# A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) [2,3] and the chaoticness degree (through the largest Lyapunov exponent, Λ

_{max}) [4–7]. The main finding of these reports is a reduction of these two quantifiers during an epileptic seizure, suggesting that a transition takes place at the seizure onset in the dynamic behavior of the neural network, from a complex behavior to a simpler one [8]. Furthermore, some researchers report a significant decrease of these quantifiers a few minutes before the seizure onset, raising the hypothesis that epileptic seizure could be predicted [3,5,6]. However, despite the obvious physiological relevance of such findings, a basic requirement for nonlinear dynamic metric tools (chaos theory) to be applied to experimental data is the stationarity of the time series, which suggests that the time series is representative of a unique and stable attractor. Unfortunately, this is not the case with EEGs. To make the situation even worse, the evaluation of D

_{2}and Λ

_{max}(defined as asymptotic properties of the attractor) requires the use of long time recordings.

- We develop a novel extension of this methodology, using the wavelet leaders for the corresponding information theory quantifier evaluation.
- We exemplify both treatments with the analysis of a scalp epileptic EEG signal and compare the results of both methodologies for a scalp EEG recorded in the right central location (Channel C4), obtained from one patient.

## 2. Wavelet Methodology and Information Theory Quantifiers

#### 2.1. Wavelet Transform

_{a,b}} is the set of elemental functions generated by (i) scaling and (ii) translation of an admissible mother wavelet ψ(x) [11]:

^{2}(ℝ)—the space of real square summable functions-is defined as the correlation between the function (signal) f(x) with the family wavelet ψ

_{a,}

_{b}(x) for each a and b: [10–12]:

_{a,b}) represent the wavelet coefficients. In principle, the CWT produces an infinite number of coefficients. The information displayed at closely-spaced scales or at closely-spaced time points is highly correlated. As a consequence, the CWT provides a redundant representation of the signal under analysis. It is also time consuming to compute directly.

#### 2.2. Discrete Wavelet Transform and Quantifiers

_{a,b}and (ii) the discrete set of parameters, a

_{j}= 2

^{−}

^{j}and b

_{j,k}= 2

^{−}

^{j}k with j, k ∈ ℤ (the set of integers), the family F= {ψ

_{j,k}(x) = 2

^{j}

^{/2}ψ(2

^{j}x−k)} constitutes an orthonormal basis of L

^{2}(ℝ), the space of finite-energy signals. Each scale a

_{j}= 2

^{−}

^{j}is related to a given frequency band, and j is known as the resolution level.

^{2}(ℝ) can be recovered by:

^{2}(ℝ) sense, where the inner-product coefficients,

^{2}(ℝ). This scheme brought to light a link with filter banks and a fast wavelet transform algorithm decomposing signals of N samples with $\mathcal{O}$ operations. We refer the reader to [11,12,40,41] for detailed expositions of these topics.

_{max}≤ log

_{2}(N), according to Equation (3), the wavelet expansion of the signal is,

_{j,k}can be interpreted as the local residual errors between successive signal approximations at scales j − 1 and j, respectively, and contain the information of the signal f(x) corresponding to the frequency interval ${2}^{j-{j}_{max}-2}$, where ω

_{s}is the sample frequency.

_{j,k}(x)} is an orthonormal basis for L

^{2}(ℝ), the concept of energy is linked with the usual notions derived from the Fourier theory. The energy at resolution level j = 1, ⋯ ,j

_{max}will be given by:

_{tot}= ||f||

^{2}of the signal is:

_{j}-values, which represent the relative wavelet energy (RWE):

_{max}.

_{j}yield, at different scales, the probability distribution for the energy. Clearly, ${\sum}_{j=1}^{{j}_{max}}{\rho}_{j}=1$. The distribution ${\mathcal{P}}^{(w)}$ can be considered as a time-scale probability density that constitutes a suitable tool for detecting and characterizing specific phenomena in both the time and the frequency planes [13–15].

_{0}is a normalization constant equal to the inverse of the maximum possible value of $\mathcal{J}$, so that Q ∈ [0,1]. Q

_{0}is obtained when one of the components of ${\mathcal{P}}^{(w)}$

_{n}, is equal to one and the remaining p

_{i}are equal to zero.

^{(min)}≤ C ≤ C

^{(max)}, meaning that additional information related to the dependence structure between the components of the system and the emergence of nontrivial collective behavior is provided by evaluating the statistical complexity. Moreover, it should be noted that statistical complexity fulfills two additional properties required for a suitable definition of complexity in physics [54]: (a) the quantifier must be measurable in different physical systems; and (b) it should enable physical interpretation and comparison between two measurements. Indeed, the definition of complexity in Equation (11) also depends on the scale. For a given system at each scale of observation, a new set of accessible states appears with its corresponding probability distribution, so that complexity changes, and therefore, different values for H and C are obtained.

