Power Complexity Feature-based Seizure Prediction Using DNN and Firefly-BPNN Optimization Algorithm

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Power Complexity Feature-based Seizure Prediction Using DNN and Firefly-BPNN Optimization Algorithm

Morteza Behnam

Department of Electrical Engineering, Najafabad Branch, Islamic Azad University,

Najafabad, Isfahan, Iran.

[email protected]

Hossein Pourghassem Department of Electrical Engineering, Najafabad Branch, Islamic Azad University,

Najafabad, Isfahan, Iran.

[email protected]

Abstract— Epileptic seizure prediction is an online clinical application for pediatric patient monitoring. In this paper, we have introduced a novel method for detecting and predicting the seizure attack. After signal preprocessing, the time and frequency domain features are extracted. In our scenario, by estimating the power spectrum using time samples of windowed signal, the features such as non-linearity model and complexity of power for demonstrating the signal behavior are extracted. Our complexity- based feature is named Power Complexity Feature (PCF). The optimal features are selected by a hybrid model of Firefly optimization algorithm (FA) and Back Propagation Neural Network (BPNN). With these features, initial optimized MLP is trained in offline mode. A Dynamic Neural Network (DNN) based on Non-Auto Regressive (NAR) architecture estimates the EEG signal. With the trained classifier in offline mode, the predicted signals with optimal features are recognized in two classes. The initial classifier in each training stage is updated. Also, the initial dead part of signal and length of prediction by Monte-Carlo analysis and considering a similarity criterion are improved.

Ultimately, the seizure signals by optimized features are recognized with accuracy rate of 86.8% in offline mode and also accuracy rate of 85.7% for the predicted signal with prediction time of 3.12 seconds is obtained.

Keywords- Seizure, Firefly algorithm, Prediction, Non-auto regressive architecture, Power complexity feature.

I. INTRODUCTION

The EEG signal as non-invasive method is a clinical application to analyze the brain disorder. Epileptic seizure attack is one of important disorders with the symptoms on the EEG signals [1]. About 50 millions of people in the world have this disease. When the epileptic seizure happens, the patients need to special cares such as drug therapy and behavioral cares [1]. So, the prediction of the seizure attack can be helpful. The predictor system and its algorithm can be used in clinics and the devices for monitoring the patients [1, 2]. The EEG signal is a random process with determined band width of frequency.

Normal EEG and abnormal EEG have the same frequency behaviors. So, the feature extraction has importance in the real- time EEG signal processing [2]. In general, we can observe a processing system for signal prediction and event detection in many researches. To predict the EEG signal as a time series, the estimation tools are need. Adaptive filters are commonly systems for predicting the signal [2]. The wiener filter based on Autoregressive (AR) model as initial filter and Least Mean

Square (LMS), Recursive Least Squares (RLS) and the Kalman filtering are the predictor systems [3]. Also, Dynamic Neural Network (DNN) based on linear and non-linear autoregressive models estimates the EEG signal on time domain [4].

With predicting the EEG signal, the features must be extracted. The time domain, frequency and spectrum-based features also chaotic features such as Lyapunov exponents, Higuchi dimension and correlation dimension are usually used [5]. The processing time and order of algorithm is important for real-time processing. These extracted features are recognized by the trained classifier in offline mode. Extracting the high performance features with low processing time is important [6].

So, estimating the features can be helpful in this application. On the other hand, these features should be optimized by a suitable feature selection algorithm. These optimization algorithms are accomplished in online or offline procedures. These methods are based on the evolutionary algorithms such as Genetic [7], Particle Swarm [8], Ant colony and etc. Also, the statistical scenarios such as LDA, PCA and the kernel-based methods of them are used for optimal feature selection [7]. The EEG signals are predicted and the patterns are classified in real-time state by optimized features. Choosing the convenient features with high efficiency and low order of the computation is so important. Also, the predictor algorithm with high accuracy and ability to estimate the EEG time series in more samples is another challenge to design the predictor algorithm. The optimization algorithm for selecting the features with more efficiency can improve the accuracy of signal classification in the form of real-time.

