Esophageal epithelium modeling based on globally coupled map: an approach toward precancerous lesion diagnosis.

Esophageal squamous cell carcinoma is the most predominant malignancy of the esophagus. Its histological precursors (dysplasia) emerge in the esophageal epithelium that their progression into the underlying layers leads to cancer. The epithelium is the origin of many solid cancers and, accordingly, the focus of numerous computational models. In this work, we proposed a framework to establish a two-dimensional, globally coupled map to model the epithelium dynamics. The model aims at diagnosing the early stage of dysplasia based on microscopic images of endoscopic biopsies. We used the logistic map as a black-box model for the epithelial cells. By relating between the structure and dynamic of the epithelium, we defined the coupling function and proposed a case-dependent model in which the parameters were adjusted based on fractal geometry of each pathological image. Thus, by assigning different attractors to the cells' behavior, the lattice dynamic was investigated by the Lyapunov exponent. The decreasing pattern of Lyapunov exponent variations across the epithelium thickness had reasonable performance in diagnosing the normal specimens from the low-grade dysplasia ones. The results showed that there could be a direct relationship between the structural complexity of this system and its uncertainty of dynamics. Graphical abstract The modeling process of the esophageal epithelium to classify the experimental data at normal and LGD stages.

Nonlinear Analysis of Electroencephalogram Signals while Listening to the Holy Quran.

BACKGROUND: Electrical activity of the brain, resulting from electrochemical signaling between neurons, is recorded by electroencephalogram (EEG). The neural network has complex behavior at different levels that strongly confirms the nonlinear nature of interactions in the human brain. This study has been designed and implemented with the aim of determining the effects of religious beliefs and the effect of listening to Holy Quran on electrical activity of the brain of the Iranian Persian-speaking Muslim volunteers. METHODS: The brain signals of 47 Persian-speaking Muslim volunteers while listening to the Holy Quran consciously, and while listening to the Holy Quran and the Arabic text unconsciously were used. Therefore, due to the nonlinear nature of EEG signals, these signals are studied using approximate entropy, sample entropy, Hurst exponent, and Detrended Fluctuation Analysis. RESULTS: Statistical analysis of the results has shown that listening to the Holy Quran consciously increases approximate entropy and sample entropy, and decreases Hurst Exponent and Detrended Fluctuation Analysis compared to other cases. CONCLUSION: Consciously listening to the Holy Quran decreases self-similarity and correlation of brain signal and instead increases complexity and dynamicity in the brain.

Predicting tipping points of dynamical systems during a period-doubling route to chaos.

Classical indicators of tipping points have limitations when they are applied to an ecological and a biological model. For example, they cannot correctly predict tipping points during a period-doubling route to chaos. To counter this limitation, we here try to modify four well-known indicators of tipping points, namely the autocorrelation function, the variance, the kurtosis, and the skewness. In particular, our proposed modification has two steps. First, the dynamic of the considered system is estimated using its time-series. Second, the original time-series is divided into some sub-time-series. In other words, we separate the time-series into different period-components. Then, the four different tipping point indicators are applied to the extracted sub-time-series. We test our approach on an ecological model that describes the logistic growth of populations and on an attention-deficit-disorder model. Both models show different tipping points in a period-doubling route to chaos, and our approach yields excellent results in predicting these tipping points.