Cycling reduces the entropy of neuronal activity in the human adult cortex.

Brain Complexity (BC) have successfully been applied to study the brain electroencephalographic signal (EEG) in health and disease. In this study, we employed recurrence entropy to quantify BC associated with the neurophysiology of movement by comparing BC in both resting state and cycling movement. We measured EEG in 24 healthy adults and placed the electrodes on occipital, parietal, temporal and frontal sites on both the right and left sides of the brain. We computed the recurrence entropy from EEG measurements during cycling and resting states. Entropy is higher in the resting state than in the cycling state for all brain regions analysed. This reduction in complexity is a result of the repetitive movements that occur during cycling. These movements lead to continuous sensorial feedback, resulting in reduced entropy and sensorimotor processing.

Correlation Fuzzy measure of multivariate time series for signature recognition.

Distinguishing different time series, which is determinant or stochastic, is an important task in signal processing. In this work, a correlation measure constructs Correlation Fuzzy Entropy (CFE) to discriminate Chaos and stochastic series. It can be employed to distinguish chaotic signals from ARIMA series with different noises. With specific embedding dimensions, we implemented the CFE features by analyzing two available online signature databases MCYT-100 and SVC2004. The accurate rates of the CFE-based models exceed 99.3%.

Single-molecule evidence of Entropic Pulling by Hsp70 chaperones.

Hsp70 chaperones are central components of the cellular network that ensures the structural quality of proteins. Despite crucial roles in processes such as protein disaggregation and protein translocation into organelles, their physical mechanism of action has remained hotly debated. To the best of our knowledge, no experimental data has directly proven any of the models proposed to date (Power Stroke, Brownian Ratchet, or Entropic Pulling) due to a lack of suitable methods. Here, we use nanopores, a powerful single-molecule tool, to investigate the mechanism of Hsp70s. We demonstrate that Hsp70s extract trapped polypeptide substrates from the nanopore by generating strong forces (equivalent to 46 pN over distances of 1 nm), that rely on the size of Hsp70. The findings provide unambiguous evidence of the Entropic Pulling mechanism, thus solving a long-standing debate, and proposing a potentially universal principle governing diverse cellular processes. Additionally, these results highlight the utility of biological nanopores for protein studies.

Gaze transition entropy as a measure of attention allocation in a dynamic workspace involving automation.

Real-world work environments require operators to perform multiple tasks with continual support from an automated system. Eye movement is often used as a surrogate measure of operator attention, yet conventional summary measures such as percent dwell time do not capture dynamic transitions of attention in complex visual workspace. This study analyzed eye movement data collected in a controlled a MATB-II task environment using gaze transition entropy analysis. In the study, human subjects performed a compensatory tracking task, a system monitoring task, and a communication task concurrently. The results indicate that both gaze transition entropy and stationary gaze entropy, measures of randomness in eye movements, decrease when the compensatory tracking task required more continuous monitoring. The findings imply that gaze transition entropy reflects attention allocation of operators performing dynamic operational tasks consistently.

Using mindfulness-based intervention to promote executive function in young children: a multivariable and multiscale sample entropy study.

Early childhood marks a pivotal period in the maturation of executive function, the cognitive ability to consciously regulate actions and thoughts. Mindfulness-based interventions have shown promise in bolstering executive function in children. This study used the functional near-infrared spectroscopy technique to explore the impact of mindfulness-based training on young children. Brain imaging data were collected from 68 children (41 boys, aged 61.8 ± 10.7 months) who were randomly assigned to either an intervention group (N = 37, aged 60.03 ± 11.14 months) or a control group (N = 31, aged 59.99 ± 10.89 months). Multivariate and multiscale sample entropy analyses were used. The results showed that: (1) brain complexity was reduced in the intervention group after receiving the mindfulness-based intervention in all three executive function tasks (ps < 0.05), indicating a more efficient neural processing mechanism after the intervention; (2) difference comparisons between the intervention and control groups showed significant differences in relevant brain regions during cognitive shifting (left dorsolateral prefrontal cortex and medial prefrontal cortex) and working memory tasks (left dorsolateral prefrontal cortex), which corroborates with improved behavioral results in the intervention group (Z = -3.674, P < 0.001 for cognitive shifting; Z = 2.594, P < 0.01 for working memory). These findings improve our understanding of early brain development in young children and highlight the neural mechanisms by which mindfulness-based interventions affect executive function. Implications for early intervention to promote young children's brain development are also addressed.