II. SEIZURE PATTERN PREDICTION ALGORITHM

In this paper, the offline seizure detection is an important section of online seizure prediction. The offline processing is as shown in Fig. 1. In preprocessing, the EEG signal is filtered and windowed to some epochs. In the proposed algorithm, a novel feature that is called Power Complexity Feature (PCF) is introduced. A hybrid model based on Firefly optimization algorithm (FA) and Back Propagation Neural Network (BPNN) for optimal feature selection is used. Optimized MLP neural network in the hidden layer is trained using optimal features.

This classifier is used for recognizing the signal after predicting.

By Non-Autoregressive (NAR) neural network as a Dynamic Neural Network (DNN), the samples of EEG signal as a time series are estimated. In this algorithm, the dead part of signal for initial training with large length is considered. The processing

22nd Iranian Conference on Biomedical Engineering(ICBME 2015), Iranian Research Organization for Science and Technology (IROST), Tehran, Iran, 25-27 November 2015

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time is dependent on the computational order, so the prediction time is equal to the optimal estimated samples. Fig. 2 presents the seizure prediction algorithm; at first the NAR neural network estimates the samples of signal. The estimated signal is filtered by band pass filter. In the next training, the length of estimation is modified. In each estimated time series, optimal features are extracted. These features are classified by optimal classifier that has been trained with optimal features in the offline processing. The weights of this classifier are updated in each iteration based on the similarity measure between the estimated signal in the previous iteration and the observed signal. By Monte-Carlo analyzing, the parameters of NAR neural network such as sample number of estimation and initial length of signal for the first training are optimized using the similarity criterion.

III. F^EATUREEXTRACTION

To design a classifier for attack prediction, the extracted features should have two attributes. The processing time is an important issue for online signal processing also the variation rate of signal into upcoming the seizure attack as complexity of this occurrence is main problem for detection. The estimated features have been represented in this section.

A. Dataset Preprocessing

In this paper, the EEG signal dataset are recorded from pediatric patients and the children with seizure disorder and intractable epileptic seizure. These signals have been collected from Children's Hospital Boston (CHB-MIT). For surgery and medical intervention, after withdrawal the anti-epileptic drug, the patients have monitored for a few days [9]. Here, we have used from 100 hours of the EEG signals. The sampling frequency of EEG signal is 256 Hz, also the signals have 16-Bit resolution.

By dividing each signal with length of 1 hour to N=120epochs, we have 12480 signals that each one is 30 seconds as length time. 2040 signals or about 16.3% of all signals have the symptoms of seizure. The next step of signal conditioning is dataset filtration. For filtering the EEG signal, the Kaiser–

Bessel filtering method is applied as FIR method for windowing design. The cut-off frequencies of filtration ω_C₁and ω_C₂have been tuned on 0.5 Hz and 35 Hz, respectively [1, 10].

B. Maximum Domain and Number of Peaks

In time domain, the Absolute Maximum Value (AMV) and the Number of Local Maximum (NLM) are suitable features [10]. The AMV in each epoch of signal is obtained as,

( ) { [ ]

⁰

}

_i

AMV i =m ax s n n≥ (1) where i is the number of epoch of each signal and ^{s n}

[ ]

^is

EEG signal. Also, n is the number of samples over the time.

The NLM feature in each epoch of signal is attained by,

( ) {

^{0 1}

[ ] [ ]

^{& 1}

[ ] [ ] }

_i

NLM i = n ≥ s n+ <s n s n− <s n (2) C. Power Complexity Feature (PCF)

Here, we introduce a novel method for feature extraction with applications in the epileptic seizure prediction and detection. This feature is based on the power spectrum estimation and calculating the Kolmogorov complexity of the power in different windows.

Figure 1. Block diagram of epileptic seizure pattern detection algorithm in the offline mode.

1) Power Spectrum Estimation (PSE)

By supposing that the epoch of EEG signal is a random process, we can say:

[ ]

0 1 1 T

s n =⎡⎣s s …sM₋ ⎤⎦ (3) where the length of random process ^{s n}

[ ]

^isM samples. The usual computation of autocorrelation matrix is very time consuming, because the expectation value calculation to obtain the autocorrelation matrix is costly [3, 11]. So, similar to LMS estimation algorithm as a commonly methods of wiener filter, with canceling the expectation computing and sub-situating the time samples, a time-based estimation of autocorrelation matrix instead of R_s is obtained, so we have [12]:

[ ]

^.

