Nigina Toktassynova

Hassen Fourati

Batyrbek Suleimenov

Toktassynova Nigina

Modelling and Control Structure of a Phosphorite Sinter Process with Grey System Theory

Keywords: Grey System, Sintering Process, Particle Swarm Optimization, Predictive Model, Prediction Optimization

The sintering process of phosphorite ore occurs with a large amount of return caused by untimely process control. The control task of the phosphorite ore sintering is to regulate parameters of the process to obtain a high-quality sinter. The parameter clearly responsible for the sinter quality is the temperature in the wind box (also called burn through point (BTP)). Therefore, in order to solve the real-time control task, it is necessary to predict the BTP. In this paper, the grey system theory is used as a predictive approach, which makes it possible to obtain an adequate model that has the character of a "generalized energy system" and uses a small initial sample. Based on the grey model GMC(1,n), which is constructed in real-time by using real data at the beginning of the process, the temperature is well predicted at the end of the sintering process. When the temperature does not match the set value or to find out an optimal regulation, a control synthesis is carried out through an optimization of the prediction according to the "particle swarm" algorithm.

Introduction

Sintering in metallurgy is a thermal process that occurs in a metallurgical charge, composed of ore pellets, concentrates, and fuel (coke). Due to the process nonlinearity, the real-time quality control is a complicated task. In practice, the operator makes changes to the process after the product is obtained, which leads to a large number of returns and expenses for re-sintering. In this regard, it becomes necessary to predict sinter quality in advance and control the process based on predictive data. One of the key indicators of the sintering quality is the burn through point (BTP) that indicates the sintering process completion and represents the point with the highest temperature. The problem of BTP prediction and control is studied in many works using various algorithms such as neural networks, genetic algorithms, cluster analysis, and fuzzy control. Due to the evolution and widespread use of neural networks, a large number of works related to prediction, use this method in various fields of research such as the BTP prediction and control. For example in the work [START_REF] Feng | Adaptive prediction system of sintering through point based on self-organize artificial neural network[END_REF] , a new predictive parameter (the mathematics inflexion point of waste gas temperature curve in the middle of the strand) was measured at different times (600 groups of data) and fed to the input of a multilayer neural network, whose output predicts the BTP values by 5 steps forward. The neural network is also used in the work [START_REF] Peng | Sintering finish point intelligent control[END_REF] , where strand speed and BTP at the previous instants of time were given to the network inputs. The network, together with the training algorithm, was used to update the BTP model and called the neural network identifier, which used in the adaptive pole placement algorithm as an accurate model. In the work [START_REF] Du | Intelligent coordinating control between burn-through point and mixture bunker level in an iron ore sintering process[END_REF] the current value of BTP, temperatures in the middle, at the end of the process, and the strand speed were given to the input of a neural network to predict the BTP and make an intelligent control of the iron ore sintering process. Some works use 2 BTP predictive models: temporary and technological. So to predict the permeability of lead-zinc ore in work [START_REF] Wu | Intelligent optimal control for lead-zinc sintering process state[END_REF] the temporary neural network was supplied with 6 previous values for permeability, and the technological neural network used the temperature of the fire, the humidity, the sulfur, lead, silicon dioxide content, and the strand speed. In the work [START_REF] Wu | Neural-network-based integrated model for predicting burnthrough point in lead-zinc sintering process[END_REF] as a time sequence model, the grey model GM (1,1) of BTP of lead-zinc ore was applied, and parameters of the charge permeability and the strand speed of the pallets were fed to the technological neural network input. The the work [START_REF] Wu | An intelligent control system based on prediction of the burn-through point for the sintering process of an iron and steel plant[END_REF] for BTP prediction of iron ore sintering also used the integration of grey model and neural networks. Here the result of the grey model GM (1,1), especially the gas temperature in wind boxes, is one of the inputs of the backpropagation neural network, along with the strand speed and the BTP at the current time. All three considered works with two predictive models used a fuzzy expert controller that maintains the BTP desired position within the specified boundaries. In addition to standard learning algorithms for neural networks, genetic algorithms are used to optimize weights values. Thus, in the work [START_REF] Cheng | An application of adaptive genetic-neural algorithm to sinter's BTP process[END_REF] dedicated to the BTP control of iron ore sintering process, an adaptive genetic algorithm was used, where the input layer of the neural network is parameters of the initial material, density, strand speed, and ignition temperature, and the output layer is responsible for the values of temperature and pressure of sintering gases and gases in wind boxes. The genetic neural network was also used for the BTP prediction of iron ore sintering in the paper [START_REF] Cheng | Prediction system of burning through point (BTP) based on adaptive pattern clustering and feature map[END_REF] , where 707 groups of data were given to the input after clustering and classification of temperature and pressure vectors from 18 wind boxes. The system of adaptive structural clustering in this work used methods of spatial clustering of initial data, a self-organizing neural network map for extracting data relevancy properties, and a Kohonen map for learning network. The idea of clustering was used in the work [START_REF] Shang | Data-driven prediction of sintering burn-through point based on novel genetic programming[END_REF] for the BTP prediction model of iron ore sintering. The K-means clustering module, whose inputs are the cold-charge permeability model, the ignition temperature, and the coke residue values, were used to form clusters. The predictive model in this paper did not use neural network algorithms. The clusters from the Kmeans module were fed to the dynamic model of temperature