The impact of controlled breathing on autonomic nervous system modulation: analysis using phase-rectified signal averaging, entropy and heart rate variability.

Objective.The present study investigated how breathing stimuli affect both non-linear and linear metrics of the autonomic nervous system (ANS).Approach.The analysed dataset consisted of 70 young, healthy volunteers, in whom arterial blood pressure (ABP) was measured noninvasively during 5 min sessions of controlled breathing at three different frequencies: 6, 10 and 15 breaths min-1. CO2concentration and respiratory rate were continuously monitored throughout the controlled breathing sessions. The ANS was characterized using non-linear methods, including phase-rectified signal averaging (PRSA) for estimating heart acceleration and deceleration capacity (AC, DC), multiscale entropy, approximate entropy, sample entropy, and fuzzy entropy, as well as time and frequency-domain measures (low frequency, LF; high-frequency, HF; total power, TP) of heart rate variability (HRV).Main results.Higher breathing rates resulted in a significant decrease in end-tidal CO2concentration (p< 0.001), accompanied by increases in both ABP (p <0.001) and heart rate (HR,p <0.001). A strong, linear decline in AC and DC (p <0.001 for both) was observed with increasing breathing rate. All entropy metrics increased with breathing frequency (p <0.001). In the time-domain, HRV metrics significantly decreased with breathing frequency (p <0.01 for all). In the frequency-domain, HRV LF and HRV HF decreased (p= 0.038 andp= 0.040, respectively), although these changes were modest. There was no significant change in HRV TP with breathing frequencies.Significance.Alterations in CO2levels, a potent chemoreceptor trigger, and changes in HR most likely modulate ANS metrics. Non-linear PRSA and entropy appear to be more sensitive to breathing stimuli compared to frequency-dependent HRV metrics. Further research involving a larger cohort of healthy subjects is needed to validate our observations.

On the Stabilizing Effect of Aspartate and Glutamate and Its Counteraction by Common Denaturants.

By performing differential scanning calorimetry(DSC) measurements on RNase A, we studied the stabilization provided by the addition of potassium aspartate(KAsp) or potassium glutamate (KGlu) and found that it leads to a significant increase in the denaturation temperature of the protein. The stabilization proves to be mainly entropic in origin. A counteraction of the stabilization provided by KAsp or KGlu is obtained by adding common denaturants such as urea, guanidinium chloride, or guanidinium thiocyanate. A rationalization of the experimental data is devised on the basis of a theoretical approach developed by one of the authors. The main contribution to the conformational stability of globular proteins comes from the gain in translational entropy of water and co-solute ions and/or molecules for the decrease in solvent-excluded volume associated with polypeptide folding (i.e., there is a large decrease in solvent-accessible surface area). The magnitude of this entropic contribution increases with the number density and volume packing density of the solution. The two destabilizing contributions come from the conformational entropy of the chain, which should not depend significantly on the presence of co-solutes, and from the direct energetic interactions between co-solutes and the protein surface in both the native and denatured states. It is the magnitude of the latter that discriminates between stabilizing and destabilizing agents.

Thermodynamics-inspired explanations of artificial intelligence.

In recent years, predictive machine learning models have gained prominence across various scientific domains. However, their black-box nature necessitates establishing trust in them before accepting their predictions as accurate. One promising strategy involves employing explanation techniques that elucidate the rationale behind a model's predictions in a way that humans can understand. However, assessing the degree of human interpretability of these explanations is a nontrivial challenge. In this work, we introduce interpretation entropy as a universal solution for evaluating the human interpretability of any linear model. Using this concept and drawing inspiration from classical thermodynamics, we present Thermodynamics-inspired Explainable Representations of AI and other black-box Paradigms, a method for generating optimally human-interpretable explanations in a model-agnostic manner. We demonstrate the wide-ranging applicability of this method by explaining predictions from various black-box model architectures across diverse domains, including molecular simulations, text, and image classification.

