In this study, features of the financial returns of the PSI20index, related to market efficiency, are captured using waveletand entropy-based techniques. This characterization includes the following points. First, the detection of long memory, associated with low frequencies, and a global measure of the time series: the Hurst exponent estimated by several methods, including wavelets. Second, th...

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservati...

We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive uncertainty associated with a specific state, rather than averaged over all states. We relate the specific entropy rate to popular ‘complexity’ measures such...

This paper proposed a new entropy measure, Fuzzy Measure Entropy (FuzzyMEn), for the analysis of heart rate variability (HRV) signals. FuzzyMEn was calculated based on the fuzzy set theory and improved the poor statistical stability in the approximate entropy (ApEn) and sample entropy (SampEn). The simulation results also demonstrated that the FuzzyMEn had better algorithm discrimination abilit...

The disease epilepsy is characterized by a sudden and recurrent malfunction of the brain that is termed seizer. The electroencephogram (EEG) has a lot of information about brain and also used in several automated epilepsy detection systems. In this study, the wavelet subband decomposition and Approximate Entropy (ApEn) is used for epilepsy detection from EEG signals. In first stage, EEG signals...

The vibration signal is one of the significant signals that reflects the fault. In allusion to the shortcomings of traditional signal analysis method in the high-frequency and nonstationary signal analysis, the wavelet theory and approximate entropy algorithm are introduced into the signal analysis in order to propose a new vibration signal analysis (WTAEAVSA) method in this paper. In the propo...

More than 370,000 Americans die every year from coronary artery disease (CAD). Early detection and treatment are crucial to reducing this number. Current diagnostic and disease-monitoring methods are invasive, costly, and time-consuming. Using an electronic stethoscope and spectral and nonlinear dynamics analysis of the recorded heart sound, we investigated the acoustic signature of CAD in subj...

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measure-valued functions. This main result implies existence of solutions...

Calculation of approximate entropy (ApEn) requires to select the correct threshold “r”. Previous studies recommended r to be between 0.1 and 0.25 times the signal standard deviation, and now r=0.2 is used in almost all HRV studies. Recently it has been claimed that for fast signal dynamics, r=0.2 may lead to erroneous conclusions, while r maximizing ApEn, rMAX, correctly assesses entropy. We ve...

1 This research work was funded, in part, by an MRI grant from the National Science Foundation (Grant #: CNS – 0619069). ABSTRACT Code injections can aid successful intrusion attempts, thereby allowing viruses and worms to spread. Current research into intrusion detection is notably focused on application behavior profiling through system call trace analysis. Studying the system call layer has ...