#### 2.3. Wavelet Leaders and Quantifiers

_{0}∈ ℝ, the real number set, in the domain of a locally-bound function f, as:

^{α}(x

_{0}) if there exists C > 0 and a polynomial ${\mathcal{P}}_{{x}_{0}}$ of degree less than α, such that, near the point x

_{0},

^{α}and $f$ continuously extended, with 0 < α ≤ 1, ω >> 1, β > 0, have h

_{f}(0) = α and h

_{f}(x) = +∞, otherwise. This fact shows that the pointwise Hölder exponent captures a singularity in a regular environment. Note that the pointwise Hölder exponent is the usual and most preferable regularity exponent used in signal and image processing [55]. However, other exponents and parameters can be used to extend the local regularity analysis for non-locally bound functions [56,57].

^{r}, r ∈ ℕ, with derivatives that have a fast decay, and ψ has r vanishing moments, that is,

^{2}(ℝ),

_{j,k}and the pointwise Hölder regularity. If f is in the class C

^{α}(x

_{0}), it is proven in [58] that the wavelet coefficients of f satisfy, for all j ≥ 0,

_{j,k}is localized on the dyadic interval ${I}_{j,k}$, which means that the wavelet coefficient of f in I

_{j,k}has information related to this interval.

_{0}is in the domain of f, I

_{j}(x

_{0}) denotes the unique dyadic interval I

_{j,k}containing x

_{0}for the level j. Then, the wavelet leader for x

_{0}in the level j is defined as:

^{α}(x

_{0}), with α > 0. Then, for all j > 0,

^{r}has fast decay derivatives ψ

^{(}

^{n}

^{)}, 0 ≤ n ≤ r, with r > α.

_{0}in the domain of a bounded function f. That is a pdf based on the wavelet leaders. Recalling that d

_{j}(x

_{0}) is the wavelet leader coefficient for x

_{0}in the level j defined by Equation (19), this pdf is defined, at each x

_{0}in the domain of f, as:

_{j}(x

_{0}) ≠ 0 and ϱ

_{i}= 0, otherwise.

_{0}∈ Dom(f) is:

_{j}= 0, it is defined ϱ

_{j}log

_{2}(̺ϱ

_{j}) = 0. In analogous form, by use of Equation (11), we can also introduce the wavelet leader statistical complexity (WLSC) at each x

_{0}in the domain of a bounded function f as,

_{f}(x

_{0}). If f ∈ C

^{h}(x

_{0}) and f is uniformly Hölder, then, for each a > 1, there exists a resolution level m, such that:

_{f}(x

_{0}) takes values close to its maximum log

_{2}(m) when h

_{f}(x

_{0}) takes values close to zero. Otherwise, recalling that $Q$ and $S$, then C

_{f}(x

_{0}) takes values close to zero when S

_{f}(x

_{0}) takes values close to its maximum log

_{2}(m). Consequently, the irregular structures of the signal are related on the highest values of S

_{f}(x

_{0}) and the lowest values of C

_{f}(x

_{0}).

- Via the Mallat algorithm [40], compute c
_{j,k}for the resolution levels j = 1, ⋯, j_{max}(see Equation (16)). Considering the data series {f(n) : n = 1, ⋯, N} at the finest level, then j_{max}≤ log_{2}(N). - From the definition given by Equation (19), estimate the wavelet leaders ${({d}_{j}(n))}_{j=1,\cdots ,{j}_{max}}$ using the following equation:$${d}_{j}$$
- Calculate S
_{f}(n) and C_{f}(n) for the resolution level j_{max}, using Equations (24)–(26), entering the Jensen-Shannon divergence (Equation (12)) in the Q definition.

## 3. qEEG Analysis of a Tonic-Clonic Epileptic Signal

#### 3.1. Clinical Data and the Experimental Setup

_{s}= 102.4 Hz, in a PC hard drive. Recordings were performed under video control in order to have an accurate determination of the different stages of the seizure. The different stages of EEG signals were determined by the team of physicians. Off-line analysis was performed with characterization of semiological features. When possible, the onset and definition of the anatomical focus for each event were timed. The analysis for each event included 60 s of EEG before the seizure onset and 120 s of seizure and post-seizure phases.