Changes in physiological signal entropy in patients with obstructive sleep apnoea: a systematic review.

Background and Objective.Obstructive sleep apnoea (OSA) affects an estimated 936 million people worldwide, yet only 15% receive a definitive diagnosis. Diagnosis of OSA poses challenges due to the dynamic nature of physiological signals such as oxygen saturation (SpO2) and heart rate variability (HRV). Linear analysis methods may not fully capture the irregularities present in these signals. The application of entropy of routine physiological signals offers a promising method to better measure variabilities in dynamic biological data. This review aims to explore entropy changes in physiological signals among individuals with OSA.Approach.Keyword and title searches were performed on Medline, Embase, Scopus, and CINAHL databases. Studies had to analyse physiological signals in OSA using entropy. Quality assessment used the Newcastle-Ottawa Scale. Evidence was qualitatively synthesised, considering entropy signals, entropy type, and time-series length.Main results.Twenty-two studies were included. Multiple physiological signals related to OSA, including SpO2, HRV, and the oxygen desaturation index (ODI), have been investigated using entropy. Results revealed a significant decrease in HRV entropy in those with OSA compared to control groups. Conversely, SpO2and ODI entropy values were increased in OSA. Despite variations in entropy types, time scales, and data extraction devices, studies using receiver operating characteristic curves demonstrated a high discriminative accuracy (>80% AUC) in distinguishing OSA patients from control groups.Significance. This review highlights the potential of SpO2entropy analysis in developing new diagnostic indices for patients with OSA. Further investigation is needed before applying this technique clinically.

Titanium Carbide-Based Spatiotemporally Selectable-Activated Entropy-Driven DNA Nanoplatform for Amplified MicroRNA Imaging and Photothermal Therapy In Vivo.

Engineering an elaborate nanotheranostic platform that can achieve spatiotemporally selective microRNA (miRNA) imaging and imaging-guided therapy in time is critical for precise cancer diagnosis and efficient treatment, yet remains a challenge. Herein, we present an on-site-activatable nanotheranostic platform (Ti3C2-NEDR) that engineers a photothermal-activated entropy-driven strand displacement reaction (NEDR) module on a photothermal conversion module (Ti3C2) for achieving spatiotemporally controlled miRNA-21 imaging in vivo and imaging-guided photothermal therapy only by varying the power of the near-infrared (NIR) laser. The upstream NIR photothermal conversion module, Ti3C2, can act not only as a DNA circuit carrier to deliver the NEDR module but also as a photothermal agent to activate the downstream NEDR module in low-power NIR laser irradiation. Once the NEDR module is activated by the NIR laser, the entropy-driven strand displacement reaction can be innated by intracellular miRNA-21 to generate an amplified fluorescence signal for the spatiotemporally selective imaging of miRNA-21 in vivo. Thereafter, the imaging-guided in vivo photothermal therapy can be achieved in time only by switching to the high-power NIR laser. It is envisioned that this strategy of NIR light-activated spatiotemporally selective miRNA imaging and imaging-guided on-demand therapy may expand the nanotheranostic platform for precise cancer diagnosis and personalized therapy in time, providing a remarkable prospect in biomedical diagnosis and therapy.

Elucidating the link between binding statistics and Shannon information in biological networks.

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding.

Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test.

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

Machine learning of the prime distribution.

In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a theoretical argument explaining the experimental observations of Y.-H. He about the learnability of primes, and posit that the Erdos-Kac law would very unlikely be discovered by current machine learning techniques. Numerical experiments that we perform corroborate our theoretical findings.

Space-time cluster analysis and maximum entropy modeling of Peste des petits ruminants (PPR) in Türkiye.