and vacuum. The dynamic model was constructed using the novel genetic programming. A firework algorithm based on a genetic algorithm was proposed in [10] to optimize the sintering terminal prediction model of the support vector machine. Seven main parameters were used as input to predict the BTP. Models that do not use the neural networks for BTP prediction are based on equations of temperature or burn through time. Thus, for example, in the work [START_REF] Kwon | Event-based modeling and control for the burnthrough point in sintering processes[END_REF] predicted value of the burn through time was determined by the least-squares method based on the historical data and, depending on the signal of the event-based model which determines the time until the end of the movement, the control of strand speed is carried out. The event-based model for the BTP of iron ore sintering is represented by a linear time-constant discrete model in the state space, using the idea of breaking a continuous model into discrete events. In the work [START_REF] Terpak | Control of burn-through point for agglomeration belt[END_REF], a parabolic model was used to change the control temperature of BTP, compiled from the measured values in three wind boxes. It was used to determine and correct the volume of sintering gases, calculated from the volume of oxygen, humidity, and composition data of the charge. The work [START_REF] Wang | Hierarchical intelligent control system and its application to the sintering process[END_REF] describes a two-level hierarchical control system (intelligent control and automation level) of BTP and the vertical sintering rate of the iron ore sintering process, where the BTP model represents a piecewise-quadratic temperature depends on the strand position. In the work [START_REF] Wu | Design and application of generalized predictive control strategy with closed-loop identification for burn-through point in sintering process[END_REF] , a BTP control of iron ore sintering is divided into 2 parts: a closed-loop identification model and a generalized predictive control model. In the first part, the BTP is found based on the dynamic autoregressive exogenous model to calculate which strand speed, amount of moisture, the height of the charge, air volume, and vacuum is used. The closed-system identification method was used to determine the model parameters dynamically. In the second part, based on the transfer function obtained from the identification model, the BTP prediction was made to control the strand speed. The state of BTP also was predicted using a particle swarm optimization algorithm (PSO) [START_REF] Shi | Soft sensing of the burning through point in iron-making process[END_REF] , where the degree of four influence parameters: suction pressure, air input, velocity of sintering machine, and ignition temperature, is found by PSO. According to the literature, we can conclude that: (1) prediction of BTP based on different parameters: data of vertical sintering rate, vacuum, permeability, the height of the charge, the temperature in wind boxes or sintering gases, strand speed, previous values of BTP; (2) high accuracy of the predictive model is achieved by using a large initial sample or historical data; (3) control of BTP is carried out by influence on strand speed. However, in practice, due to lack of automation, only the main process parameters are often measured, such as temperature in wind boxes, vacuum, strand speed, charge height and mass values of the main components. The values of such properties as permeability, the volume of sintering gases, or properties of charge are obtained only by laboratory experiments. Therefore, it becomes necessary to construct a predictive model using the main measured parameters; in this work, we use the temperature in the wind boxes and vacuum. Obtaining a large sample of initial data is also difficult in production -it requires a long time to collect data and accumulate them to improve predictive accuracy. In this case, if certain conditions of the process (properties of the initial charge, charge height, pellet size, ignition gas, etc.) change, it will be necessary to collect data again and retrain the predictive model for obtaining accurate results. Therefore, it is necessary to use such a predictive model that will be adequate for training on a small initial sample and will be built in real-time. To solve this problem, the theory of grey systems developed by J. Deng in 1982 is used, which is focused on solving prediction problems with a small volume of the original sample and with poor information. The idea of the grey system theory is to consider the process as a "generalized energy system" and emphasize that non-negative smooth discrete functions can be transformed into a sequence having the approximate exponential law, which is the so-called grey exponential law [START_REF] Deng | Introduction to grey system theory[END_REF] . The application of grey models was considered in the works [START_REF] Wu | Neural-network-based integrated model for predicting burnthrough point in lead-zinc sintering process[END_REF][START_REF] Wu | An intelligent control system based on prediction of the burn-through point for the sintering process of an iron and steel plant[END_REF] as a part of BTP prediction. In the considered studies, the GM(1,1) model was used, in which only the previous values of the predicted variable influence the subsequent prediction. The disadvantage of this approach is the lack of consideration of influencing factors. Therefore, in this paper, an improved grey model, the convolution integral model GMC(1,n) is used [START_REF] Tien | The indirect measurement of tensile strength of material by the grey prediction model GMC(1,n)[END_REF] , which allows us to take into account (n-1) influencing factors on the prediction of the charge highest temperature. The BTP prediction is necessary for the sintering process control. Since the model takes into account not only temperature but also pressure in wind boxes, the control task can be organized by changing two variables, the strand speed (standard approach) and the pressure. Then, the proposed approach in this paper is intended to solve the problem of the phosphorite ore sintering process control and based on the optimization of the prediction model. The paper is organized as follows. Section 2 gives a general description of the sintering process and presents the three samples of the main parameters, which are obtained in the workshop. Section 3 is devoted to the grey predictive models, the convolution model construction algorithm, and the way to find the minimum volume of the initial sample. Section 4 presents the structure of the sintering process control based on predictive optimization. Section 5 presents some concluding remarks.

