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550
ESTIMATION OF THE SPECTRAL EXPONENT OF 1 = f γ PROCESS CORRUPTED BYWHITE NOISE
"... 1 = f γ noise is used to model a large number of processes; such as network trafc data, GPS (Global Positioning System) noise, nancial and biological data. However, observations on real data have shown that assumption of a purely 1 = f γmodel may be inadequate, as the measured data may contain tre ..."
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1 = f γ noise is used to model a large number of processes; such as network trafc data, GPS (Global Positioning System) noise, nancial and biological data. However, observations on real data have shown that assumption of a purely 1 = f γmodel may be inadequate, as the measured data may contain trend, periodicity or noise. These are considerable factors effecting the estimation of γ. In this work, we examine real data from GPS noise and network trafc data and apply a wavelet based method for the removal of the effect of white noise in these data sets. 1.
doi:10.1155/2007/63219 Research Article Estimation of Spectral Exponent Parameter of 1/f Process in Additive White Background Noise
"... An extension to the waveletbased method for the estimation of the spectral exponent, γ,ina1/f γ process and in the presence of additive white noise is proposed. The approach is based on eliminating the effect of white noise by a simple difference operation constructed on the wavelet spectrum. The γ ..."
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An extension to the waveletbased method for the estimation of the spectral exponent, γ,ina1/f γ process and in the presence of additive white noise is proposed. The approach is based on eliminating the effect of white noise by a simple difference operation constructed on the wavelet spectrum
The Joint Spectral Radius
, 2001
"... 72. [115] F. Wirth, Dynamics of timevarying discretetime linear systems: Spectral theory and the projected system, SIAM J. Control Optim., 36(2), (1998):447487. [116] F. Wirth, On stability of in [110] J.N. Tsitsiklis and V. Blondel, The Lyapunov exponent and joint spectral radius of pairs of m ..."
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Cited by 130 (2 self)
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72. [115] F. Wirth, Dynamics of timevarying discretetime linear systems: Spectral theory and the projected system, SIAM J. Control Optim., 36(2), (1998):447487. [116] F. Wirth, On stability of in [110] J.N. Tsitsiklis and V. Blondel, The Lyapunov exponent and joint spectral radius of pairs
The Lyapunov exponent and joint spectral radius of pairs of matrices are hard  when not impossible  to compute and to approximate
, 1997
"... We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities  the lower spectral radius and th ..."
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Cited by 94 (18 self)
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We analyse the computability and the complexity of various definitions of spectral radii for sets of matrices. We show that the joint and generalized spectral radii of two integer matrices are not approximable in polynomial time, and that two related quantities  the lower spectral radius
An emerging groundbased aerosol climatology: Aerosol Optical Depth from AERONET
 J. Geophys. Res
, 2001
"... Abstract. Longterm measurements by the AERONET program of spectral aerosol optical depth, precipitable water, and derived Angstrom exponent were analyzed and compiled into an aerosol optical properties climatology. Quality assured monthly means are presented and described for 9 primary sites and 21 ..."
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Cited by 200 (15 self)
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Abstract. Longterm measurements by the AERONET program of spectral aerosol optical depth, precipitable water, and derived Angstrom exponent were analyzed and compiled into an aerosol optical properties climatology. Quality assured monthly means are presented and described for 9 primary sites
2000 Universal twinkling exponents for spectral uctuations associated with mixed chaology
 Proc. R. Soc. Lond. A
"... For systems that are neither fully integrable nor fully chaotic, bifurcations of periodic orbits give rise to semiclassically emergent singularities in the ®uctuating part N ® of the energylevel counting function. The bifurcations dominate the spectral moments Mm(~) = h ( N ®)2mi in the limit ~! 0 ..."
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Cited by 2 (2 self)
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For systems that are neither fully integrable nor fully chaotic, bifurcations of periodic orbits give rise to semiclassically emergent singularities in the ®uctuating part N ® of the energylevel counting function. The bifurcations dominate the spectral moments Mm(~) = h ( N ®)2mi in the limit
Using Empirical mode decomposition and Hilbert spectral analysis to extract multifractal exponents
"... Empirical Mode Decomposition (EMD, or HilbertHuang Transform, HHT) was introduced by Norden E. Huang about ten years ago. It is an alternative timefrequency analysis method with very local ability both in physical domain and frequency domain. In this talk, we will propose a new method, namely arbi ..."
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arbitrary order Hilbert spectral analysis (HSA), to characterize the scale invariant intermittency of a time series directly in amplitudefrequency space (Huang, et al. 2008). This method is an extended version of EMD. It provides an interesting information of the joint amplitudefrequency pdf $p
Lyapunov Exponents for Unitary Anderson Models
, 2006
"... We study a unitary version of the onedimensional Anderson model, given by a five diagonal deterministic unitary operator multiplicatively perturbed by a random phase matrix. We fully characterize positivity and vanishing of the Lyapunov exponent for this model throughout the spectrum and for arbitr ..."
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Cited by 3 (1 self)
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and for arbitrary distributions of the random phases. This includes Bernoulli distributions, where in certain cases a finite number of critical spectral values, with vanishing Lyapunov exponent, exists. We establish similar results for a unitary version of the random dimer model.
Lyapunov exponents and spectral analysis of ergodic Schrödinger operators: A survey of Kotani theory and its applications
 in “Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday
, 2007
"... Abstract. The absolutely continuous spectrum of an ergodic family of onedimensional Schrödinger operators is completely determined by the Lyapunov exponent as shown by Ishii, Kotani and Pastur. Moreover, the part of the theory developed by Kotani gives powerful tools for proving the absence of absol ..."
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Cited by 28 (7 self)
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Abstract. The absolutely continuous spectrum of an ergodic family of onedimensional Schrödinger operators is completely determined by the Lyapunov exponent as shown by Ishii, Kotani and Pastur. Moreover, the part of the theory developed by Kotani gives powerful tools for proving the absence
The Generalized Spectral Radius and Extremal Norms
, 2000
"... The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm alway ..."
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Cited by 58 (10 self)
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The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm
Results 1  10
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550