Peste des petits ruminants (PPR) is an economically important highly serious transboundary disease that mainly occurs in small ruminants such as sheep and goats. The aim of this study was to identify the probability of risk and and space-time clusters of Peste des Petits Ruminants (PPR) in Türkiye. The occurrence of PPR in Türkiye from 2017 to 2019 was investigated in this study using spatial analysis based on geographic information system (GIS). Between these dates, it was determined that 337 outbreaks and 18,467 cases. The highest number of outbreaks were detected in the Central Anatolia region. It was determined that PPR is seen more intensely in sheep compared to goats in Türkiye. In this study, 34 environmental variables (19 bioclimatic, 12 precipitation, altitude and small livestock density variables) were used to explore the environmental influences on PPR outbreak by maximum entropy modeling (Maxent). The clusters of PPR in Türkiye were identified using the retrospective space-time scan data that were computed using the space-time permutation model. A PPR prediction model was created using data on PPR outbreaks combination with environmental variables. Nineteen significant (p < 0.001) space-time clusters were determined. It was discovered that the variables altitude, sheep density, precipitation in june, and average temperature in the warmest season made important contributions to the model and the PPR outbreak may be strongly related with these variables. In this study, PPR in Türkiye has been characterized significantly spatio-temporal and enviromental factors. In this context, the disease pattern and obtained these findings will contribute to policymakers in the prevention and control of the disease.

Dynamics of gas exchange and heart rate signal entropy in standard cardiopulmonary exercise testing during critical periods of growth and development.

Standard cardiopulmonary exercise testing (CPET) produces a rich dataset but its current analysis is often limited to a few derived variables such as maximal or peak oxygen uptake (V̇O2). We tested whether breath-by-breath CPET data could be used to determine sample entropy (SampEn) in 81 healthy children and adolescents (age 7-18 years old, equal sex distribution). To overcome challenges of the relatively small time-series CPET data size and its nonstationarity, we developed a Python algorithm for short-duration physiological signals. Comparing pre- and post-ventilatory threshold (VT1) CPET phases, we found: (1) SampEn decreased by 9.46% for V̇O2 and 5.01% for V̇CO2 (p < 0.05), in the younger, early-pubertal participants; and (2) HR SampEn fell substantially by 70.8% in the younger and 77.5% in the older participants (p < 0.001). Across all ages, females exhibited greater HR SampEn than males during both pre- and post VT1 CPET phases by 14.10% and 23.79%, respectively, p < 0.01. In females, late-pubertal had 17.6% lower HR SampEn compared to early-pubertal participants (p < 0.05). Breath-by-breath gas exchange and HR data from CPET are amenable to SampEn analysis that leads to novel insight into physiological responses to work intensity, and sex and maturational effects.

Assessment of alternative metrics in the application of infrared thermography to detect muscle damage in sports.

Objective.The association between muscle damage and skin temperature is controversial. We hypothesize that including metrics that are more sensitive to individual responses by considering variability and regions representative of higher temperature could influence skin temperature outcomes. Here, the objective of the study was to determine whether using alternative metrics (TMAX, entropy, and pixelgraphy) leads to different results than mean, maximum, minimum, and standard deviation (SD) skin temperature when addressing muscle damage using infrared thermography.Approach.Thermal images from four previous investigations measuring skin temperature before and after muscle damage in the anterior thigh and the posterior lower leg were used. The TMAX, entropy, and pixelgraphy (percentage of pixels above 33 °C) metrics were applied.Main results.On 48 h after running a marathon or half-marathon, no differences were found in skin temperature when applying any metric. Mean, minimum, maximum, TMAX, and pixelgraphy were lower 48 h after than at basal condition following quadriceps muscle damage (p< 0.05). Maximum skin temperature and pixelgraphy were lower 48 h after than the basal condition following muscle damage to the triceps sural (p< 0.05). Overall, TMAX strongly correlated with mean (r= 0.85) and maximum temperatures (r= 0.99) and moderately with minimum (r= 0.66) and pixelgraphy parameter (r= 0.64). Entropy strongly correlates with SD (r= 0.94) and inversely moderately with minimum temperature (r= -0.53). The pixelgraphy moderately correlated with mean (r= 0.68), maximum (r= 0.62), minimum (r= 0.58), and TMAX (r= 0.64).Significance.Using alternative metrics does not change skin temperature outcomes following muscle damage of lower extremity muscle groups.

