Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282–288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2) self-similar processes

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part I

Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009. The main aims of this contribution are: (i) To suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be possible to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we attempt, through a multidisciplinary analysis, to provide elements of a definition. (ii) To link the detected MHz and kHz EM anomalies with equivalent last stages of the L'Aquila earthquake preparation process. (iii) To put forward physically meaningful arguments to support a way of quantifying the time to global failure and the identification of distinguishing features beyond which the evolution towards global failure becomes irreversible. The whole effort is unfolded in two consecutive parts. We clarify we try to specify not only whether or not a single EM anomaly is pre-seismic in itself, but mainly whether a combination of kHz, MHz, and ULF EM anomalies can be characterized as pre-seismic one

Wavelet-Based Multiscale Intermittency Analysis: The Effect of Deformation

Intermittency represents a certain form of heterogeneous behavior that has interest in diverse fields of application, particularly regarding the characterization of system dynamics and for risk assessment. Given its intrinsic location-scale-dependent nature, wavelets constitute a useful functional tool for technical analysis of intermittency. Deformation of the support may induce complex structural changes in a signal. In this paper, we study the effect of deformation on intermittency. Specifically, we analyze the interscale transfer of energy and its implications on different wavelet-based intermittency indicators, depending on whether the signal corresponds to a ‘level’- or a ‘flow’-type physical magnitude. Further, we evaluate the effect of deformation on the interscale distribution of energy in terms of generalized entropy and complexity measures. For illustration, various contrasting scenarios are considered based on simulation, as well as two segments corresponding to different regimes in a real seismic series before and after a significant earthquake.PID2021-128077NB-I00 and PGC2018-098860- B-I00MCIN/AEI/10.13039/501100011033/ERDF A way of making Europe, EUCEX2020-001105-M funded by MCIN/AEI/10.13039/50110001103

Brain image clustering by wavelet energy and CBSSO optimization algorithm

Previously, the diagnosis of brain abnormality was significantly important in the saving of social and hospital resources. Wavelet energy is known as an effective feature detection which has great efficiency in different utilities. This paper suggests a new method based on wavelet energy to automatically classify magnetic resonance imaging (MRI) brain images into two groups (normal and abnormal), utilizing support vector machine (SVM) classification based on chaotic binary shark smell optimization (CBSSO) to optimize the SVM weights. The results of the suggested CBSSO-based KSVM are compared favorably to several other methods in terms of better sensitivity and authenticity. The proposed CAD system can additionally be utilized to categorize the images with various pathological conditions, types, and illness modes

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed