COMPLEXITY MEASURE: A QUANTUM INFORMATION APPROACH

In the past decades, all of the efforts at quantifying systems complexity with a general tool has usually relied on using Shannon's classical information framework to address the disorder of the system through the Boltzmann-Gibbs-Shannon entropy, or one of its extensions. However, in recent years, there were some attempts to tackle the quantification of algorithmic complexities in quantum systems based on the Kolmogorov algorithmic complexity, obtaining some discrepant results against the classical approach. Therefore, an approach to the complexity measure is proposed here, using the quantum information formalism, taking advantage of the generality of the classical-based complexities, and being capable of expressing these systems' complexity on other framework than its algorithmic counterparts. To do so, the Shiner-Davison-Landsberg (SDL) complexity framework is considered jointly with linear entropy for the density operators representing the analyzed systems formalism along with the tangle for the entanglement measure. The proposed measure is then applied in a family of maximally entangled mixed state.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short-and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.