数据分析、统计与概率

The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the…

A Bayesian method application to the deconvolution of EXAFS spectra is considered. It is shown that for purposes of EXAFS spectroscopy, from the infinitely large number of Bayesian solutions it is possible to determine an optimal range of…

Criticisms of so called `subjective probability' come on the one hand from those who maintain that probability in physics has only a frequentistic interpretation, and, on the other, from those who tend to `objectivise' Bayesian theory,…

Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z,…

A generalization of the maximum noise fraction (MNF) transform is proposed. Powers of each band are included as new bands before the MNF transform is performed. The generalized MNF (GMNF) is shown to perform better than the MNF on a time…

The proper way of averaging is an important question with regards to Tsallis' Thermostatistics. Three different procedures have been thus far employed in the pertinent literature. The third one, i.e., the Tsallis-Mendes-Plastino (TMP)…

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing…

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean $X = {\mu P P_s \over P_e}$, with $\mu$ the mean gas…

We present a new wavelet based method for the denoising of {\it event related potentials} ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be…

We apply a simple clustering algorithm to a large dataset of cellular telecommunication records, reducing the complexity of mobile phone users' full trajectories and allowing for simple statistics to characterize their properties. For the…

We give an overview of track fitting using the Kalman filter method in the NOMAD detector at CERN, and emphasize how the wealth of by-product information can be used to analyze track breakpoints (discontinuities in track parameters caused…

Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…

Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…

A subtractionless method for solving Fermi surface sheets ({\tt FSS}), from measured $n$-axis-projected momentum distribution histograms by two-dimensional angular correlation of the positron-electron annihilation radiation ({\tt 2D-ACAR})…

An expression is proposed for determining the error caused on entropy estimates by finite sample effects. This expression is based on the Ansatz that the ranked distribution of probabilities tends to follow an empirical Zipf law.

Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and…

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In…

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…

It is shown that prize changes of the US dollar - German Mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore we show that from the empirical data the Kramers-Moyal coefficients can…