**TI**= 80 s, with a “discharge” of slow waves superposed by fast ones with a lower amplitude. This discharge lasts ~8 s and has a mean amplitude of 100 μV. Afterward, the seizure spreads, making the analysis of the EEG more complicated due to muscle artifacts. However, it is possible to establish the beginning of the clonic phase at around

**T2**= 125 s and the end of the seizure at

**TF**= 155 s, where there is an abrupt decay of the signal amplitude. The start and ending epileptic recruiting rhythm are expected at

**T1**~ 75 s and

**T3**~ 110 s, according to Gastaut and Broughton [62,63].

_{j}(j = 1, ⋯ , 14). Their frequency limits, wavelet levels, as well as their correspondence with traditional EEG frequency bands are given in Table 1. As mentioned above, in the present work, we use an orthogonal cubic B-spline function as a mother wavelet. We eliminate the high frequency muscle activity by using wavelet analysis. We define j

_{max}= log

_{2}N = 14 (N = 18, 432 being the total number of data in our time series) frequency bands for an appropriate wavelet analysis within the multiresolution scheme to be used. Their frequency limits are given by ${2}^{j-{j}_{max}-2}$ where ω

_{s}= 102.4 Hz is the sample frequency. Their correspondence with traditional EEG frequency bands is given in Table 1.

_{9}to B

_{12}, 0.8–12.8 Hz). We did not consider the contributions from bands B

_{13}(25.6–12.8 Hz) and B

_{14}(51.2–25.6 Hz) with wavelet resolution levels j = 13 and j = 14, respectively, both containing high frequency artifacts related to muscle activity that blurred the EEG [64]. Although high frequency brain activity is also eliminated, their contributions during the seizure stage are not as important as those of the middle and low frequencies, as has been previously shown in [18]. In fact, the inclusion of these high frequency bands, which present a very disordered activity, makes the mathematical distinction between pre-seizure and during the seizure EEG (mean values and standard deviation over time intervals) more difficult. In particular, it is not possible to define and quantify the epileptic recruitment rhythm correctly.

_{13}and B

_{14}and the EEG signal reconstructed using wavelet resolution levels j = 9 to j = 12. In order to study the temporal evolution of the information theory quantifiers based on ODWT coefficients, the analyzed signal is divided into non-overlapping temporal windows of length L = 2.5 s each (N = 256 data), and for each interval, the quantifiers are evaluated.

#### 3.2. Analysis Based on a Set of ODWT Coefficients

_{9}to B

_{12}) for the EEG tonic-clonic epileptic record shown in Figure 2.

_{9}+ ρ

_{10}] ~ 50%). The seizure starts at

**TI**= 80 s with a discharge of slow waves superimposed with low voltage fast activity. This discharge lasts approximately 8 s and produces a marked rise in low frequency bands (delta activity), which reaches [ρ

_{9}+ ρ

_{10}] ~ 80% of the RWE. From 90 s onwards, the low frequency activity, represented by B

_{9}and B

_{10}, decreases abruptly to values lower than 10%, and the other frequency bands (alpha and theta activity, represented by B

_{11}and B

_{12}frequency bands, respectively) alternatively dominate.

_{11}, and after 140 s, when clonic discharges begin to separate further, B

_{10}rises up again until the end of the seizure, when B

_{9}also increases very quickly and both frequencies bands are dominant. The RWE contribution of frequency bands B

_{9}and B

_{10}(ρ

_{9}and ρ

_{10}) maintains this behavior throughout the post-seizure phase. We could conclude from this example that the seizure was dominated by the middle frequency bands B

_{11}and B

_{12}(alpha and theta rhythms, 3.2–12.8 Hz), with a corresponding abrupt activity decrease in the low frequency bands B

_{9}and B

_{10}(delta rhythm, 0.8–3.2 Hz). Clearly, this behavior can be associated with the putative “epileptic recruiting rhythm” (ERR) described by Gastaut and Broughton [63] and represented by the time interval between vertical lines

**T1**and

**T3**in Figure 4.

_{9}to B

_{14}are included), while the other line corresponds to results that ignore the contributions coming from high frequency bands (B

_{13}and B

_{14}), which mainly contain electromyographic activity.

