Approximate entropy (ApEn) as a complexity measure.

This paper pioneers a novel exploration of environmental impacts in livestock farming, focusing on pig farming’s intersection with climate change and sustainability. It emphasizes the transformative potential of data-driven Artificial Intelligence (AI) methodologies, specifically the Internet of Things (IoT) and multimodal data analysis, in promoting equitable and sustainable food systems. The study observes five pigs aged 86 to 108 days using a tripartite sensor that records heart rate, respiration rate, and accelerometer data. The unique experimental design alternates between periods of isolation during feeding and subsequent pairing, enabling the investigation of stress-induced changes. Key inquiries include discerning patterns in heart rate data during isolation versus paired settings, fluctuations in respiration rates, and behavioral shifts induced by isolation or pairing. The study also explores the potential detection of gait abnormalities, correlations between pigs’ age and their gait or activity patterns, and the evolution of pigs’ walking abilities with age. The paper scrutinizes accelerometer data to detect activity changes when pigs are paired, potentially indicating increased stress or aggression. It also examines the adaptation of pigs to alternating isolation and pairing over time and how their heart rate, respiration rate, and activity data reflect this process. The study considers other significant variables, such as time of day and isolation duration, affecting the pigs’ physiological parameters. Sensor data are further utilized to identify behavioral patterns during periods of feeding, isolation, or pairing. In conclusion, this study harnesses IoT and multimodal data analysis in a groundbreaking approach to pig welfare research. It underscores the compelling potential of technology to inform about overall pig welfare, particularly stress levels and gait quality, and the power of data-driven insights in fostering equitable, healthy, and environmentally conscious livestock production systems.

: We compared the electrocardiographic (ECG) and heart rate data from a multi lead electrocardiographic recorder to the pulse rate data obtained from an oxygen saturation (O2 Sat) monitor in 77 pediatric patients undergoing exercise testing for the evaluation of exercise induced bronchospasm (EIB). PURPOSE: To assess the accuracy of pulse rate data during exercise in pediatric patients tested for EIB and the ability to document significant diagnostic findings using a multi lead electrocardiographic recorder. METHODS: Seventy-seven pediatric patients were evaluated for EIB utilizing a treadmill protocol designed to exhaust the patient within 6 to 8 minutes and elicit an 85% or greater maximal heart rate response for the last 4 minutes of the protocol. The patients were continuously monitored with a GE Medical Case 8000 ECG recorder and a Nellcor N-595 O2 Sat monitor utilizing a temple oxisensor. The heart rate (HR) and pulse rate (PR) data were indexed against the measured maximal heart rate as a measure of maximal exercise intensity. RESULTS: The average age was 13.6±2.4 years old with 36 males and 71 Caucasian, 5 African Americans and 1 Asian. Weight was 54±16Kilograms; Body Mass Index (BMI) was 21±4. The referral pattern for the patients was 57% from Pediatric Pulmonologists, 26% from community based Pediatricians, 14% from Pediatric Cardiologists and 3% from Pediatric Thoracic Surgeons. The O2 Sat monitor pulse rate function failed in 4/77 patients (5.2%).TableSignificant electrocardiographic findings included pathologic ST depression in 1 patient, continued prolonged QTc during exercise in 1 patient, exercise induced ventricular arrhythmia in 20 patients and exercise induced atrial arrhythmia in 9 patients. CONCLUSIONS: These findings support the use of a multi lead electrocardiographic recording system for exercise testing in patients evaluated for EIB. This conclusion is based on the documentation of frequent exercise induced electrocardiographic abnormalities and the significantly low pulse rate readings from the O2 sat monitor.

