Entropy spectrum and its application in fractal measurement

2003 ◽  
Author(s):  
Wu Minjin
Keyword(s):  
Entropy Spectrum

QUANTIZATION OF ENTROPY SPECTRA OF BLACK HOLES

2013 ◽  
Vol 22 (02) ◽  
pp. 1330001 ◽  
Author(s):  
YONGJOON KWON ◽  
SOONKEON NAM
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Correspondence Principle ◽  
Scattering Problem ◽  
Classical System ◽  
Quasinormal Modes ◽  
Entropy Spectrum ◽  
Total Transmission ◽  
Transmission Modes ◽  
Characteristic Modes

From the quasinormal modes (QNM) of black holes, we obtain the quantizations of the entropy and horizon area of black holes via Bohr–Sommerfeld quantization, based on Bohr's correspondence principle. For this, we identify the appropriate action variable of the classical system corresponding to a black hole. By considering the BTZ black holes in topologically massive gravity as well as Einstein gravity, it is found that the spectra of not the horizon areas but the entropies of black holes are equally spaced. We also propose that other characteristic modes of black holes, which are non-QNM or holographic QNM, can be used in quantization of entropy spectra just like QNM. From these modes, it is found that only the entropy spectrum of the warped AdS3 black hole is equally spaced as well. Furthermore, by considering a scattering problem in a black hole, we propose that the total transmission modes and total reflection modes of black holes can be regarded as characteristic modes of black holes and result in the equally spaced entropy of the Kerr and Reissner–Nordström black holes. Finally, we conclude that there is a universal behavior that the entropy spectra of various black holes are equally spaced.

Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements

2015 ◽  
Vol 47 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Venkat Anantharam ◽  
François Baccelli
Keyword(s):  
Large Deviations ◽  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Hard Core ◽  
Entropy Spectrum ◽  
Probability Of Error ◽  
Error Exponent ◽  
Error Exponents ◽  
Noise Process

Consider a real-valued discrete-time stationary and ergodic stochastic process, called the noise process. For each dimension n, we can choose a stationary point process in ℝn and a translation invariant tessellation of ℝn. Each point is randomly displaced, with a displacement vector being a section of length n of the noise process, independent from point to point. The aim is to find a point process and a tessellation that minimizes the probability of decoding error, defined as the probability that the displaced version of the typical point does not belong to the cell of this point. We consider the Shannon regime, in which the dimension n tends to ∞, while the logarithm of the intensity of the point processes, normalized by dimension, tends to a constant. We first show that this problem exhibits a sharp threshold: if the sum of the asymptotic normalized logarithmic intensity and of the differential entropy rate of the noise process is positive, then the probability of error tends to 1 with n for all point processes and all tessellations. If it is negative then there exist point processes and tessellations for which this probability tends to 0. The error exponent function, which denotes how quickly the probability of error goes to 0 in n, is then derived using large deviations theory. If the entropy spectrum of the noise satisfies a large deviations principle, then, below the threshold, the error probability goes exponentially fast to 0 with an exponent that is given in closed form in terms of the rate function of the noise entropy spectrum. This is obtained for two classes of point processes: the Poisson process and a Matérn hard-core point process. New lower bounds on error exponents are derived from this for Shannon's additive noise channel in the high signal-to-noise ratio limit that hold for all stationary and ergodic noises with the above properties and that match the best known bounds in the white Gaussian noise case.

Universality of spectra of black holes

2014 ◽  
Vol 29 (36) ◽  
pp. 1450191 ◽  
Author(s):  
Xiao-Xiong Zeng ◽  
Qiang Li ◽  
Yi-Wen Han
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Area Spectrum ◽  
Spherically Symmetric ◽  
Action Variable ◽  
Intrinsic Properties ◽  
Entropy Spectrum ◽  
Symmetric Black Hole

Using exclusively an action variable, we quantize a static, spherically symmetric black hole. The spacings of the quantized entropy spectrum and area spectrum are found to be equal to the values given by Bekenstein. Interestingly, we find the spectra are independent of the hairs of the black holes and the mode of motion of a particle outside the spacetime, which depends only on the intrinsic properties of the gravity. Our result shows that the spectra are universal provided the spacetime owns a horizon.

