Search Results (73)

Background: DNA methylation is a key epigenetic mechanism whose dynamics are closely linked to ageing. Modern epigenetic clocks predict biological age based on the average methylation level. The concept of “epigenetic rejuvenation” posits that at early stages of development, the biological age of the embryo may decrease, reaching a minimum (“ground zero”) at the gastrulation stage. However, standard averaging methods may not account for important rearrangements in the internal structure of methylation. Objective: To apply the apparatus of information theory and topological data science to the analysis of scNMT-seq data and to test whether DNA methylation entropy decreases from stage E4.5 to E6.5, which would correspond to an approach towards the biological zero state. Methods: Publicly available scNMT-seq data (GSE121690) were analyzed. Five entropy measures were calculated for each cell (Shannon, Renyi, Tsallis, LZ-complexity, local gradient entropy (entropy of variations in the smoothed histogram of the methylation distribution), and persistent entropy (PE)—a topological complexity measure). For the five-dimensional entropy feature space, a Rips complex was constructed, and persistence diagrams H_0 and H_1 were computed. Results: All five entropy measures decreased significantly, with LZ complexity showing the largest relative reduction (−28.4%) and the strongest independent signal (partial r = −0.181). Among all the complexity measures studied, LZ complexity exhibited the largest relative reduction, underscoring its heightened sensitivity to the progressive ordering of the epigenetic landscape. Notably, the ternary encoding of LZ complexity showed strong correlation with Shannon entropy (r = 0.71), indicating that algorithmic complexity, when accounting for partial methylation states, aligns closely with statistical entropy while retaining sensitivity to spatial order. The consistency of results across binary and ternary encodings confirms the robustness of LZ complexity as a structural biomarker. Persistent entropy confirmed the general dynamics (decrease from 15.91 to 14.89, p = 0.01). Topological analysis of the multidimensional space revealed a qualitative reorganization: at stage E6.5, stable cyclic structures (H₁) emerge, while at E4.5 the space is dominated by a single large-scale cycle. Null model validation confirmed that the observed H₁-cycles are genuine topological features rather than random fluctuations. Comprehensive topological characterization showed that normalized persistent entropy increases from 0.846 to 0.882 (p < 0.001), while maximum persistence decreases from 0.446 to 0.218 (p < 0.001), reflecting a transition from a homogeneous state to structured diversification—multiple, evenly distributed cycles corresponding to distinct cell lineages. Consistent with this, regional disorder (RE/RD) at the single-cell level decreases from E4.5 to E6.5 (RE: −25.5%, RD: −27.4%, p < 10⁻¹³), while global entropy also decreases, together painting a picture of epigenetic rejuvenation as ordered consolidation at the whole-genome scale. An SVM model trained on 15 entropy and structural features achieved stage classification with an accuracy of 93.4% and AUC of 0.981, confirming the diagnostic potential of the approach. Conclusions: The decrease in DNA methylation entropy from E4.5 to E6.5 corresponds to an approach to “ground zero”—the point of minimum biological age in embryogenesis—and supports the hypothesis of a link between decreasing entropy and epigenetic rejuvenation. The addition of topological analysis reveals the hidden organization of epigenetic diversity, showing that ordering does not lead to homogenization but is accompanied by the formation of distinguishable cell lineages. Full article

Spurious correlations between time series are a persistent problem: simple, low-complexity patterns are abundant, so unrelated series can easily exhibit high Pearson correlation. We argue that Kolmogorov complexity—a series’ resistance to compression—provides a principled diagnostic for flagging such cases. We prove an algorithmic trilemma: a pair of binary sequences cannot simultaneously be algorithmically independent, highly correlated, and highly complex. This gives a deterministic complexity ceiling for independent correlated pairs and a probabilistic bound under which spurious correlations among independent high-complexity pairs are exponentially rare; we further bridge these results to an effective Hausdorff dimension obstruction. These guarantees hold for binary sequences under Hamming correlation; their extension to real-valued series via serialisation and LZ compression is empirically validated rather than proved, so the joint indicator $J_{\mathrm{LZ}}=\min \{{\tilde{C}}_{\mathrm{LZ}}\left(x\right),{\tilde{C}}_{\mathrm{LZ}}\left(y\right)\}$ is a calibrated diagnostic, not a causal test. On two toy models—coupled logistic maps and multivariate fractional Brownian motion (${\dim }_H=2-H$)—false positives are far more common among low-complexity series. Because noise inflates complexity and non-stationary processes can be both complex and spuriously correlated, we recommend a two-stage workflow: establish stationarity, then report $J_{\mathrm{LZ}}$ alongside $\rho$. Full article