The purpose of this study is to determine if spectral analysis of beat-to-beat heart rate variability will provide important data on autonomic nervous system function during either spinal or epidural anesthesia that is not apparent from the monitoring of mean heart rate and blood pressure. Twelve ASA I patients presenting for elective cesarean delivery (7 epidural and 5 spinal anesthetics) were prospectively selected for study. Control and postblock 10-minute segments of instantaneous heart rates were analyzed for each patient. The total spectral power (Ps, 0.02-0.5 Hz), low frequency spectral power (PLF, 0.02-0.12 Hz), and high frequency spectral power (PHF, 0.12-0.5 Hz) were calculated for each data segment. The complexity of the heart rate time series was estimated by calculating the approximate entropy. Neither spinal or epidural anesthesia had any effect on heart rate or blood pressure. Both spinal and epidural anesthesia did produce a significant decrease in PS, PLF, and PHF. Although there were significant decreases in both the PLF and PHF, there was no change in the PLF/PHF ratio. There was a significant reduction in approximate entropy with spinal and epidural anesthesia, indicating a decrease in complexity of the heart rate dynamics. These data suggest that autonomic tone decreased with spinal and epidural anesthesia but the sympathetic-parasympathetic balance (expressed as PLF/PHF) did not change. Spectral measures, as well as approximate entropy, provide an independent evaluation of the integrity of the autonomic nervous system and cardiovascular control mechanisms that cannot be discerned from mean heart rate and blood pressure.

According to the van der Waals picture, attractive and repulsive forces play distinct roles in the structure of simple fluids. Here, we examine their roles in dynamics; specifically, in the degree of deterministic chaos using the Kolmogorov-Sinai (KS) entropy rate and the spectra of Lyapunov exponents. With computer simulations of three-dimensional Lennard-Jones and Weeks-Chandler-Andersen fluids, we find repulsive forces dictate these dynamical properties, with attractive forces reducing the KS entropy at a given thermodynamic state. Regardless of interparticle forces, the maximal Lyapunov exponent is intensive for systems ranging from 200 to 2000 particles. Our finite-size scaling analysis also shows that the KS entropy is both extensive (a linear function of system-size) and additive. Both temperature and density control the "dynamical chemical potential," the rate of linear growth of the KS entropy with system size. At fixed system-size, both the KS entropy and the largest exponent exhibit a maximum as a function of density. We attribute the maxima to the competition between two effects: as particles are forced to be in closer proximity, there is an enhancement from the sharp curvature of the repulsive potential and a suppression from the diminishing free volume and particle mobility. The extensivity and additivity of the KS entropy and the intensivity of the largest Lyapunov exponent, however, hold over a range of temperatures and densities across the liquid and liquid-vapor coexistence regimes.

Congestive heart failure (CHF) is a very complex clinical syndrome that may lead to ischemic cerebral hypoxia condition. The aim of the present study is to analyze the effects of CHF on brain activity through electroencephalographic (EEG) complexity measures, like approximate entropy (ApEn). Twenty patients with CHF and 18 healthy elderly people were recruited. ApEn values were evaluated in the total spectrum (0.2-47 Hz) and main EEG frequency bands: delta (2-4 Hz), theta (4-8 Hz), alpha 1 (8-11 Hz), alpha 2 (11-13 Hz), beta 1 (13-20 Hz), beta 2 (20-30 Hz), and gamma (30-45 Hz) to identify differences between CHF group and control. Moreover, a correlation analysis was performed between ApEn parameters and clinical data (i.e., B-type natriuretic peptides (BNP), New York Heart Association (NYHA), and systolic blood pressure (SBP)) within the CHF group. Statistical topographic maps showed statistically significant differences between the two groups in the total spectrum and theta frequency band. Within the CHF group, significant negative correlations were found between total ApEn and BNP in O2 channel and between theta ApEn and NYHA scores in Fp1, Fp2, and Fz channels; instead, a significant positive correlation was found between theta ApEn and SBP in C3 channel and a nearly significant positive correlation was obtained between theta ApEn and SBP in F4 channel. EEG abnormalities in CHF are very similar to those observed in cognitive-impaired patients, suggesting analogies between the effects of neurodegeneration and brain chronic hypovolaemia due to heart disorder and underlying high brain sensitivity to CHF.