_{9}to B

_{14}are included. A comparison is to be made with normalized SWS values in the pre-seizure stage. If the wavelet frequency bands B

_{13}and B

_{14}(bands that mainly reflect muscular activity) are not included, the mean normalized SWS value is lower than that for the pre-seizure one. Thus, the behavior of the normalized SWS after the onset of the seizure is compatible with an increase in the degree of disorder of the system, induced by a high frequency activity. Superimposed low and medium frequency activities, however, are responsible for the “remaining-signal’s more orderly behavior”. The decreasing values of the normalized SWS after

**T1**= 90 s (in both cases, with and without inclusion of high frequency bands) are indicative that the system presents a tendency to a more ordered behavior. This tendency is better appreciated without muscle activity. The normalized SWS behavior is clearly correlated with the ERR described by Gastaut and Broughton [63] and represented by the time interval between vertical lines

**T1**and

**T3**in the figure. Moreover, note that the normalized SWS in the last case adopts a minimum value around

**T2**= 125 s, coincident with the beginning of the clonic phase. The peak observed in the normalized SWS at

**T3**≅ 145 s could be associated with the disappearance of the ERR, again in agreement with Gastaut and Broughton’s description. After this point, the normalized SWS displays increasing values until

**TF**= 155 s, which is defined as the seizure’s ending time. Quantitatively, the normalized SWS for the post-seizure stage presents almost constant values, comparable to those obtained for the pre-seizure stage.

_{13}and B

_{14}are included or left out in their evaluation.

_{13}and B

_{14}. Excluding these two bands yields quite different behavior, especially in the time interval identified with the ERR. There, the complexity values are significantly bigger than in the pre- and post-seizure period.

#### 3.3. Analysis Based on a Set of Wavelet Leader Coefficients

_{max}= 14 ≤ log

_{2}(18, 432). For the first approach, we do not consider the contributions from the levels j = 13 and j = 14 associated with high frequency muscle activity at computing the probability distribution ${\mathcal{P}}_{{x}_{0}}$ in Formula (23).

_{f}(n). There are several techniques to estimate the pointwise Hölder exponent, and this one is an efficient alternative; see [65] and [55] for further information on this topic.

_{0}. However, in the case of a natural series, it is practically impossible, so that the maximum corresponds to the position of highest irregularity. In the same sense, this choice in the construction of the pdf also determines that the WLSC reaches minimum values at the points of greatest irregularity. Then, the range variation of the wavelet leader-based quantifiers, the wavelet leader entropy (WLSS) and wavelet leader complexity (WLSC) are the inverse of those quantifiers based on ODWT, that is the wavelet Shannon entropy (SWS) and wavelet statistical complexity (WSC), respectively.

_{2}(12) indicate an irregularity in the signal; otherwise, the lowest values of the WLSC also indicate this fact. It is possible to observe an increase of the WLSS during the TCES, and conversely, the values of the pointwise Hölder exponent and the WLSC fall during the TCES. The maximum values of the WLSS are between T2 and T3, while the pointwise Hölder exponent and WLSC take the minimum values. The inverse relation between the WLSS and the Hölder exponents can also be observed, coinciding with the result proven in [32].

**T2**and

**T3**.

#### 3.4. Discussion

## 4. Final Remarks

^{2}of the brain surface and, hence, from many millions of neurons. With such large numbers, it seems quite natural to model the neocortex as a continuous sheet of neurons (neuronal matter) whose activity varies with time. Taking into account the results that we have obtained for: (1) the chaoticity (biggest Lyapunov exponent with stationary constrained removed) as a function of time [7,19] and (2) the biggest Lyapunov exponent for the selected portion of the EEG signal, we conclude that a chaotic behavior can be associated with the whole EEG signal, although it becomes less noticeable during the recruiting phase [7,19]). We have shown here that the recruiting phase also exhibits larger values of statistical complexity. As pointed out by many authors (see, for instance, [20]), the coexistence of chaos with ordering and increasing complexity for an extended system is a manifestation of self-organization. On the basis of (1) experimental EEG data and (2) the use of appropriate statistical tools, the following conjecture could be proposed in the case of secondary generalized TCES: the epileptic focus triggers a self-organized brain state characterized by both order and maximal complexity. As a consequence, it becomes clear that quantifiers of the epileptic recruiting rhythm are useful tools for the characterization of the genesis and spreading of this type of seizure. In this context, we consider that the wavelet-based informational tools reviewed in the present work and their evaluation could be profitably employed for developing models, as well as for illuminating a number of aspects of the spatio-temporal dynamics of the generalized TCES-EEG data that had not previously been appreciated.

- The analysis is local, and wavelet leader-based quantifiers can detect a higher resolution in the changes of the signals than Shannon wavelet entropy and wavelet statistical complexity. Moreover, the video recordings of the patient present some inaccurate information on these changes.
- As mentioned above, the results obtained for the filtered signal (i.e., without the contribution of muscle-noise contaminated bands) is essentially identical to the original signal. This property has two advantages, it reduces the use of mathematical tools, such as signal pre-processing filters, and second, it simplifies the calculation process.
- Pre-seizure and post-seizure fluctuation values in the evaluation of SWS and WSC quantifiers make average evaluation necessary to find the plateau that occurs naturally in wavelet leader-based quantifiers (WLSS and WLSC). Moreover, this fact clearly marks discontinuities in the signal (such as shown at ~60 s).
- The maximum wavelet leader Shannon entropy WLSS occurs slightly after 120 s, marking a transition from the tonic to the clonic phase, in agreement with what was found by computing the SWS and WSC.

