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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Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study
TL;DR: The feasibility of a BD episodes classification analysis while using entropy measures is confirmed, since the three states that are involved in BD, depression, mania, and remission, can be significantly distinguished.
Journal ArticleDOI
Classification of periodic, chaotic and random sequences using approximate entropy and Lempel–Ziv complexity measures
TL;DR: It is shown that LZ and ApEn complexity measures can characterize the data complexities correctly for data sequences as short as 20 in length while Shannon’s entropy fails for length less than 50.
Journal ArticleDOI
Testing and mapping non-stationarity in animal behavioral processes: A case study on an individual female bean weevil
TL;DR: Statistical analysis based on two characteristics of a small-world network, and on Lempel-Ziv's measure of Kolmogorov-Chaitin's algorithmic complexity are proposed to scan through an individual behavioral sequence for possible existence of non-stationarity.
Journal ArticleDOI
Dynamic-Disorder-Induced Enhancement of Entanglement in Photonic Quantum Walks
Qin-Qin Wang,Xiao-Ye Xu,Wei-Wei Pan,Kai Sun,Jin-Shi Xu,Geng Chen,Yong-Jian Han,Chuan-Feng Li,Guang-Can Guo +8 more
TL;DR: In this paper, the authors report an experiment demonstrating the enhancement of the entanglement in quantum walks using dynamic disorder, which is a key property beyond the transport behaviors of quantum walks.
Journal ArticleDOI
Climate predictions: the chaos and complexity in climate models
TL;DR: In this article, the Lyapunov exponent of a coupled system of equations, often used in climate models, is analyzed and the horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators is analyzed.
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.
Journal ArticleDOI
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.