Many children on the autism spectrum engage in challenging behaviors, like aggression, due to difficulties communicating and regulating their stress. Identifying effective intervention strategies is often subjective and time-consuming. Utilizing unobservable internal physiological data to predict strategy effectiveness may help simplify this process for teachers and parents. This study examined whether heart rate data can predict strategy effectiveness. Teachers and coders from the research team recorded behavioral and heart rate data over three months for each participating student on the autism spectrum using the KeepCalm app, a platform that provides in-the-moment strategy suggestions based on heart rate and past behavioral data, across 226 instances of strategy interventions. A binary logistic regression was performed to assess whether heart rate reduction, time to return to heart rate baseline, and documented skills and challenging behaviors predicted strategy effectiveness. Results suggested that heart rate reduction may be a significant predictor, and supported the existing practice of using behavioral patterns as proxies for strategy effectiveness. Additional analyses indicate proactive strategies are more effective and are associated with greater reduction in heart rate, relative to reactive strategies. Further exploration of how internal physiological data can complement observable behaviors in assessing intervention strategy effectiveness is warranted given the novelty of our findings.

The problem of simultaneously approximating a vector of irrational numbers with rationals is analyzed in a geometrical setting using notions of dynamical systems theory. We discuss here a (vectorial) multidimensional continued-fraction algorithm (MCFA) of additive type, the generalized mediant algorithm (GMA), and give a geometrical interpretation to it. We calculate the invariant measure of the GMA shift as well as its Kolmogorov-Sinai (KS) entropy for arbitrary number of irrationals. The KS entropy is related to the growth rate of denominators of the Euclidean algorithm. This is the first analytical calculation of the growth rate of denominators for any MCFA.

Heart rate variability in the individual fetus

Rolling element bearing is not only the most important failure unit in rotary machinery, but it is also the most common, and its performance degradation assessment has been proposed to realize equipment’s near-zero downtime and maximum productivity. Therefore, exploring effective indices is crucial. Rolling element bearing’s vibration signals often contain complex, non-stationary and nonlinear characteristics. In this work, the changes of complexity, which are measured by two nonlinear methods: correlation dimension and approximate entropy, in the performance degradation process of rolling element bearing based on simulation and bearing accelerated life test data have been studied. Results show that the complexity decreases with the development of obvious defects, and that correlation dimension and approximate entropy have different sensitivities to different performance degradation stages, with the different ability of reflecting the first degradation stage being explained by their different computation processes.

Spinal anaesthesia consists of administering a local anaesthetic in the subarachnoid space, thus causing sensory, motor, and autonomic nerve conduction block. Currently, recovery from spinal anaesthesia is evaluated by the return of motor function, without considering the autonomic blockade, which is responsible for most complications of the technique. Heart rate variability (HRV) is an indirect method to measure the autonomic nervous system and may be useful in assessing autonomic recovery after spinal anaesthesia. The study objective was to evaluate the autonomic function, through HRV, at the moment of return of motor function in patients who received spinal anaesthesia when clonidine is used as an adjuvant. This was a randomised, double-blind clinical trial. The sample consisted of 64 ASA I-II patients who underwent spinal anaesthesia and were divided into 2 groups. Group C received 20 mg of bupivacaine with 75 mcg of clonidine, and group B received 20 mg of bupivacaine. HRV was evaluated at rest (T1) and at the time of motor function recovery (T2). Data were collected using a Polar V800® heart rate monitor and then analysed and filtered using Kubios 3.0® software. There was no difference in the values of the low-frequency/high-frequency (LF/HF) ratio, Poincaré plot standard deviation (SD2/SD1), detrended fluctuation analysis (DFAα1, DFAα2), or correlation dimension (D2) indices in any of the groups between the 2 moments. In the clonidine group, there was a difference only in approximate entropy (ApEn), where a P of 0.0124 was obtained considering a 95% confidence interval ranging from 17.83 to 141.47. There was no significant difference between the duration of sympathetic blockade and motor blockade in spinal anaesthesia.