[ ]

ˆs H

R =s n s n (4) To estimate the PSE, the DTFT of ˆR_s has been computed.

The PSE on logarithmic scale (dB) is presented as following:

( )

^, ^10log

{ { }

^ˆ^s

}

PSE i n = FT R (5)

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Figure 2. Block diagram of online seizure pattern prediction algorithm.

By considering a windowing method based on Hamming window that is defined by:

[ ]

0.54 0.46cos ² n , 0

w n π n ψ

ψ

⎛ ⎞

= − ⎜ ⎟ ≤ ≤

⎝ ⎠ (6) where ψ is the sample number of window [10]. Also, the value of ψ is dependent on 3 factors,

ψ =L Mμ (7) where L is width of the windows and μ is also window factor.

With using this window and PSE, the power of each windowed signal is estimated. So, this method is called Windowed Power Spectrum Estimation (WPSE). To obtain WPSE, the windowed signal is considered instead of ^{s n}

[ ]

. The WPSE is represented with following relationship [11, 12],

[ ] [ ] [ ]

^.

sw n =s n w n (8)

( )

^, ^10log

{ { }

^ˆ^sw

}

WPSE i n = FT R (9) whereμis appropriately selected as a constant value for length of window, the parameter L is defined by maximum value in WPSE vector. So, the following conditions based on a threshold of WPSE are mentioned as,

( )

^,

{ ( )

^, ^{| ,} ⁰

}

MP i λ =m ax WPSE i n i n > (10)

( ) ( )

¹1

, , 0.5 , , 2

th i i

MP i P L L

λ

λ ⁻₋

⎧ > =

⎪⎨ < =

⎪⎩ (11) where MP is the maximum value in WPSE vector that i is the epoch number and n is the sample number of WPSE, λ is also

sample number of MP vector which is deferent for each signal.

After computing the MP, in the next step the windowing procedure is carried out again with 50% overlapping to reduce the variance of estimation for remaining it to form unbiased [10, 12]. After this iterative procedure for each signal a vector with deferent length is provided. By averaging, this vector is converted to one number as mean of maximum value of WPSE. So, this parameter is Spectral Estimation Vector (SEV), we can say that,

( ) ( )

1

1 ,

j

SEV i MP i j

λ

λ ₌

=

∑

(12) In fact, this averaging in final procedure has been used instead of mathematical expectation that canceled at first [12].

The SEV value for each signal will be used in the other features as main basis.

2) Kolmogorov Complexity

Here, we present a novel feature to detect and predict the seizure based on complexity measure of power variation in different windows. The numerical complexity is a model for analyzing the complexity of feature structure [13]. For this purpose, a numerical scenario based on the Kolmogorov complexity is used. This approach is derived from Lempel and Ziv method [13, 14]. With converting the SEV for signal i-th to 8-bit string, it is denoted by,

( ) {

¹

( )

^, ²

( )

^{, . . . ,} ⁸

( ) }

bin bin bin bin

SEV i = SEV i SEV i SEV i (13)

So, the Kolmogorov complexity of SEVbin

( )

i for the string

( ) { }

^0,1^*

SEVbin i ∈ with respect to ξ is defined as [14],

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(

^bin

( ) ) {

^;

^{{ }}

^{0,1 &}^*

^{( )}

^bin

^{( )} }

C SEV_ξ i =min p p∈ ξ p =SEV i where Kolmogorov complexity depends on choosing the descriptive languageξ. So, with using the invariance theorem, a recursive function U has been considered. For constant

0

c> , we have [14]:

( ( ) )

U bin bin

C SEV i ≤ C SEV_ξ i +c (15) where the machine U satisfies the theorem in some sense minimal among all machines. At last, the normalized measure of complexity as a feature is achieved by,

( )

C_U

(

SEV_bin

( )

i

)

. log2n n K Complexity i

− = n (16)

where n is the number of bit to define the SEVbin

( )

i values.

So, n K Complexity i−

( )

value as a measure describes the numerical complexity of the estimated power spectrum in different windows of EEG signal. In this paper, this feature is named Power Complexity Feature (PCF).

