Fast Autocorrelated Context Models for Data Compression

A method is presented to automatically generate context models of data by calculating the data's autocorrelation function. The largest values of the autocorrelation function occur at the offsets or lags in the bitstream which tend to be the most highly correlated to any particular location. These offsets are ideal for use in predictive coding, such as predictive partial match (PPM) or context-mixing algorithms for data compression, making such algorithms more efficient and more general by reducing or eliminating the need for ad-hoc models based on particular types of data. Instead of using the definition of the autocorrelation function, which considers the pairwise correlations of data requiring O(n^2) time, the Weiner-Khinchin theorem is applied, quickly obtaining the autocorrelation as the inverse Fast Fourier transform of the data's power spectrum in O(n log n) time, making the technique practical for the compression of large data objects. The method is shown to produce the highest levels of performance obtained to date on a lossless image compression benchmark.Comment: v2 includes bibliograph

The "spurious regression problem" in the classical regression model framework

I analyse the "spurious regression problem" from the Classical Regression Model (CRM) point of view. Simulations show that the autocorrelation corrections suggested by the CRM, e.g., feasible generalised least squares, solve the problem. Estimators are unbiased, consistent, efficient and deliver correctly sized tests. Conversely, first differencing the data results in inefficiencies when the autoregressive parameter in the error process is less than one. I offer practical recommendations for handling cases suspected to be in the "spurious regression" class.spurious regression, classical regression model, generalised least squares, autocorrelation corrections

On detecting the large separation in the autocorrelation of stellar oscillation times series

The observations carried out by the space missions CoRoT and Kepler provide a large set of asteroseismic data. Their analysis requires an efficient procedure first to determine if the star is reliably showing solar-like oscillations, second to measure the so-called large separation, third to estimate the asteroseismic information that can be retrieved from the Fourier spectrum. We develop in this paper a procedure, based on the autocorrelation of the seismic Fourier spectrum. We have searched for criteria able to predict the output that one can expect from the analysis by autocorrelation of a seismic time series. First, the autocorrelation is properly scaled for taking into account the contribution of white noise. Then, we use the null hypothesis H0 test to assess the reliability of the autocorrelation analysis. Calculations based on solar and CoRoT times series are performed in order to quantify the performance as a function of the amplitude of the autocorrelation signal. We propose an automated determination of the large separation, whose reliability is quantified by the H0 test. We apply this method to analyze a large set of red giants observed by CoRoT. We estimate the expected performance for photometric time series of the Kepler mission. Finally, we demonstrate that the method makes it possible to distinguish l=0 from l=1 modes. The envelope autocorrelation function has proven to be very powerful for the determination of the large separation in noisy asteroseismic data, since it enables us to quantify the precision of the performance of different measurements: mean large separation, variation of the large separation with frequency, small separation and degree identification.Comment: A&A, in pres

Statistical properties of the attendance time series in the minority game

We study the statistical properties of the attendance time series corresponding to the number of agents making a particular decision in the minority game (MG). We focus on the analysis of the probability distribution and the autocorrelation function of the attendance over a time interval in the efficient phase of the game. In this regime both the probability distribution and the autocorrelation function are shown to have similar behaviour for time differences corresponding to multiples of $2\cdot 2^{m}$, which is twice the number of possible history bit strings in a MG with agents making decisions based on the most recent $m$ outcomes of the game.Comment: 3 pages, 4 Postscript figures, \documentstyle[aps,epsf]{revtex

With missing title of the paper. Overrelaxation Algorithm for coupled Gauge-Higgs systems

In this letter we extent the overrelaxation algorithm, known to be very efficient in gauge theories, to coupled gauge-Higgs systems with a particular emphasis on the update of the radial mode of the Higgs field. Our numerical tests of the algorithm show that the autocorrelation times can be reduced substantially.Comment: 10pages, DESY-95-04

Attacking the combination generator

We present one of the most efficient attacks against the combination generator. This attack is inherent to this system as its only assumption is that the filtering function has a good autocorrelation. This is usually the case if the system is designed to be resistant to other kinds of attacks. We use only classical tools, namely vectorial correlation, weight 4 multiples and Walsh transform