In analogy of classical Kolmogorov complexity we define a notion of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides with the new quantum Kolmogorov complexity restricted to the classical domain. Quantum Kolmogorov complexity is upper bounded and can be effectively approxim...

We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that the higher-order structure functions diverge for orders larger than a certain threshold, as theorized in some recent work. The significance of the results for...

This report compares a variety of computable information measures for finite strings. These include Shannon’s n-block entropy, the three best known versions of the Lempel-Ziv production complexity (LZ-76, LZ-77, and LZ-78), and the lesser known T-entropy. We apply these measures to strings of known entropy, each derived from the logistic map. Pesin’s identity allows us to deduce corresponding S...

In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides with the new quantum Kolmogorov complexity restricted to the classical domain. Quantum Kolmogorov complexity is upper bounded and can be effectively approxi...

This paper introduces a bootstrap procedure, accounting for data dependence and parameter estimation error, which facillitates the construction of parametric speci ̄cation tests of di®usion processes. The bootstrap method hinges on a twofold extension of the Politis and Romano (1994) stationary bootstrap. First we provide an empirical process version of this bootstrap, and second, we account for...

This paper introduces the two-sample Anderson-Darling (AD) test of goodness of fit as a tool for comparing distributions, response time distributions in particular. We discuss the problematic use of pooling response times across participants, and alternative tests of distributions, the most common being the Kolmogorov-Smirnoff (KS) test. We compare the KS test and the AD test, presenting conclu...

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the KolmogorovSmirnov two sample statistic. ...

Until 6 October 2005 sixteen redshifts have been measured of long gamma-ray bursts discovered by the Swift satellite. Further 45 redshifts have been measured of the long gamma-ray bursts discovered by other satellites. Here we perform five statistical tests comparing the redshift distributions of these two samples assuming as the null hypothesis identical distribution for the two samples. Three...

By using the brute force algorithm, the application of the two-dimensional two-sample Kolmogorov–Smirnov test can be prohibitively computationally expensive. Thus a fast algorithm for computing the two-sample Kolmogorov–Smirnov test statistic is proposed to alleviate this problem. The newly proposed algorithm is O(n) times more efficient than the brute force algorithm, where n is the sum of the...

We present a general method for testing gamma-ray burst (GRB) jet structure and carry out a comprehensive analysis about the prevalent jet structure models. According to the jet angular energy distribution, we can not only derive the expected distribution of the GRB isotropic-equivalent energy release for any possible jet structure, but also obtain a two-dimensional distribution including redsh...