Novel techniques for improving NNetEn entropy calculation for short and noisy time series

Heidari, Hanif; Velichko, Andrei; Murugappan, M.; Chowdhury, Muhammad E. H.

doi:10.1007/s11071-023-08298-w

Cited by 12 publications

(16 citation statements)

References 52 publications

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“…Interested readers are referred to the work of Heidari et al. (2023) where a detailed description of constant offset, B , is given. The offset value is estimated by averaging all the AE index time series investigated

(B=370)

.Then a signal preprocessing is applied to the AE index using Equation .…”

Section: Data Acquisition and Methods Of Analysismentioning

confidence: 99%

“…The NNetEn algorithm estimates the entropy in the following stages: the stage 1 involves loading the time series X = ( x 1 , x 2 , x 3 , … , x N ) into the reservoir. In the reservoir, transformation of the input vector ( Y ) through a time series ( X ) is achieved by filling the matrix of the reservoir with the time series using row‐wise filling time series stretching, method 3 (Heidari et al., 2023). The maximum length of the time series ( N max ) is determined by the numbers of elements in the reservoir ( N max = Y max × P max = 19,625).…”

Section: Data Acquisition and Methods Of Analysismentioning

confidence: 99%

“…Where 𝐴𝐴 AE𝑛𝑛 is the Auroral Electrojet time series while 𝐴𝐴 AE ′ 𝑛𝑛 is the modified Auroral Electrojet time series and B is the constant offset value, also known as bias component. Interested readers are referred to the work of Heidari et al (2023) where a detailed description of constant offset, B, is given. The offset value is estimated by averaging all the AE index time series investigated 𝐴𝐴 (𝐵𝐵 = 370) .Then a signal preprocessing is applied to the AE index using Equation 2.…”

Section: Calculation Of Neural Network Entropy Measuresmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical Complexity Transitions During High‐Intensity Long Duration Continuous Auroral Activities (HILDCAA) Events: Feature Analysis Based on Neural Network Entropy

Oludehinwa,

Velichko,

Ogunsua

et al. 2023

Space Weather

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In this study, we examine the dynamical complexity transitions during HILDCAA events. HILDCAA preceded by an Interplanetary Coronal Mass Ejection (ICME) storm recovery phase, HILDCAA preceded by a Corotating Interaction Region (CIR) storm recovery phase, and non‐storm driven HILDCAA and geomagnetically quiet periods were investigated using the Auroral Electrojet index time series. Neural Network Entropy (NNetEn) was used to capture the dynamical complexity transitions during these sporadic events. The NNetEn was able to decipher the distinct dynamical features associated with the emergence of HILDCAA and the geomagnetically quiet periods. Our analysis revealed a high value of NNetEn during HILDCAA signifying that the complexity levels of the coupled solar wind‐magnetosphere‐ionosphere system for HILDCAA, driven by different interplanetary structures were high with no significance difference. Thus, indicating that during HILDCAA, the dynamical behavior of the underlying physical processes due to the energy deposition driven either by ICME, CIR or non‐storm HILDCAA remain the same. However, a deciphering feature of dynamical complexity between the geomagnetically quiet period and HILDCAA events was evident. It was noticed that as the HILDCAA emerges, the NNetEn depicts an increment in entropy value signifying that the complexity levels of the coupled solar wind‐magnetosphere‐ionosphere system increases, and as the dynamics transcend to its recovery state, a reduction in entropy was observed implying a decline in complexity levels. Low values of NNetEn revealing lower complexity levels are found to be associated with geomagnetically quiet periods.

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(B=370)

.Then a signal preprocessing is applied to the AE index using Equation .…”

Section: Data Acquisition and Methods Of Analysismentioning

confidence: 99%

Section: Data Acquisition and Methods Of Analysismentioning

confidence: 99%

Section: Calculation Of Neural Network Entropy Measuresmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical Complexity Transitions During High‐Intensity Long Duration Continuous Auroral Activities (HILDCAA) Events: Feature Analysis Based on Neural Network Entropy

Oludehinwa,

Velichko,

Ogunsua

et al. 2023

Space Weather

Self Cite

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“…The PRE summary statistic is based on Shannon's entropy. 24,25,[32][33][34][35][36][37][38][39] It is defined as follows:…”

Section: Theorymentioning

confidence: 99%

“…The PRE summary statistic is based on Shannon's entropy 24,25,32–39 . It is defined as follows:

PRE goodbreak= goodbreak- \sum_{i = 1}^{n} normalp ((), x_{i}) \log_{2} normalp ((), x_{i}),

where

normalp ((), x_{i})

is the “probability” of observing a signal (intensity value) in a spectrum.…”

Section: Theorymentioning

confidence: 99%

Surface analysis insight note: Analysis of X‐ray photoelectron spectroscopy images with summary statistics

Moeini

Linford

2023

Surface & Interface Analysis

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Developments in X‐ray photoelectron spectroscopy (XPS) instrumentation and the need for spatial information in surface characterization have led to advances in XPS imaging and related image processing techniques. In this Insight Note, we demonstrate the use of summary statistics as simple, but effective, tools for understanding XPS hyperspectral images (data cubes) prior to more advanced image processing. An XPS image obtained from a silicon surface patterned with different thicknesses of oxide was analyzed with three summary statistics: a tool in the MATLAB programming environment, the mean, and pattern recognition entropy (PRE). The MATLAB tool largely separates the spectra into two groups. The mean does a somewhat better job differentiating between the spectra, and PRE is even more effective. The results of the MATLAB summary statistic are confirmed by plotting the average and standard deviation spectra of different regions of the image it produces. The results of the mean and PRE summary statistics are confirmed by evenly segmenting the results and examining the average and standard deviation spectra of these segments. Fitting these average spectra demonstrates the greater effectiveness of the PRE summary statistic in segmenting the spectra into chemically distinct groups.

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Chaotic discrete map of pulse oscillator dynamics with threshold nonlinear rate coding

Boriskov

2024

Nonlinear Dyn

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The study presents 1D discrete map (DM) to describe the dynamics of the oscillator with chaotic pulse position modulation (PPM). The model circuit has pulse voltage-controlled oscillator (PVCO) and feedback (FB) loop with a threshold of pulse rate coding, which performs nonretriggerable monostable multivibrator (MMV). DM is based on the analysis of this circuit using a simple approximation of the frequency modulation, which includes a threshold condition on the pulse period and sigmoid function of rate coding. The model circuit and DM demonstrate dynamic chaos in a wide range of control parameters. The transition to the chaos occurs by a jump either from a fixed point (tangent bifurcation), or from a limit cycle. An experimental (digital-analog) circuit of the chaotic pulse oscillator, in which the FB unit is MMV with a microcontroller (MC), is implemented. The relationship between the presented DM and the well-known sawtooth (Bernoulli) map (STM), widely used in engineering, is discussed.

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Novel techniques for improving NNetEn entropy calculation for short and noisy time series

Cited by 12 publications

References 52 publications

Dynamical Complexity Transitions During High‐Intensity Long Duration Continuous Auroral Activities (HILDCAA) Events: Feature Analysis Based on Neural Network Entropy

Dynamical Complexity Transitions During High‐Intensity Long Duration Continuous Auroral Activities (HILDCAA) Events: Feature Analysis Based on Neural Network Entropy

Surface analysis insight note: Analysis of X‐ray photoelectron spectroscopy images with summary statistics

Chaotic discrete map of pulse oscillator dynamics with threshold nonlinear rate coding

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