In the context of Kolmogorov complexity, the complexity of an object can be characterized by the length of the shortest algorithm required to describe or compute it. In condensed matter systems under equilibrium and nonequilibrium conditions, macroscopic properties distinct from elementary ones can emerge from large numbers of particles. Such a large system size allows system properties to change as control parameters change, producing phase transitions. Inspired by this analogy, it is natural to consider that an optimized computing system may undergo a transition from an initially random organization to a functionally organized state. In this paper, by adopting a specific multi-task setting based on a typical dynamical system, we propose an evolutionary echo state network that realizes the functional differentiation of a random neural network into two subnetworks—one specialized for memory and the other for program execution. The model suggests a minimal neural mechanism for dynamic processes that extract rules embedded in input sequences and store information over short or long time scales. Because the proposed evolutionary model is driven by constraints that jointly reduce task errors and structural redundancy, the resulting network can be regarded as an optimized descriptor of memory and program functions. To clarify the relationship between the proposed model and algorithmic complexity, we introduce Lempel–Ziv-based complexity indices for both network structure and node-wise reservoir dynamics. Although neither density, effective spectral radius, nor the Lempel–Ziv-based complexity indices were prescribed or optimized in the eESN, the evolved network exhibited structural complexity comparable to conventional ESNs in the corresponding region and slightly higher dynamical complexity. These results suggest that the advantage of eESN is not attributable to a direct maximization of complexity itself, but rather to the evolutionary organization of complexity into a functionally differentiated reservoir that supports both memory-like retention and program-like rule extraction. Full article

Recent advances in automated learning techniques have enhanced the analysis of biomedical signals for detecting sleep stages and related health abnormalities. However, many existing models face challenges with imbalanced datasets and the dynamic nature of evolving sleep states. In this study, we present a robust algorithm for classifying sleep states using electroencephalogram (EEG) data collected from 33 healthy participants. We extracted dynamic, brain-inspired features, such as microstates and Lempel–Ziv complexity, which replicate intrinsic neural processing patterns and reflect temporal changes in brain activity during sleep. An optimal feature set was identified based on significant spectral ranges and classification performance. The classifier was developed using a convolutional neural network (CNN) combined with gated recurrent units (GRUs) within a reinforcement learning framework, which models adaptive decision-making processes similar to those in biological neural systems. Our proposed biomimetic framework illustrates that a multivariate feature set provides strong discriminative power for sleep state classification. Benchmark comparisons with established approaches revealed a classification accuracy of 98% using the optimized feature set, with the framework utilizing fewer EEG channels and reducing processing time, underscoring its potential for real-time deployment. These findings indicate that applying biomimetic principles in feature extraction and model design can improve automated sleep monitoring and facilitate the development of novel therapeutic and diagnostic tools for sleep-related disorders. Full article

Inferring causal relationships in the decision-making processes of machine learning models is essential for advancing explainable artificial intelligence. In this work, we propose a novel causality measure and a distance metric derived from Lempel–Ziv (LZ) complexity. We explore how these measures can be integrated into decision tree classifiers by enabling splits based on features that cause the most changes in the target variable. Specifically, we design (i) a causality-based decision tree, where feature selection is driven by the LZ-based causal score; (ii) a distance-based decision tree, using LZ-based distance measure. We compare these models against traditional decision trees constructed using Gini impurity and Shannon entropy as splitting criteria. While all models show comparable classification performance on standard datasets, the causality-based decision tree significantly outperforms all others on the Coupled Auto Regressive (AR) dataset, which is known to exhibit an underlying causal structure. This result highlights the advantage of incorporating causal information in settings where such a structure exists. Furthermore, based on the features selected in the LZ causality-based tree, we define a causal strength score for each input variable, enabling interpretable insights into the most influential causes of the observed outcomes. This makes our approach a promising step toward interpretable and causally grounded decision-making in AI systems. Full article