Scaling Laws for Protein Folding under Confinement.

Spatial confinement significantly affects protein folding. Without the confinement provided by chaperones, many proteins cannot fold correctly. However, the quantitative effect of confinement on protein folding remains elusive. In this study, we observed scaling laws between the variation in folding transition temperature and the size of confinement, (Tf - Tfbulk)/Tfbulk ∼ L-ν. The scaling exponent v is significantly influenced by both the protein's topology and folding cooperativity. Specifically, for a given protein, v can decrease as the folding cooperativity of the model increases, primarily due to the heightened sensitivity of the unfolded state energy to changes in cage size. For proteins with diverse topologies, variations in topological complexity influence scaling exponents in multiple ways. Notably, v exhibits a clear positive correlation with contact order and the proportion of nonlocal contacts, as this complexity significantly enhances the sensitivity of entropy loss in the unfolded state. Furthermore, we developed a novel scaling argument yielding 5/3 ≤ ν ≤ 10/3, consistent with the simulation results.

Short-term power load forecasting in China: A Bi-SATCN neural network model based on VMD-SE.

This study focuses on improving short-term power load forecasting, a critical aspect of power system planning, control, and operation, especially within the context of China's "dual-carbon" policy. The integration of renewable energy under this policy has introduced complexities such as nonlinearity and instability. To enhance forecasting accuracy, the VMD-SE-BiSATCN prediction model is proposed. This model improves computational efficiency and reduces prediction errors by analyzing and reconstructing sequence component complexity using sample entropy (SE) following variational mode decomposition (VMD). Additionally, a self-attention mechanism is integrated into the temporal convolutional network (TCN) to overcome the traditional TCN's limitations in capturing long-term dependencies. The model was evaluated using data from the China Ninth Electrical Attribute Modeling Competition and validated with real-world data from a specific county in Shijiazhuang City, Hebei Province, China. Results indicate that the VMD-SE-BiSATCN model outperforms other models, achieving a mean absolute error (MAE) of 92.87, a root mean square error (RMSE) of 126.906, and a mean absolute percentage error (MAPE) of 0.81%.

Maximum-entropy-based metrics for quantifying critical dynamics in spiking neuron data.

An important working hypothesis to investigate brain activity is whether it operates in a critical regime. Recently, maximum-entropy phenomenological models have emerged as an alternative way of identifying critical behavior in neuronal data sets. In the present paper, we investigate the signatures of criticality from a firing rate-based maximum-entropy approach on data sets generated by computational models, and we compare them to experimental results. We found that the maximum entropy approach consistently identifies critical behavior around the phase transition in models and rules out criticality in models without phase transition. The maximum-entropy-model results are compatible with results for cortical data from urethane-anesthetized rats data, providing further support for criticality in the brain.

Symbolic information approach applied to human intracranial data to characterize and distinguish different congnitive processes.

How the human brain processes information during different cognitive tasks is one of the greatest questions in contemporary neuroscience. Understanding the statistical properties of brain signals during specific activities is one promising way to address this question. Here we analyze freely available data from implanted electrocorticography (ECoG) in five human subjects during two different cognitive tasks in the light of information theory quantifiers ideas. We employ a symbolic information approach to determine the probability distribution function associated with the time series from different cortical areas. Then we utilize these probabilities to calculate the associated Shannon entropy and a statistical complexity measure based on the disequilibrium between the actual time series and one with a uniform probability distribution function. We show that an Euclidian distance in the complexity-entropy plane and an asymmetry index for complexity are useful for comparing the two conditions. We show that our method can distinguish visual search epochs from blank screen intervals in different electrodes and patients. By using a multiscale approach and embedding time delays to downsample the data, we find important timescales in which the relevant information is being processed. We also determine cortical regions and time intervals along the 2-s-long trials that present more pronounced differences between the two cognitive tasks. Finally, we show that the method is useful to distinguish cognitive processes using brain activity on a trial-by-trial basis.