## Acknowledgments

**MSC classifications:**65T60; 94A12; 26A16; 37M10; 28D20

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Scalp EEG signal for a tonic-clonic epileptic seizure (TCES), recorded at the central right location, the C4 channel. The vertical lines mark the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s. Notice that the dramatic transition from rigidity (tonic stage) to convulsions (clonic stage) around

**T2**= 125 s is not clearly discernible.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 3.**Noise-free signal, reconstructed from wavelet frequency bands B

_{9}to B

_{12}of the scalp EEG signal for a TCES, recorded at the central right location, the C4 channel. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 4.**Time evolution of the relative wavelet energy (RWE) corresponding to the EEG noise-free signal (Figure 3), for the frequency bands B

_{9}, B

_{10}, B

_{11}and B

_{12}. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 5.**Temporal evolution of the normalized Shannon wavelet entropy (normalized SWS). One line represents the normalized SWS when frequency bands B

_{9}to B

_{14}are included, while the other corresponds to results that ignore the contributions coming from high frequency bands, B

_{13}and B

_{14}, which mainly contain electromyographic activity. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 6.**Temporal evolution of the wavelet statistical complexity (WSC). One line represents the time evolution of the normalized WSC when frequency bands B

_{9}to B

_{14}are included, while the other corresponds to results that ignore contributions coming from high frequency bands, B

_{13}and B

_{14}, which mainly contain electromyographic activity. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 7.**Wavelet leader Shannon entropy temporal evolution of the filtered signal, without the inclusion of frequency bands containing muscle activity. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 8.**Wavelet leader statistical complexity temporal evolution of the filtered signal, without the inclusion of frequency bands containing muscle activity. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 9.**Pointwise Hölder exponent time evolution of the filtered signal, without the inclusion of frequency bands containing muscle activity. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 10.**Temporal evolution of the wavelet leader Shannon entropy for the original signal corresponding to tonic-clonic epileptic EEG record. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 11.**Temporal evolution of the wavelet leader Shannon entropy for the original signals corresponding to tonic-clonic epileptic EEG records in different channels. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Figure 12.**Temporal evolution of the wavelet leader statistical complexity for the original signals corresponding to tonic-clonic epileptic EEG records in different channels. The vertical lines indicate the following transitions: The seizure starts at

**TI**= 80 s and the clonic phase at

**T2**= 125 s. The seizure ends at

**TF**= 155 s.

**T1**= 90 s and

**T3**= 145 s mark the expected beginning and end of the epileptic recruiting rhythm (ERR).

**Table 1.**Frequency boundaries (in Hz) associated with the different orthogonal discrete wavelet transform (ODWT) resolution wavelet levels j with sample frequency ω

_{s}= 102.4 Hz and time series length N = 18,432. The traditional EEG frequency bands correspond to the following frequencies: δ (0.5–.5 Hz); θ (3.5–.5 Hz); α (7.5–12.5 Hz); β (12.5–30.0 Hz); γ (>30.0 Hz).

B_{j} | ω_{min} (Hz) | ω_{max} (Hz) | j-Level | EEG Band |
---|---|---|---|---|

B_{14} | 25.6 | 51.2 | 14 | β, γ |

B_{13} | 12.8 | 25.6 | 13 | β |

B_{12} | 6.4 | 12.8 | 12 | θ, α |

B_{11} | 3.2 | 6.4 | 11 | θ |

B_{10} | 1.6 | 3.2 | 10 | δ |

B_{9} | 0.8 | 1.6 | 9 | δ |

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**MDPI and ACS Style**

Rosenblatt, M.; Figliola, A.; Paccosi, G.; Serrano, E.; Rosso, O.A.
A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients. *Entropy* **2014**, *16*, 5976-6005.
https://doi.org/10.3390/e16115976

**AMA Style**

Rosenblatt M, Figliola A, Paccosi G, Serrano E, Rosso OA.
A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients. *Entropy*. 2014; 16(11):5976-6005.
https://doi.org/10.3390/e16115976

**Chicago/Turabian Style**

Rosenblatt, Mariel, Alejandra Figliola, Gustavo Paccosi, Eduardo Serrano, and Osvaldo A. Rosso.
2014. "A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients" *Entropy* 16, no. 11: 5976-6005.
https://doi.org/10.3390/e16115976