This work analyzes the behavior of the boundary layer subjected to stresses by obstacles using hourly measurements, in the form of time series, of meteorological variables (temperature (T), relative humidity (RH), and magnitude of the wind speed (WS)) in a given period. The study region is Santiago, the capital of Chile. The measurement location is in a rugged basin geography with a nearly pristine atmospheric environment. The time series are analyzed through chaos theory, demonstrating that they are chaotic through the calculation of the parameters Lyapunov exponent (λ > 0), correlation dimension (D_C < 5), Kolmogorov entropy (S_K > 0), Hurst exponent (0.5 < H < 1), and Lempel–Ziv complexity (LZ > 0). These series are simultaneous measurements of the variables of interest, before and after, of three different volumetric geometries arranged as obstacles: a parallelepiped, a cylinder, and a miniature mountain. The three geometries are subject to the influence of the wind and present the same cross-sectional area facing the measuring instruments oriented in the same way. The entropies calculated for each variable in each geometry are compared. It is demonstrated, in a first approximation, that volumetric geometry impacts the magnitude of the entropic fluxes associated with the measured variables, which can affect micrometeorology and, by extension, the climate in general. Furthermore, the study examines which geometry favors greater information loss or greater fractality in the measured variables. Full article

Although Lempel–Ziv complexity (LZC) can reflect changes in object characteristics by measuring changes in independent patterns in the signal, it can only be applied to one-dimensional time series and cannot be directly applied to two-dimensional images. To address this issue, this paper proposed a two-dimensional Lempel–Ziv complexity by combining the concept of local receptive field in convolutional neural networks. This extends the application scenario of LZC from one-dimensional time series to two-dimensional images, further broadening the scope of application of LZC. First, the pixels and size of the image were normalized. Then, the image was encoded according to the sorting of normalized values within the 4 × 4 region. Next, the encoding result of the image was rearranged into a vector by row. Finally, the Lempel–Ziv complexity of the image could be obtained based on the rearranged vector. The proposed method was further used for defect detection in conjunction with the dilation operator and Sobel operator, and validated by two practical cases. The results showed that the proposed method can effectively identify independent pattern changes in images and can be used for defect detection. The accuracy rate of defect detection can reach 100%. Full article

Background/Objectives: The YSK olfactory function (YOF) test is a culturally adapted psychophysical tool that assesses threshold, discrimination, and identification. This study evaluated whether functional near-infrared spectroscopy (fNIRS) synchronized with routine YOF testing, combined with machine learning, can predict YOF subdomain performance in healthy adults, providing an objective neural correlate to complement behavioral testing. Methods: In this prospective diagnostic-accuracy (feasibility/validation) study in healthy adults with algorithm development, 100 healthy adults completed the YOF test while undergoing prefrontal/orbitofrontal fNIRS during odor blocks. Feature sets from ΔHbO/ΔHbR included time-domain descriptors, complexity (Lempel–Ziv), and information-theoretic measures (mutual information); the identification task used a hybrid attention–CNN. Separate models were developed for threshold (binary classification), discrimination (binary classification), and identification (binary classification). Performance was summarized with accuracy, area under the curve (AUC), F1-score, and (where applicable) sensitivity/specificity, using participant-level cross-validation. Results: The threshold classifier achieved accuracy 0.86, AUC 0.86, and F1 0.86, indicating strong discrimination of correct vs. incorrect threshold responses. The discrimination model yielded accuracy 0.75, AUC 0.76, and F1 0.75. The identification model (attention–convolutional neural network [CNN]) achieved accuracy 0.88, sensitivity 0.86, specificity 0.91, and F1 0.88. Feature-attribution (e.g., SHapley Additive exPlanations [SHAP]) provided interpretable links between fNIRS features and task performance for threshold and discrimination. Conclusions: Olfactory-evoked fNIRS signals can accurately predict YOF subdomain performance in healthy adults, supporting the feasibility of non-invasive, portable, near–real-time olfactory monitoring. These findings are preliminary and not generalizable to clinical populations; external validation in diverse cohorts is warranted. The approach clarifies the scientific essence of the method by (i) aligning psychophysical outcomes with objective hemodynamic signatures and (ii) introducing a feature-rich modeling pipeline (ΔHbO/ΔHbR + Lempel–Ziv complexity/mutual information; attention–CNN) that advances prior work. Full article

