Entropic Approach to the Detection of Crucial Events

Multiscale Diffusion Entropy Analysis for the Detection of Crucial Events in Cardiac Pathology

The significance of crucial events in explaining the dynamics of a physiological system has only been recently emerging. Crucial events are yet to be fully understood and implemented in clinical applications of physiological signal processing. This paper proposes the application of modified diffusion entropy (MDEA) and novel multiscale diffusion entropy analyses (MSDEA) on measuring the temporal complexity of the ECG time series to improve crucial events detection performance. Thirty samples of each of three groups of ECG datasets from PhysioNet with recordings of cardiac arrhythmia (ARR), congestive heart failure (CHF) and normal sinus rhythm (NSR) were analyzed using MDEA with stripes followed by MSDEA. Healthy NSR ECGs showed an approximate 15% greater inverse power law (IPL) and scaling δ indices than pathologic CHF and ARR signals. Additionally, the scaling indices for the pathologic groups showed higher standard deviations, indicating that crucial events determined by MDEA reveal latent differences in ECG complexity that could better be investigated across multiple time scales of temporally decomposed signals using MSDEA which combines multiscale entropy (MSE) and MDEA. Hence, MSDEA showed an improved, clearer discrimination between the healthy and pathological cardiac signals (p<0.0005) characterized by a range of NSR complexity indices twice the range of the pathological values associated with ARR and CHF across twenty temporal scales as well as more reliable trend lines (R2>=0.95).Clinical Relevance- This research proposes a novel and enhanced diagnostic discrimination across healthy and pathologic cardiac conditions based on biomedical signal processing of ECG recordings utilizing the principle of crucial events detection.

Neural and behavioral adaptations to frontal theta neurofeedback training: A proof of concept study

Previous neurofeedback research has shown training-related frontal theta increases and performance improvements on some executive tasks in real feedback versus sham control groups. However, typical sham control groups receive false or non-contingent feedback, making it difficult to know whether observed differences between groups are associated with accurate contingent feedback or other cognitive mechanisms (motivation, control strategies, attentional engagement, fatigue, etc.). To address this question, we investigated differences between two frontal theta training groups, each receiving accurate contingent feedback, but with different top-down goals: (1) increase and (2) alternate increase/decrease. We hypothesized that the increase group would exhibit greater increases in frontal theta compared to the alternate group, which would exhibit lower frontal theta during down- versus up-modulation blocks over sessions. We also hypothesized that the alternate group would exhibit greater performance improvements on a Go-NoGo shooting task requiring alterations in behavioral activation and inhibition, as the alternate group would be trained with greater task specificity, suggesting that receiving accurate contingent feedback may be the more salient learning mechanism underlying frontal theta neurofeedback training gains. Thirty young healthy volunteers were randomly assigned to increase or alternate groups. Training consisted of an orientation session, five neurofeedback training sessions (six blocks of six 30-s trials of FCz theta modulation (4-7 Hz) separated by 10-s rest intervals), and six Go-NoGo testing sessions (four blocks of 90 trials in both Low and High time-stress conditions). Multilevel modeling revealed greater frontal theta increases in the alternate group over training sessions. Further, Go-NoGo task performance increased at a greater rate in the increase group (accuracy and reaction time, but not commission errors). Overall, these results reject our hypotheses and suggest that changes in frontal theta and performance outcomes were not explained by reinforcement learning afforded by accurate contingent feedback. We discuss our findings in terms of alternative conceptual and methodological considerations, as well as limitations of this research.

Scale-Free Functional Brain Networks Exhibit Increased Connectivity, Are More Integrated and Less Segregated in Patients with Parkinson's Disease following Dopaminergic Treatment

Dopaminergic treatment (DT), the standard therapy for Parkinson's disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory ( H ( 2 ) ) and multifractal strength ( Δ H 15 ) of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by H ( 2 ) or Δ H 15 . Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the Δ H 15 networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the H ( 2 ) networks. Significant positive correlations were also found between the metrics of H ( 2 ) networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies.

