Dynamical complexity of short and noisy time series: Compression-Complexity vs. Shannon entropy

Shannon entropy has been extensively used for characteriz- ing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two such Compression-Complexity Measures namely Lempel-Ziv complexity(LZ)andEffort-To-Compress( ETC)onshorttimeseriesfrom chaoticdynamicalsystemsinthepresenceofnoise.Both LZ and ETC outperform Shannon entropy (H) in accurately characterizing the dynamical complexity of such systems. For very short binary sequences (which arise in neuroscience applications), ETC has higher number of distinct complexity values than LZ and H, thus enabling a finer resolution. For two-state ergodic Markov chains, we empirically show that ETC converges to a steady state value faster than LZ. Compression-Complexity measures are promising for applications which involve short and noisy time series

Measuring Complexity of Chaotic Systems with Cybernetics Applications

Measuring complexity of systems is very important in Cybernetics. An aging human heart has a lower complexity than that of a younger one indicating a higher risk of cardiovascular diseases, pseudorandom sequences used in secure information storage and transmission systems are designed to have high complexity (to resist malicious attacks), brain networks in schizophrenia patients have lower complexity than corresponding networks in a healthy human brain. Such systems are typically modeled as deterministic nonlinear (chaotic) system which is further corrupted with stochastic noise (Gaussian or uniform distribution). After briefly reviewing various complexity measures, this chapter explores characterizing the complexity of deterministic nonlinear chaotic systems (tent, logistic and Hénon maps, Lorenz and Rössler flows) using specific measures such as Lempel-Ziv complexity, Approximate Entropy and Effort-To-Compress. Practical applications to neuron firing model, intra-cranial pressure monitoring, and cardiac aging detection are indicated

A new complexity measure for time series analysis and classification

Complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and Algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the “Effort To Compress” the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip)

Chaos or randomness? Effect of vagus nerve stimulation during sleep on heart-rate variability

Loss of complexity and chaos of heart rate variability (HRV) of an individual increases the risk of mortality from cardiovascular diseases. Abnormalities in HRV associated with intractable epilepsy may even lead to “sudden death in epilepsy” (SUDEP). By activating the parasympathetic division of the autonomic nervous system, Vagus Nerve Stimulation (VNS) has the potential to restore the natural chaotic behavior of the heart which can be measured by the increase in complexity of HRV as indicated by complexity measures such as Effort-To-Compress (ETC) and Lempel-Ziv Complexity (LZC). In this study, we formulate and test two hypothesis – (A) chaotic time series exhibit lower temporal correlation of complexity measures such as LZ and ETC than uniformly random time series, and (B) Vagus Nerve Stimulation (VNS ON) results in chaotic cardiovascular dynamics. Hypothesis-A is verified by a simulated study on chaotic time series from the Logistic map where we see a clear decrease in temporal correlation between ETC and LZC values as the degree of chaos increases. Hypothesis-B is supported by an experimental study on a VNS implanted patient and not implanted controls. A temporal correlation analysis between complexity measures (ETC and LZC) on HRV data samples shows that VNS during sleep increases chaotic behavior in contrast to lack of VNS and in control subjects. Surrogate analysis further confirmed that VNS activation led to deterministic chaos and not stochastic randomness. Our approach proposes a clear methodology to determine the efficacy of VNS intervention in restoring the chaoticity of cardiovascular dynamics

Compression-Complexity Measures for Analysis and Classification of Coronaviruses

Finding a vaccine or specific antiviral treatment for a global pandemic of virus diseases (such as the ongoing COVID-19) requires rapid analysis, annotation and evaluation of metagenomic libraries to enable a quick and efficient screening of nucleotide sequences. Traditional sequence alignment methods are not suitable and there is a need for fast alignment-free techniques for sequence analysis. Information theory and data compression algorithms provide a rich set of mathematical and computational tools to capture essential patterns in biological sequences. In this study, we investigate the use of compression-complexity (Effort-to-Compress or ETC and Lempel-Ziv or LZ complexity) based distance measures for analyzing genomic sequences. The proposed distance measure is used to successfully reproduce the phylogenetic trees for a mammalian dataset consisting of eight species clusters, a set of coronaviruses belonging to group I, group II, group III, and SARS-CoV-1 coronaviruses, and a set of coronaviruses causing COVID-19 (SARS-CoV-2), and those not causing COVID-19. Having demonstrated the usefulness of these compression complexity measures, we employ them for the automatic classification of COVID-19-causing genome sequences using machine learning techniques. Two flavors of SVM (linear and quadratic) along with linear discriminant and fine K Nearest Neighbors classifer are used for classification. Using a data set comprising 1001 coronavirus sequences (causing COVID-19 and those not causing COVID-19), a classification accuracy of 98% is achieved with a sensitivity of 95% and a specificity of 99.8%. This work could be extended further to enable medical practitioners to automatically identify and characterize coronavirus strains and their rapidly growing mutants in a fast and efficient fashion