Journal ArticleDOI
On the Complexity of Finite Sequences
A. Lempel,Jacob Ziv +1 more
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TLDR
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.Abstract:
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented. The proposed complexity measure is related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated. It is further related to the number of distinct substrings and the rate of their occurrence along the sequence. The derived properties of the proposed measure are discussed and motivated in conjunction with other well-established complexity criteria.read more
Citations
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Conceptualizing and Measuring Variety in the Execution of Organizational Work Processes
TL;DR: Three measures of sequential variety in organizational processes are proposed and compared and compared using a simulated data set that embodies the range of variation likely to be encountered in empirical studies.
Journal ArticleDOI
Electroencephalographic Order Pattern Analysis for the Separation of Consciousness and Unconsciousness : An Analysis of Approximate Entropy, Permutation Entropy, Recurrence Rate, and Phase Coupling of Order Recurrence Plots
TL;DR: In this article, the hypnotic component of anesthesia was measured by permutation entropy, recurrence rate, and phase coupling of order recurrence plots, which are suitable for any type of time series, whether deterministic or noisy.
Mechanisms of mutagenesis and the role of local DNA sequence complexity
TL;DR: Manual analysis served to confirm that the majority of indels are explicable in terms of a two‐step process involving established mutational mechanisms, and to propose likely mechanisms and pathways for indel generation on an individual basis.
Journal ArticleDOI
Quantifying physiological data with Lempel-Ziv complexity-certain issues
TL;DR: The use of the surrogate data technique is suggested to avoid spurious interpretation of the measure of complexity of the Lempel-Ziv complexity and the results obtained include the uterine contraction obtained during active labor.
Journal ArticleDOI
Complexity of subthalamic 13-35 Hz oscillatory activity directly correlates with clinical impairment in patients with Parkinson's disease.
Chiung Chu Chen,Yi Ting Hsu,Hsiao-Lung Chan,Shang Ming Chiou,Po Hsun Tu,Shih Tseng Lee,Chon-Haw Tsai,Chin Song Lu,Peter Brown +8 more
TL;DR: An advanced nonlinear dynamical analysis method based on the Lempel-Ziv estimator is used to show frequency band and symptom-subset specific correlations between STN local field potential (LFP) complexity and motor impairment in PD patients and strengthens the association between the dynamic structure of synchonised LFP activity in the beta frequency band in the STN and akinesia-rigidity.
References
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Journal ArticleDOI
Three approaches to the quantitative definition of information
TL;DR: In this article, three approaches to the quantitative definition of information are presented: information-based, information-aware and information-neutral approaches to quantifying information in the context of information retrieval.
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The definition of random sequences
TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
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Process complexity and effective random tests
TL;DR: A variant of the Kolmogorov concept of complexity which yields a common theory of finite and infinite random sequences and some concepts of effective tests which are proved to be equivalent are established.
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Information-Theoretic Limitations of Formal Systems
TL;DR: An attempt is made to apply information-theoretic computational complexity to meta-mathematics by measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theoremic proofs.