(1) Background: Quantitative EEG (QEEG) offers potential for identifying objective neurophysiological biomarkers in psychiatric disorders and guiding neurofeedback interventions. This study examined whether three nonlinear QEEG metrics—Lempel–Ziv Complexity, Tsallis Entropy, and Renyi Entropy—can distinguish children with autism spectrum disorder (ASD) from typically developing (TD) peers, and assessed their relevance for neurofeedback targeting. (2) Methods: EEG recordings from 19 scalp channels were analyzed in children with ASD and TD. The three nonlinear metrics were computed for each channel. Group differences were evaluated statistically, while machine learning classifiers assessed discriminative performance. Dimensionality reduction with t-distributed Stochastic Neighbor Embedding (t-SNE) was applied to visualize clustering. (3) Results: All metrics showed significant group differences across multiple channels. Machine learning classifiers achieved >90% accuracy, demonstrating robust discriminative power. t-SNE revealed distinct ASD and TD clustering, with nonlinear separability in specific channels. Visual processing–related channels were prominent contributors to both classifier predictions and t-SNE cluster boundaries. (4) Conclusions: Nonlinear QEEG metrics, particularly from visual processing regions, differentiate ASD from TD with high accuracy and may serve as objective biomarkers for neurofeedback. Combining complexity and entropy measures with machine learning and visualization techniques offers a relevant framework for ASD diagnosis and personalized intervention planning. Full article

Background: In recent years, complexity analysis has attracted considerable attention in the field of neural mechanism exploration due to its nonlinear characteristics, providing a new perspective for revealing the complex information processing mechanisms of the brain. In precision sports such as shooting, complexity analysis can quantify the complexity of activity in different areas of the brain and dynamic changes. Methods: This study extracted multiple complexity indicators based on microstate and traceability analysis and examined brain complexity during the shooting preparation stage and the brain’s reaction mechanisms under audiovisual limitations. Results: Microstate Lempel-Ziv complexity and microstate fluctuation complexity in low-light environment were significantly higher than those in normal environment. The complexity of the brain increases and then decreases during shooting. In low-light conditions, nine brain regions—insula R’, posterior cingulate R’, entorhinal, superior frontal L’, caudal anterior cingulate L’, rostral anterior cingulate L’, posterior cingulate R’, medial orbitofrontal L’ and rostral middle frontal R’—exhibited differential results. SSV-R_PHC-COG and SSV-R_LOF-SCORE showed strong negative correlations with behavioral indicators. Conclusions: First, during shooting, the processing of visual information mainly relies on the secondary cortex and visual connection functions, rather than the primary cortex. Furthermore, there are automated processes based on experience in shooting sports. Second, noise has little effect on shooting, but low light has a multifaceted impact on shooting. This is mainly reflected in difficulties in integrating sensorimotor information, excessive memory retrieval, reduced movement stability, triggering of negative emotions, and changes in shooting strategies. Full article

Natural dynamical systems can often display various long-term behaviours, ranging from entirely predictable decaying states to unpredictable, chaotic regimes or, more interestingly, highly correlated and intricate states featuring emergent phenomena. That, of course, imposes a level of generality on the models we use to study them. Among those models, coupled oscillators and cellular automata (CA) present a unique opportunity to advance the understanding of complex temporal behaviours because of their conceptual simplicity but very rich dynamics. In this contribution, we review the work completed by our research team over the last few years in the development and application of an alternative information-based characterization scheme to study the emergent behaviour and information handling of nonlinear systems, specifically Adler-type oscillators under different types of coupling: local phase-dependent (LAP) coupling and Kuramoto-like local (LAK) coupling. We thoroughly studied the long-term dynamics of these systems, identifying several distinct dynamic regimes, ranging from periodic to chaotic and complex. The systems were analysed qualitatively and quantitatively, drawing on entropic measures and information theory. Measures such as entropy density (Shannon entropy rate), effective complexity measure, and Lempel–Ziv complexity/information distance were employed. Our analysis revealed similar patterns and behaviours between these systems and CA, which are computationally capable systems, for some specific rules and regimes. These findings further reinforce the argument around computational capabilities in dynamical systems, as understood by information transmission, storage, and generation measures. Furthermore, the edge of chaos hypothesis (EOC) was verified in coupled oscillators systems for specific regions of parameter space, where a sudden increase in effective complexity measure was observed, indicating enhanced information processing capabilities. Given the potential for exploiting this non-anthropocentric computational power, we propose this alternative information-based characterization scheme as a general framework to identify a dynamical system’s proximity to computationally enhanced states. Furthermore, this study advances the understanding of emergent behaviour in nonlinear systems. It explores the potential for leveraging the features of dynamical systems operating at the edge of chaos by coupling them with computationally capable settings within machine learning frameworks, specifically by using them as reservoirs in Echo State Networks (ESNs) for time series forecasting and predictive modeling. This approach aims to enhance the predictive capacity, particularly that of chaotic systems, by utilising EOC systems’ complex, sensitive dynamics as the ESN reservoir. Full article