D. Number of Windows

With regard to previous section, the number of windows in each signal is dependent on the dynamics of EEG signal, so λ or the length of MP as a feature for epileptic seizure detection and in future for the prediction is used.

E. Non-Linear Energy of WPSE

To compute the values of Non-Linear Energy (NLE) of windowed power spectrum estimation, we calculate the Non- Linearity (NL) criterion for each epoch of signal [15]. For this purpose, the NL for each sample of the signal is defined as,

( ) ( )

^, ²

(

^, ^{1 .}

) (

^, ¹

)

NL i =MP i λ −MP i λ− MP i λ+ (17) So, to evaluate the non-linear energy of each WPSE for one epoch, a simple weighting method is applied. In this scenario,

( ) ( ) ( )

( ) ( )

¹2

( )

, , . , , .

W W

NL i Threshold NL i W NL i NL i Threshold NL i W NL i

λ λ

⎧ < =

⎪⎨ > =

⎪⎩ (18)

where W₁and W₂are the weights with constant values for all signals that considered in the optimized state using iterative programming. By defining the weighted form of this non- linearity parameter, the averaging value for each signal as non- linear energy of WPSE is as obtained by [15],

( )

¹

( )

2

1 ,

2 _j ^W

NLE i NL i j

λ

−

=

= −

∑

(19) F. Absolute Value of DFT

Complex analysis based on the frequency domain and the spectrum features are costly for online seizure prediction. So, we focus on the time domain and estimated features, but to consider the frequency coefficients, the Discrete Fourier Transform (DFT) on each epoch of signal is used [8, 10]. So, the first 5 absolute values of coefficients are obtained as frequency features.

IV. OPTIMAL FEATURE SELECTION

To optimize the feature vector for classifying the EEG signals, a hybrid model based on Firefly optimization algorithm and back propagation neural network is used. Ultimately, this algorithm converges to optimal features and these features are used in the seizure detection and prediction algorithms.

A. Firefly and BPNN Optimization Algorithm

The Firefly optimization algorithm (FA) is a meta-heuristic processing. The FA is one of the optimization algorithms for solving the multi-agent problems. The fireflies are about two thousand species. So, each type has a model of pattern for flashing the lights. By supposing the initial descriptions, we can start the original algorithm. So, the all of fireflies must be unisex and they are in one of species categories [16]. Therefore, all of them follow a particular of flashing light pattern. A firefly can be responded to the others fireflies. A prototype of firefly with particular brightness attracts to another one with more brightness. In special case, if all fireflies have brightness with equal intensity, the attractive procedure will be randomly [16].

To employ the FA, in the first step, the objective function (OF) must be defined. This function is obtained based on the MLP neural network with BPNN learning algorithm [17]. To evaluate the objective function for each firefly, we consider a MLP neural network with BP algorithm to learn that is called BPNN [17]. This net is used as EEG signal classifier in two classes, seizure signal and non-seizure signal. The Levenberg- Marquardt (LM) as training function of neural network is used [8, 10]. In each training of net, we consider a firefly with high intensity, in fact each firefly is binary sub-vector where describes the supposed optimal feature vector. The firefly optimization algorithm is maximization solver. The error of data classification for each sample of population in offline processing based on target of signal is computed. So, by considering the Mean Square Error (MSE) of neural network, we introduce an objective function to evaluate the optimal feature vector [10, 17]. The unbiased estimator of MSE is obtained as,

( ) ( )

( )

²

1

1 2

N

j

MSE Target j Output j C N ₌

=

∑

− (20)

( ) (

¹

)

OF i = MSE Neural Network (21) where N is the number of features in the training set and C is the number of classes [8, 17]. Our main issue is a Minimum MSE (MMSE) problem. In each training epoch of net, 70% of the signals (sub-dataset for offline processing) are used for training and 30% of the signals are considered for the test. The number of hidden layer neurons of net is set to double length of the feature vector for each subspace. The dimension of feature space is d =10. Our purpose is the optimal features selection [7]. With generating an initial population of fireflies as feature vector, a single value as light intensity of firefly is assigned for firefly i-th that is determined by I_i =OF FV( _i)where FV is feature vector. Also, by considering a coefficient of light absorption γ the evolutionary algorithm is run. In iterative algorithm, we have a local search and updating the intensities under the name

