Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy-convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.Comment: 11 pages, 5 figures, http://www.santafe.edu/projects/CompMech/papers/2dnnn.htm

Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them focuses on one feature of randomness, leading authors to have to use multiple measures. Here we describe and advocate for the use of the accepted universal measure for randomness based on algorithmic complexity, by means of a novel previously presented technique using the the definition of algorithmic probability. A re-analysis of the classical Radio Zenith data in the light of the proposed measure and methodology is provided as a study case of an application.Comment: To appear in Behavior Research Method

An Analysis of Resting-State Functional Transcranial Doppler Recordings from Middle Cerebral Arteries

Functional transcrannial Doppler (fTCD) is used for monitoring the hemodynamics characteristics of major cerebral arteries. Its resting-state characteristics are known only when considering the maximal velocity corresponding to the highest Doppler shift (so called the envelope signals). Significantly more information about the resting-state fTCD can be gained when considering the raw cerebral blood flow velocity (CBFV) recordings. In this paper, we considered simultaneously acquired envelope and raw CBFV signals. Specifically, we collected bilateral CBFV recordings from left and right middle cerebral arteries using 20 healthy subjects (10 females). The data collection lasted for 15 minutes. The subjects were asked to remain awake, stay silent, and try to remain thought-free during the data collection. Time, frequency and time-frequency features were extracted from both the raw and the envelope CBFV signals. The effects of age, sex and body-mass index were examined on the extracted features. The results showed that the raw CBFV signals had a higher frequency content, and its temporal structures were almost uncorrelated. The information-theoretic features showed that the raw recordings from left and right middle cerebral arteries had higher content of mutual information than the envelope signals. Age and body-mass index did not have statistically significant effects on the extracted features. Sex-based differences were observed in all three domains and for both, the envelope signals and the raw CBFV signals. These findings indicate that the raw CBFV signals provide valuable information about the cerebral blood flow which can be utilized in further validation of fTCD as a clinical tool. © 2013 Sejdić et al

Fast algorithms for computing sequence distances by exhaustive substring composition

The increasing throughput of sequencing raises growing needs for methods of sequence analysis and comparison on a genomic scale, notably, in connection with phylogenetic tree reconstruction. Such needs are hardly fulfilled by the more traditional measures of sequence similarity and distance, like string edit and gene rearrangement, due to a mixture of epistemological and computational problems. Alternative measures, based on the subword composition of sequences, have emerged in recent years and proved to be both fast and effective in a variety of tested cases. The common denominator of such measures is an underlying information theoretic notion of relative compressibility. Their viability depends critically on computational cost. The present paper describes as a paradigm the extension and efficient implementation of one of the methods in this class. The method is based on the comparison of the frequencies of all subwords in the two input sequences, where frequencies are suitably adjusted to take into account the statistical background

Rpair: Rescaling RePair with Rsync

Data compression is a powerful tool for managing massive but repetitive datasets, especially schemes such as grammar-based compression that support computation over the data without decompressing it. In the best case such a scheme takes a dataset so big that it must be stored on disk and shrinks it enough that it can be stored and processed in internal memory. Even then, however, the scheme is essentially useless unless it can be built on the original dataset reasonably quickly while keeping the dataset on disk. In this paper we show how we can preprocess such datasets with context-triggered piecewise hashing such that afterwards we can apply RePair and other grammar-based compressors more easily. We first give our algorithm, then show how a variant of it can be used to approximate the LZ77 parse, then leverage that to prove theoretical bounds on compression, and finally give experimental evidence that our approach is competitive in practice

Time-Frequency Representations as Phase Space Reconstruction in Symbolic Recurrence Structure Analysis

To appear as a book chapter in the Springer series “Contributions to Statistics”Recurrence structures in univariate time series are challenging to detect. We propose a combination of symbolic and recurrence analysis in order to identify recurrence domains in the signal. This method allows to obtain a symbolic representation of the data. Recurrence analysis produces valid results for multidimensional data, however, in the case of univariate time series one should perform phase space reconstruction first. In this chapter, we propose a new method of phase space reconstruction based on signal's time-frequency representation and compare it to the delay embedding method. We argue that the proposed method outperforms the delay embedding reconstruction in the case of oscillatory signals. We also propose to use recurrence complexity as a quantitative feature of a signal. We evaluate our method on synthetic data and show its application to experimental EEG signals

Complexity analysis of the fetal heart rate variability: early identification of severe intrauterine growth-restricted fetuses

The main goal of this work is to suggest new indices for a correct identification of the intrauterine growth-restricted (IUGR) fetuses on the basis of fetal heart rate (FHR) variability analysis performed in the antepartum period. To this purpose, we analyzed 59 FHR time series recorded in early periods of gestation through a Hewlett Packard 1351A cardiotocograph. Advanced analysis techniques were adopted including the computation of the Lempel Ziv complexity (LZC) index and the multiscale entropy (MSE), that is, the entropy estimation with a multiscale approach. A multiparametric classifier based on k-mean cluster analysis was also performed to separate pathological and normal fetuses. The results show that the proposed LZC and the MSE could be useful to identify the actual IUGRs and to separate them from the physiological fetuses, providing good values of sensitivity and accuracy (Se = 77.8%, Ac = 82.4%)