With the increasing complexity of the power system and the increasing load volatility, accurate load forecasting plays a vital role in ensuring the safety of power supply, optimizing scheduling decisions and resource allocation. However, the traditional single model has limitations in extracting the multi-frequency features of load data and processing components with varying complexity. Therefore, this paper proposes a complementary forecasting method based on bi-level decomposition and complexity analysis. In the paper, Pyraformer is used as a complementary model for the Single Channel Enhanced Periodicity Decoupling Framework (SCEPDF). Firstly, a Hodrick Prescott Filter (HP Filter) is used to decompose the electricity data, extracting the trend and periodic components. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is used to further decompose the periodic components to obtain several IMF components. Secondly, based on the sample entropy, spectral entropy, and Lempel–Ziv complexity, a complexity evaluation index system is constructed to comprehensively analyze the complexity of each IMF component. Then, based on the comprehensive complexity of each IMF component, different components are fed into the complementary model. The predicted values of each component are combined to obtain the final result. Finally, the proposed method is tested on the quarterly electrical load dataset. The effectiveness of the proposed method is verified through comparative and ablation experiments. The experimental results show that the proposed method demonstrates excellent performance in short-term electricity load forecasting tasks. Full article

Carbon price forecasting and pricing are critical for stabilizing carbon markets, mitigating investment risks, and fostering economic development. This paper presents an advanced decomposition-integration framework which seamlessly integrates econometric models with machine learning techniques to enhance carbon price forecasting. First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is employed to decompose carbon price data into distinct modal components, each defined by specific frequency characteristics. Then, Lempel–Ziv complexity and dispersion entropy algorithms are applied to analyze these components, facilitating the identification of their unique frequency attributes. The framework subsequently employs GARCH models for predicting high-frequency components and a gated recurrent unit (GRU) neural network optimized by the grey wolf algorithm for low-frequency components. Finally, the optimized GRU model is utilized to integrate these predictive outcomes nonlinearly, ensuring a comprehensive and precise forecast. Empirical evidence demonstrates that this framework not only accurately captures the diverse characteristics of different data components but also significantly outperforms traditional benchmark models in predictive accuracy. By optimizing the GRU model with the grey wolf optimizer (GWO) algorithm, the framework enhances both prediction stability and adaptability, while the nonlinear integration approach effectively mitigates error accumulation. This innovative framework offers a scientifically rigorous and efficient tool for carbon price forecasting, providing valuable insights for policymakers and market participants in carbon trading. Full article

Hypnotic phenomena exhibit significant inter-individual variability, with some individuals consistently demonstrating efficient responses to hypnotic suggestions, while others show limited susceptibility. Recent neurophysiological studies have added to a growing body of research that shows variability in hypnotic susceptibility is linked to distinct neural characteristics. Building on this foundation, our previous work identified that individuals with high and low hypnotic susceptibility can be differentiated based on the arrhythmic activity observed in resting-state electrophysiology (rs-EEG) outside of hypnosis. However, because previous work has largely focused on mean spectral characteristics, our understanding of the variability over time of these features, and how they relate to hypnotic susceptibility, is still limited. Here we address this gap using a time-resolved assessment of rhythmic alpha peaks and arrhythmic components of the EEG spectrum both prior to and following hypnotic induction. Using multivariate pattern classification, we investigated whether these neural features differ between individuals with high and low susceptibility to hypnosis. Specifically, we used multivariate pattern classification to investigate whether these non-stationary neural features could distinguish between individuals with high and low susceptibility to hypnosis before and after a hypnotic induction. Our analytical approach focused on time-resolved spectral decomposition to capture the intricate dynamics of neural oscillations and their non-oscillatory counterpart, as well as Lempel–Ziv complexity. Our results show that variations in the alpha center frequency are indicative of hypnotic susceptibility, but this discrimination is only evident during hypnosis. Highly hypnotic-susceptible individuals exhibit higher variability in alpha peak center frequency. These findings underscore how dynamic changes in neural states related to alpha peak frequency represent a central neurophysiological feature of hypnosis and hypnotic susceptibility. Full article