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of generation cycle. When I_i >I_j , the firefly j moves towards the firefly i in d-dimensions [16]. The severity of attractiveness for two fireflies with distance r is calculated via exponential function. This function in the name of attractiveness by the Maclaurin expansion of exponential term is as obtained by,

( )

exp⁰

(

²

)

⁰ 2

. 1 I

I r I r

γ r

= − ≈ γ

+ (22) where I₀ is initial light intensity [16]. Also for computing the distance and the firefly’s movement, the Euclidian distance between two prototypes of fireflies is calculated. So,

( )

1 2 2

, ,

1 d

ij i j i k j k

k

r FV FV FV FV

=

⎧ ⎫

⎪ ⎪

= − =⎨ − ⎬

⎪ ⎪

⎩

∑

⎭ (23) After computing the r_ijas a distance between two fireflies the motion is started [16]. The new position or new subspace of feature vector by ^g

{}

^. as a mapping function is defined as,

( ) ( ) ⁽ ⁾

{ }

1 . 0.5

t t t t

i i ij j i

FV ⁺ =g FV +I r FV −FV +α rnd− (24) where FV_i^t is a subspace of feature vector in iteration of t and α is constant value as a weight controller for tuning the distance and motion. The value of rnd is a random number between [0,1]. After this procedure, the hybrid algorithm is converged to the optimal feature vector for EEG signal classification. These optimized features are the number of peaks, number of windows, non-linear energy of WPSE and PCF.

V. SIGNAL ESTIMATION WITH NARPREDICTOR

By using a NAR predictor the EEG time series is estimated (Fig. 2). With considering a dead epoch of signal as initial tuning for the weights, we estimate the EEG signal at future epochs. The preliminary length for dead part of signal will be tuned by Monte-Carlo analysis [18], so we suppose that the length of dead part is P. The signal in the form of online are recorded and filtered. A Non-Linear Autoregressive (NAR) model based on ^{AR P}

( )

is defined as [19],

[ ] ( [

^{1 ,}

] [

^{2 ,}

]

^,

[ ] )

n

s n =h s n− s n− … s n P− +ε (25) where ^{s n}

[ ]

is the EEG signal as a random process that is defined by AR model [19]. The function h is also unknown and smooth. In this equation,

[ ] [ ] [ ]

{

n ^{| 1}^{, 2 ,}^,

}

⁰

E ε s n− s n− … s n P− = (26) where ε_n is a random variable with Gaussian distribution and variance σ². The optimal prediction for ^{s n}

[ ]

based on Minimum Mean Square Error (MMSE) with having the observation vector

[

^{1 ,}

] [

^{2 ,}

]

^,

[ ]

^T

s n s n s n P

⎡ − − … − ⎤

⎣ ⎦ by approximating the ^h

( )

^.

function the estimated value of signal is obtained as [4, 19],

[ ] [ ]

1 1

N P

i ij i

i j

n W f w s

s n j ϕ

= =

⎛ ⎞

⎜ ⎟

= − +

⎜ ⎟

⎝ ⎠

∑ ∑

(27) where ^{s n}

[ ]

is an estimated sample by feed forward non-linear neural network (FF-NAR) [4]. The function f is monotonic function such as sigmoid function. Also, by using the MLP and

considering some taps as Time Delay Neural Network (TDNN) [4, 19], we can estimate N samples of the signal to form

^{[ ]} ^ˆ

[ ] [

^{, 1 ,}^ˆ

]

^,^ˆ

[ ]

^T

s n =⎡⎣s n s n+ … s n N+ ⎤⎦ . To adjust the value of N and P for arriving to the best predictor and suitable trained weights, we have used from Monte-Carlo analysis. Ultimately, we have N samples of each epoch in an iteration of net and the value of N is converged to the optimal value as processing time or the number of estimated samples is considered as prediction time [20].

After estimating the vectors n[ ] the optimal features are extracted.

These features are classified to form real-time by trained MLP neural network [8]. To optimize the NAR net and our signal prediction, in each epoch of estimation, the NAR net and MLP are re-optimized by Monte-Carlo analysis and similarity criterion.