SINGULARITY FEATURES OF PORE-SIZE SOIL DISTRIBUTION: SINGULARITY STRENGTH ANALYSIS AND ENTROPY SPECTRUM

Fractals ◽  
2001 ◽  
Vol 09 (03) ◽  
pp. 305-316 ◽  
Author(s):  
F. J. CANIEGO ◽  
M. A. MARTÍN ◽  
F. SAN JOSÉ
Keyword(s):  
Image Analysis ◽  
Pore Size ◽  
Soil Samples ◽  
Second Step ◽  
Strength Analysis ◽  
Entropy Spectrum ◽  
Singular Measures ◽  
Experimental Measure ◽  
Soil Distribution ◽  
Smooth Density

In this paper, several features of pore-size soil distribution are first analyzed, suggesting that they are closer to those of singular measures than to those of distributions with smooth density. In a second step, the weighted singularity strength of an experimental measure obtained by image analysis of soil samples is evaluated. The results of this analysis show the singular nature of pore-size distribution. Finally, the distribution is characterized by means of a spectrum of entropies computed on distorted measures associated with the original experimental measure.

GENERALIZED SYNCHRONIZATION IN DOUBLY DRIVEN CHAOTIC SYSTEM

2006 ◽  
Vol 20 (24) ◽  
pp. 3477-3485
Author(s):  
XIA HUANG ◽  
JIAN GAO ◽  
DAIHAI HE ◽  
ZHIGANG ZHENG
Keyword(s):  
Chaotic System ◽  
Conditional Entropy ◽  
Chaotic Oscillator ◽  
Generalized Synchronization ◽  
Entropy Analysis ◽  
Entropy Spectrum ◽  
Chaotic Signals ◽  
Coupling Strengths ◽  
Conventional Methods ◽  
Parameter Values

Generalized synchronization (GS) of a chaotic oscillator driven by two chaotic signals is investigated in this paper. Both receiver and drivers are the same kind of oscillators with mismatched parameter values. Partial and global GS may appear depending on coupling strengths. An approach based on the conditional entropy analysis is presented to test the partial GS, which is difficult to determine with conventional methods. A trough in conditional entropy spectrum indicates partial GS between the receiver and one of the drivers.

Evolutive spectral analysis of sunspot data over the past 300 years

1990 ◽  
Vol 330 (1615) ◽  
pp. 529-541 ◽  
Keyword(s):  
Spectral Analysis ◽  
Maximum Entropy ◽  
Low Noise ◽  
Time Interval ◽  
Entropy Spectrum ◽  
Sunspot Numbers ◽  
Cross Entropy Method ◽  
Sunspot Data ◽  
Maximum Entropy Spectrum ◽  
Sunspot Series

We analyse the series of the Wolf sunspot number in the frequency domain to determine the dimension of the solar cycle system by using the properties of its strange attractor and to study the stability in time of this dimensionality and of the main quasiperiodicities. The two classical methods of time series analysis, Fourier harmonic and Blackman-Tukey spectral analysis, have been applied first to the series of the annual Wolf sunspot numbers to determine its overall character. To detect stationarity, periodic regression based upon the three most statistically significant quasi-periods and especially a moving form of the maximum entropy spectrum analysis (mesa) have been used. Both analyses show a splitting of the 11-year cycle before 1800, when a ± 55-year cycle is dominant, and a single 11-year and + 100-year peak after 1800. Moreover, these quasi-periods are very sensitive to the time interval over which the analysis is carried out. The reason is that the sunspot numbers constitute a widely non-stationary process, which therefore implies that Fourier techniques are not useful to predict solar activity and must be used as fitting procedure only. The minimum cross-entropy method serves to improve the maximum entropy spectrum. With a good a priori estimate and data containing a low noise level, this method allows the detection of very close peaks and the refinement of the main frequencies; it does not split nor introduce artificial peaks. The Thomson model was also applied for its superior bias control, its excellent leakage resistance and a better statistical information. The same methods were then used to study the 22-year magnetic cycle, which is formed by taking into account the change in polarity of the succeeding 11 -year cycle. The moving form of mesa confirms the 22-year cycle to be highly stable in contrast to the instability in the period of the 11-year sunspot series. This suggests the importance of working with the more invariant 22-year magnetic series to explain the complex, non-stationary behaviour of the sunspot series and of the solar—terrestrial interactions. Finally, we tried to see if the system generated by the sunspot data was allowing the existence of an attractor and tried to determine the minimum number of variables necessary to describe this system. It is shown that the dimension of the attractor is highly unstable varying from 2.21 to 4.95 in a quasi-cyclic way.

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