Online, accessible performance and heart rate data from running competitions are posted publicly or semi‐publicly to social media. We tested the efficacy of one such data resource‐ Strava‐ as a tool in exercise physiology investigations by exploring heart rate differences in mountain racing and road racing running events. Heart rate and GPS pace data were gathered from Strava activities posted by 111 males aged 21–49, from two mountain races (Mt. Washington Road Race and Pike's Peak Ascent) and two road race distances (half marathon and marathon). Variables of interest included race finish time, average heart rate, time to complete the first half (by distance) of the race, time to complete the second half, average heart rate for both the first and second half, estimated maximal heart rate, and competitiveness (finish time as percentage of winning time). Mountain runners on average showed no change in heart rate in the second versus first half of the event, while road racers at the half marathon and marathon distances showed increased second‐half heart rate. Mountain runners slowed considerably more in the second half than road runners. Heart rate increases in road races were likely reflective of cardiac drift. Altitude and other demands specific to mountain racing may explain why this was not observed in mountain races. Strava presents enormous untapped opportunity for exercise physiology research, enabling initial inquiry into physiological questions that may then be followed by targeted laboratory studies.

One of the crucial areas of pregnancy research is to analyze the pregnancy development. For this purpose, scientists analyze the different conditions of fetuses to understand their development. In this paper, we conducted complexity and information-based analyses on Phonocardiogram (PCG) signals to investigate pregnancy development. We calculated the fractal dimension, approximate entropy, and sample entropy as the measures of complexity and the Shannon entropy as the measure of the information content of signals for 24 fetuses in four ranges of gestational weeks. Based on the obtained results, increasing the gestational age of fetuses is reflected on the increment of the complexity of their PCG signals. We also observed similar findings in the case of the information content of PCG signals. Among all calculated measures, the fractal dimension of PCG signals showed significant variations among different gestational weeks. The method of analysis can be used to evaluate the alterations of other biomedical signals of fetuses (e.g., heart rate) to investigate their development.

In fetal surveillance, fetal heart rate changes are assessed using cardiotocography (CTG). Standard procedures used in the quantification of heart rate variability (HRV) are seldom applied as CTG does not deliver beat interval durations with the same accuracy as the electrocardiogram (ECG). Thus little is known about the interdependency of standard HRV measures prenatally. Using fetal magnetocardiography (FMCG: the magnetic equivalent of the fetal ECG), we investigated standard HRV measures in a homogenous group of 20 healthy fetuses. Ten HRV measures were analyzed in 60 five-minute RR interval time series derived from FMCG acquisitions (16th-40th week of gestation). Using regression analysis, we found a clear dependency on gestational age and mean RR interval for measures from the time and frequency domains as well as for a measure for complexity. Correlation analysis revealed a strong interdependency of the measures, in particular within the specific domains. An adequate description of fetal HRV may be achieved using the standard deviation from the time domain, the high frequency band (0.15-0.40 Hz) from the frequency domain and approximate entropy as a complexity measure. The results indicate that different characteristics of fetal HRV are embedded in the different domains.

Now we want to discuss a number of topics that are essential for an understanding of dynamical systems theory and which also play a role in a more detailed discussion of the relation between transport theory and dynamical systems theory. We begin with a discussion of the Kolmogorov-Sinai (KS) entropy, which is a characteristic property of those deterministic dynamical systems with ‘randomness’ properties similar to Bernoulli shifts discussed earlier. The KS entropy is essential for formulating the escape-rate expressions for transport coefficients, to be discussed in Chapters 11 and 12.

It is known that heart activity changes during aging. In this paper, we evaluated alterations of heart activity from the complexity point of view. We analyzed the variations of heart rate of patients with congestive heart failure that are categorized into four different age groups, namely 30–39, 50–59, 60–69, and 70–79 years old. For this purpose, we employed three complexity measures that include fractal dimension, sample entropy, and approximate entropy. The results showed that the trend of increment of subjects’ age is reflected in the trend of increment of the complexity of heart rate variability (HRV) since the values of fractal dimension, approximate entropy, and sample entropy increase as subjects get older. The analysis of the complexity of other physiological signals can be further considered to investigate the variations of activity of other organs due to aging.