Sintering process

The phosphorite ore sintering process is produced in the Novozhambul phosphorus plant, which is located in the south of Kazakhstan, near the Karatau phosphor field. It is the second most crucial process in the plant, after the production of yellow phosphorus, for which the sinter is a raw material. The technological process is shown in Figure 1. It begins with a primary blending of the charge with a cold and a secondary return, which is introduced into the charge without dosing and lead to significant changes of the fuel in the charge. Then, the charge is poured to the moving grate and ignited with the help of natural gas or СО2, passing under the horn (Figure 2, a). Due to the vacuum created by wind boxes, the heat from the fuel combustion is transferred to the underlying layers, evenly sintering a layer of 260 mm high as the grate moves to the end of the 78 m long sinter machine (Figure 2,b). Further, the agglomerate is cooled and crushed, and the poorly sintered charge is sent to the beginning of the process. The amount of the sintering return reaches 40-50% since the process is controlled at the end of the sinter machine by an operator's decision based on the sinter slice. The amount of return needs to be reduced through a preliminary BTP prediction and control based on predictive data. The main parameter for the prediction is the temperature in the lower part of the strand (temperature in wind boxes). Temperature curves (Figure 3) are samples of data taken at different times, under different initial conditions: different charge composition, coke amount, pressure, but at the constant speed, so they are shown only until the desired temperature is reached in order to determine the duration of the process. In addition, the pressure drop across the bed data ∆p (the difference between the pressure in upper and lower parts of bed) is measured, and the gas velocity u (Figure 4) in the lower part of the charge is calculated using Ergun equation ( ) ( )

