, Christian, Vaton, Sandrine, Pagano, Michele, TLC Network Research Group (TLCNETGRP), University of Pisa - Università di Pisa, Département informatique (INFO), Université européenne de Bretagne - European University of Brittany (UEB)-Télécom Bretagne-Institut Mines-Télécom [Paris] (IMT), and Télécom Bretagne (devenu IMT Atlantique), Ex-Bibliothèque

Subjects
Intrusion detection system, High order Markov chain, Anomaly detection, Computer Science::Cryptography and Security
Abstract

International audience; In the last few years, the number and impact of security attacks over the Internet have been continuously increasing. To face this issue, the use of Intrusion Detection Systems (IDSs) has emerged as a key element in network security. In this paper we address the problem considering a novel statistical technique for detecting network anomalies. Our approach is based on the use of different families of Markovian models (namely high order and non homogeneous Markov chains) for modeling network traffic running over TCP. The performance results shown in the paper, justify the proposed method and highlight the improvements over commonly used statistical techniques.

Published
2010

4. A new statistical approach to network anomaly detection

Author

CHRISTIAN CALLEGARI, Vaton, S., Pagano, M., TLC Network Research Group (TLCNETGRP), University of Pisa - Università di Pisa, Département informatique (INFO), Université européenne de Bretagne - European University of Brittany (UEB)-Télécom Bretagne-Institut Mines-Télécom [Paris] (IMT), and Télécom Bretagne (devenu IMT Atlantique), Ex-Bibliothèque

Subjects
[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.AP] Statistics [stat]/Applications [stat.AP], Intrusion detection system, High order Markov chain, Non-homogeneous Markov chain, Mixture transition model, [INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR], Computer Science::Cryptography and Security
Abstract

International audience; In the last few years, the number and impact of security attacks over the Internet have been continuously increasing. To face this issue, the use of Intrusion Detection Systems (IDSs) has emerged as a key element in network security. In this paper we address the problem considering a novel statistical technique for detecting network anomalies. Our approach is based on the use of different families of Markovian models (namely high order and non homogeneous Markov chains) for modeling network traffic running over TCP. The performance results shown in the paper, justify the proposed method and highlight the improvements over commonly used statistical techniques.

Published
2008

5. Modelling precipitation in Sweden using multiple step markov chains and a composite model

Author

Lennartsson, J., Baxevani, Anastassia, Chen, D., and Baxevani, Anastassia [0000-0002-7498-9048]

Subjects
Precipitation (chemical), precipitation (climatology), Meteorology, Stochastic modelling, Markov chain, Gaussian method, Northern Europe, hydrological modeling, Weather station, Copula (probability theory), Precipitation process, symbols.namesake, Generalized Pareto distribution, Applied mathematics, Precipitation, Gaussian process, Physics::Atmospheric and Oceanic Physics, Water Science and Technology, Mathematics, Sweden, stochasticity, Markov processes, Weather information services, Ketones, Empirical distribution function, Europe, Stochastic models, Probability distributions, Copula, weather, symbols, Eurasia, High order Markov chain, Scandinavia
Abstract

In this paper, we propose a new method for modelling precipitation in Sweden. We consider a chain dependent stochastic model that consists of a component that models the probability of occurrence of precipitation at a weather station and a component that models the amount of precipitation at the station when precipitation does occur. For the first component, we show that for most of the weather stations in Sweden a Markov chain of an order higher than one is required. For the second component, which is a Gaussian process with transformed marginals, we use a composite of the empirical distribution of the amount of precipitation below a given threshold and the generalized Pareto distribution for the excesses in the amount of precipitation above the given threshold. The derived models are then used to compute different weather indices. The distribution of the modelled indices and the empirical ones show good agreement, which supports the choice of the model. © 2008 Elsevier B.V. All rights reserved. 363 1-4 42 59 Cited By :23

Published
2008

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