Emerging neural theories of consciousness suggest a correlation between a specific type of neural dynamical complexity and the level of consciousness: When awake and aware, causal interactions between brain regions are both integrated (all regions are to a certain extent connected) and differentiated (there is inhomogeneity and variety in the interactions). In support of this, recent work by Ca...

We give two optimal linear-time algorithms for computing the Longest Previous Factor (LPF) array corresponding to a string w. For any position i in w, LPF[i] gives the length of the longest factor of w starting at position i that occurs previously in w. Several properties and applications of LPF are investigated. They include computing the Lempel-Ziv factorization of a string and detecting all ...

We propose a randomness test based on the T-complexity of a sequence, which can be calculated using a parsing algorithm called Tdecomposition. Recently, the Lempel-Ziv (LZ) randomness test based on LZ-complexity using the LZ78 incremental parsing was officially excluded from the NIST test suite in NIST SP 800-22. This is caused from the problem that the distribution of P-values for random seque...

Pattern matching is a simple method for studying the properties of information sources based on individual sequences (Wyner et al 1998 IEEE Trans. Inf. Theory 44 2045-56). In particular, the normalized Lempel-Ziv complexity (Lempel and Ziv 1976 IEEE Trans. Inf. Theory 22 75-88), which measures the rate of generation of new patterns along a sequence, is closely related to such important source p...

There are mainly two key points which can affect the efficiency of multi-view video capture and transmission system largely: communication between cameras and computing complexity of encoder. In this paper, we propose a practical framework of distributed multi-view video coding, in which inter-camera communication is avoided and the large computing complexity is moved from encoder to decoder. I...

This work explores the possible benefits of adopting k-means as a coarse graining technique (CGT) when measuring electroencephalograms (EEG) complexity using the Lempel-Ziv (LZ) algorithm for the diagnosis of Alzheimer’s disease (AD). A significant (p<0.01) complexity decrease between AD patients and control subjects is identified at Occipital, Parietal and Temporal regions of the brain. An acc...

This article discusses a variety of mathematically-inspired approaches to the study of complexity and their application to the study and understanding of complex systems. These approaches have their origin in the study of limitative results in logic, mathematical linguistics, and the theory of computation, based upon the work of Godel, Turing, Chomsky, and Kolmogorov, among many others. The top...