2 2 2 3 3 150 1 1.75 1 - - ∆ = + u u p L d d µ ε ρ ε ε ε (1)
where L is the height of the bed, [ ] . Pa s µ is the dynamic viscosity of gas, ε is the porosity of porous matrix, and [ ] d m is the equivalent particle size. The porosity value is calculated according to the method proposed in [START_REF] Kaymak | Iron ore sintering process model to study local permeability control[END_REF] . To check whether the gas velocity affects the charge temperature, correlation methods are used, which reveals the statical relationship between the two variables. There exist a considerable number of correlation methods, such as Pearson's twodimensional correlation, canonical, partial, point-biserial, Kendall's rank correlation, Spearman, and others. In this paper, the Spearman's rank correlation [-1;+1] is used, which is a non-parametric test and is used to measure the degree of association between two variables. The advantage of this method is that the distribution law of the original samples does not play a role. The calculation of the correlation can be found using the following function under Matlab -corr(x, y, Type, Spearman). Also, due to the use of grey models in this work, Deng's grey relational analysis (GRA [0; 1]) is also executed as

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 min max 1 max = - + - = - + - ∑ n j j j k j y k x k y k x k r n y k x k y k x k ρ ρ (2)
where 0.5 = ρ is the distinguishing coefficient, which is used to increase the most prominent differences between two arrays x and y (x and y data are represented in Appendix Table A1). One of the feature of GRA model, that it always reveals a positive correlation. Since Spearman's correlation coefficient is negative, it will be better to use the Bidirectional GRA model [START_REF] Javed | Bidirectional Absolute GRA/GIA model for Uncertain Systems: Application in Project Management[END_REF] . Algorithm of Bidiectional GRA model follows these steps:

1. Normalize the data sequences using the minimizing operator (normalized data in Appendix). 2. Generate the Mirror Sequences from normalized

( ) ( ) ( ) ( ) , 1 , ..., 1 = - ⌣ x x n x n x . 3. Calculate the Bidirectional Absolute Grey Relational Degrees ( ) ( ) max , , 0 max , , 0 ±
 + - >  =  - - <   ⌣ ⌣ ⌣ ⌣ yx yx yx yx yx yx yx yx yx ε ε ε ε ε ε ε ε ε
where 1

1

+ + = + + + - y x yx y x y x S S S S S S ε , ( ) ( ) 1 2 1 2 -
= = + ∑ n y k S y k y n , ( ) ( ) 1 2 1 2 -
= = + ∑ n x k S x k x n , and ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 -
= - = - + - ∑ n y x k S S y k x k y n x n .
It can be seen from Table 1, for each sample the gas velocity must be taken into account to determine the charge temperature, since there is a strong relation between them close to 1 . Also, according to the Javed's Grey Incidence (JGI), scale [ ] 0.7;0.8 ± = ε is a third level of the strength of association between the sequences and means appropriately strong relation.

Grey model approach

The influence of several factors on the predicted value for grey models can be considered only on the basis of model modifications GM(1,n), which is clearly demonstrated in the work [START_REF] Tien | A research on the grey prediction model GM(1,n)[END_REF] . A continuous convolution integral grey model GMC(1,n) [START_REF] Tien | The indirect measurement of tensile strength of material by the grey prediction model GMC(1,n)[END_REF] is one of the basic models with (n-1) influencing factors. On the basis of this model, other continuous linear grey models with (n-1) influencing factors were developed. For example, an interval model with a convolution integral IGDMC(1,n) [START_REF] Tien | The indirect measurement of tensile strength for a higher temperature by the new model IGDMC(1,n)[END_REF] , is intended for prediction of the interval in which the variable is located. Model FGMC(1,n) [START_REF] Tien | The indirect measurement of tensile strength by the new model FGMC (1,n)[END_REF] is developed on the basis of the idea of prediction independence from the first pair of initial sample data. The deterministic grey model with the convolution integral DGDMC(1,n) [START_REF] Tien | The deterministic grey dynamic model with convolution integral DGDMC(1,n)[END_REF] distinguishes from GMC(1,n) by the estimation of first derivative and parameters: the first derivative is estimated numerically by the cubic curve of the spline and the parameters of the model, according to the scheme of deterministic convergence. The error in the strength prediction considered by Tien is 0.54% for FGMC(1,n), 1.25% for GMC(1,n), 1.85% for DGDMC(1,n) and 3% for IGDMC(1,n). Finally, GMC(1,n) is chosen as the predictive model, since FGMC(1,n) uses an arbitrary pair of numbers that should be inserted in the front of the original series; therefore the prediction error is depending on this chosen number that can be different for the various composition of charge and difficult to find out optimal one. All GMC(1,n) models [ 23 , 24 ] are focused on optimizing the model coefficients, to improve the model accuracy.