VI. EXPERIMENTAL RESULTS

A. Monte-Carlo Analysis and NAR Optimization

The NAR network optimization scenario has three sections.

Optimizing the initial length for the first prediction, length of [ ]

s n or determining the N to predict and optimizing the MLP classifier for seizure detection algorithm. The similarity between the estimated signal in the last iteration and the observed signal is computed by,

12

1 1

[ ], [ ]) [ ]. [ ] . [ ]. [ ] (

N N

n n

s n s n s n s n s n s n

Sim

−

= =

⎛ ⎞ ⎛ ⎞

= ⎜⎜⎝

∑

⎟ ⎜⎟ ⎜⎠ ⎝

∑

⎟⎟⎠ ⁽²⁸⁾ With considering a threshold for maximum of Sim in the first iteration as a random variable with Gaussian PDF by two- sided error analysis in Monte-Carlo method [18], the best value for N and the length of the first prediction are obtained. Also, with modifying the length of the first signal for training and each epoch of prediction, the weights of the MLP classifier are re-trained and they are rounded for avoiding the over-fitting.

B. Initial Optimal Classifier and Final Prediction

With using the estimator the signal is predicted and by a trained classifier the pattern is recognized. In this paper, the MLP neural network with BP learning algorithm is as offline classifier. By defining the input neurons based on the number of optimal features, the number of input neurons is 4. For feature space complexity problem a hidden layer is considered. To optimize the number of neurons for hidden layer, the repetitive loop based on MMSE for performance of classifier is applied.

So, the number of hidden neurons has been tuned on 18. For training the initial classifier 30% of dataset is considered. To prepare the initial optimal classifier, 70% of this sub-dataset for the training, 20% for the test and 10% for the validation check are considered. The final results are demonstrated in Table I. In this table, the results of classification without optimal features, with optimal features and the results of updated classifier in the prediction procedure are shown. For the seizure prediction and updating the classification, we have used from 70% dataset as another sub-dataset. At last, we can detect the seizure attack with mean of accuracy rate of 86.8% and we have predicted the epileptic seizure attack with accuracy rate of 85.7%. Also, the prediction time of 3.12 seconds is obtained. A summary of the results for seizure detection and prediction by our proposed algorithm is obtained in Fig. 3.

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TABLE I. FINAL RESULTS OF EEGSIGNAL PREDICTION AND CLASSIFICATION. Classification Without Optimal Features

Time of EEG Signal (min) Accuracy rate (%) Parameter

Seizure Non-Seizure Correct Wrong Training 214.2 – (70%) 1096.2 – (70%) 75.4 24.6

Test 61.2 – (20%) 313.2 – (20%) 73.5 26.5 Validation 30.6 – (10%) 156.6 – (10%) 67.0 33.0 Total 306 – (30%) 1566 – (30%) 74.3 25.7

Classification With Optimal Features

Training 214.2 – (70%) 1096.2 – (70%) 87.1 12.9 Test 61.2 – (20%) 313.2 – (20%) 84.5 15.5 Validation 30.6 – (10%) 156.6 – (10%) 89.0 11.0 Total 306 – (30%) 1566 – (30%) 86.8 13.2

Epileptic Seizure Pattern Prediction

Time of EEG Signal (min) Accuracy rate (%) Parameter

Seizure Non-Seizure Correct Wrong

Validation 71.4 365.4 89.3 10.7

Total 714 – (70%) 3654 – (70%) 85.7 14.3 Prediction Analysis Results Prediction Analysis Results Mean of Accuracy 85.7% Variance of MSE 4.5 10× ⁻⁵ Mean of MSE 0.00126 Prediction Time 3.12 Sec

Figure 3. A summary of the seizure detection and prediction results.

VII. C^ONCLUSION

The symptoms of the epileptic seizure are stochastically. By convenient estimating the power spectrum, the processing time and the delay of prediction are reduced. The PCF is a suitable feature for signal classification. A hybrid model based on Firefly-BPNN optimization algorithm can search appropriately the feature space. The NAR neural network with predicting the EEG signal could be predicted the seizure signal using the optimal features and MLP classifier that trained in the offline mode. By using Monte-Carlo analysis, the online classification is optimized and the predicting time has been decreased.

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