Crucial Development: Criticality Is Important to Cell-to-Cell Communication and Information Transfer in Living Systems

In the fourth paper of this Special Issue, we bridge the theoretical debate on the role of memory and criticality discussed in the three earlier manuscripts, with a review of key concepts in biology and focus on cell-to-cell communication in organismal development. While all living organisms are dynamic complex networks of organization and disorder, most studies in biology have used energy and biochemical exchange to explain cell differentiation without considering the importance of information (entropy) transfer. While all complex networks are mixtures of patterns of complexity (non-crucial and crucial events), it is the crucial events that determine the efficiency of information transfer, especially during key transitions, such as in embryogenesis. With increasing multicellularity, emergent relationships from cell-to-cell communication create reaction-diffusion exchanges of different concentrations of biochemicals or morphogenetic gradients resulting in differential gene expression. We suggest that in conjunction with morphogenetic gradients, there exist gradients of information transfer creating cybernetic loops of stability and disorder, setting the stage for adaptive capability. We specifically reference results from the second paper in this Special Issue, which correlated biophotons with lentil seed germination to show that phase transitions accompany changes in complexity patterns during development. Criticality, therefore, appears to be an important factor in the transmission, transfer and coding of information for complex adaptive system development.

Biophotons and Emergence of Quantum Coherence-A Diffusion Entropy Analysis

We study the emission of photons from germinating seeds using an experimental technique designed to detect light of extremely small intensity. We analyze the dark count signal without germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here, called diffusion entropy analysis (DEA) and originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes, rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated either by non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur without any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity becomes dominated by the stationary infinite memory. We illustrate some conjectures ranging from stress induced annihilation of crucial events to the emergence of quantum coherence.

Caputo Fractional Derivative and Quantum-Like Coherence

We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.

Diffusion Entropy vs. Multiscale and Rényi Entropy to Detect Progression of Autonomic Neuropathy

We review the literature to argue the importance of the occurrence of crucial events in the dynamics of physiological processes. Crucial events are interpreted as short time intervals of turbulence, and the time distance between two consecutive crucial events is a waiting time distribution density with an inverse power law (IPL) index μ, with μ < 3 generating non-stationary behavior. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < μ < 2 and (b) slow evolution toward the stationary regime, with 2 < μ < 3. Human heartbeats and brain dynamics belong to the latter regime, with healthy physiological processes tending to be closer to the border with the perennial non-stationary regime with μ = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of μ with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index μ moving from the healthy condition μ = 2 toward the border with Gaussian statistics with μ = 3, as the disease progresses. Examining heart rate time series of patients affected by diabetes-induced autonomic neuropathy of varying severity, we find that the progression of cardiac autonomic neuropathy (CAN) indeed shifts μ from the border with perennial variability, μ = 2, to the border with Gaussian statistics, μ = 3 and provides a novel, sensitive index for assessing disease progression. We find that at the Gaussian border, the dynamical complexity of crucial events is replaced by Gaussian fluctuation with long-time memory.

Why Brain Criticality Is Clinically Relevant: A Scoping Review

The past 25 years have seen a strong increase in the number of publications related to criticality in different areas of neuroscience. The potential of criticality to explain various brain properties, including optimal information processing, has made it an increasingly exciting area of investigation for neuroscientists. Recent reviews on this topic, sometimes termed brain criticality, make brief mention of clinical applications of these findings to several neurological disorders such as epilepsy, neurodegenerative disease, and neonatal hypoxia. Other clinicallyrelevant domains - including anesthesia, sleep medicine, developmental-behavioral pediatrics, and psychiatry - are seldom discussed in review papers of brain criticality. Thorough assessments of these application areas and their relevance for clinicians have also yet to be published. In this scoping review, studies of brain criticality involving human data of all ages are evaluated for their current and future clinical relevance. To make the results of these studies understandable to a more clinical audience, a review of the key concepts behind criticality (e.g., phase transitions, long-range temporal correlation, self-organized criticality, power laws, branching processes) precedes the discussion of human clinical studies. Open questions and forthcoming areas of investigation are also considered.

Relating size and functionality in human social networks through complexity

Extensive empirical evidence suggests that there is a maximal number of people with whom an individual can maintain stable social relationships (the Dunbar number). We argue that this arises as a consequence of a natural phase transition in the dynamic self-organization among N individuals within a social system. We present the calculated size dependence of the scaling properties of complex social network models to argue that this collective behavior is an enhanced form of collective intelligence. Direct calculation establishes that the complexity of social networks as measured by their scaling behavior is nonmonotonic, peaking around 150, thereby providing a theoretical basis for the value of the Dunbar number. Thus, we establish a theory-based bridge spanning the gap between sociology and psychology.