Convolution integral grey model GMC(1,n)

The gas velocity, calculated from the known pressure ∆p, which is measured in realtime was selected as an influencing factor. Convolution integral grey model GMC(1,n) [START_REF] Tien | The indirect measurement of tensile strength of material by the grey prediction model GMC(1,n)[END_REF] (where n=2) with one influencing factor is a linear differential model

( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 2 + = + dY t b Y t b X t u dt (3) GMC(1, n) (n=2) is represented by (3) in which ( ) 0
Y is the predicted series, ( ) 0 X is the associated series, b1 and u are the developmental coefficient and the grey control parameter respectively, and b2 is the associated coefficients corresponding to the associated series ( )

0 X . ( ) ( ) 1 Y t and ( ) ( ) 1 X t are 1-AGO data ( ) ( ) ( ) ( ) 1 0 1 = = ∑ t l Y t Y l (4) ( ) ( ) ( ) ( ) 1 0 1 = = ∑ t l X t X l (5)
The grey derivative for the first-order AGO data in ( 1) is conventionally represented as

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 lim ∆ →∞ + ∆ - = = + ∆ - ∆ t dY t Y t t Y t Y t t Y t dt t (6) when 1 t ∆ → .
The parameters of (3) are determined using the least squares method [ ] ( )

1 1 2 , , - = T T T R b b u B B B Y ( 7
)
where t changes from 1 to r which is the number of initial sample to construct the model in (1).

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.5 1 2 0.5 1 2 1 0.5 2 3 0.5 2 3 1 . . . . . . . . . 0.5 1 0.5 1 1 2 , 3 ,...,   - + +     - + +     =           - -+ -+       =   T R Y Y X X Y Y X X B Y r Y r X r X r Y Y Y Y r (8)
Prediction of the sinter temperature ( ) ( ) 0 ˆ0 -Y initial data is determined by the following equation

( ) ( ) ( ) ( ) ( ) ( ) 0 1 1 ˆˆˆ1 Y t Y t Y t = - - (9)
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( )

1 1 1 1 1 0 1 1 1 1 1 2 2 2 2 1 1 ˆ1 2 2 t b t b t b t l i Y t Y e e b X t u b X t u e b X l u - -- -- -- = = + + + + + + ∑ (10)

Size of initial sample to construct the model

The size of the initial sample for constructing a predictive model is also an important parameter, which leads to reduce the error in temperature prediction. Also, it allows us to define wind boxes, where thermocouples should be installed in the future and reduce their quantity for the economy. The main feature of the grey theory is its capability to use as few as n+3 pairs of data by GMC(1,n) [START_REF] Tien | The indirect measurement of tensile strength of material by the grey prediction model GMC(1,n)[END_REF] . For each sample, the following experiments were performed: (1) based on the n-pair of series from the sample, the model was built, (2) based on the model, the prediction of the remaining values was made, (3) the prediction results were compared to the original samples and the Root Mean Squared Percentage Error (RMSPE) according to (11) was calculated.

( )

2 2 1 .100% - = ∑ i i i i Y Y RMSPE n Y ( 11
)
During the experiments, models were built for each sample ranging from 5 (from 2.5 min from the start of the sintering process) to 20 (to 10 min from the start of the sintering process) pair of series. The results of the predicted errors for each sample are presented in Figure 5 (results from 2.5 to 5 min are omitted due to the large value of the predicted error). The predicted errors for each sample take the minimum values for different pairs of series, ranging from 14 (7 min) to 17 (8.5 min) pair of series. The mean smallest predictive error for 3 samples is achieved with 15 pairs of series (7.5 min).

Figure 5 Predictive errors depending on different sample sizes GMC(1,n) predictive models for 3 samples (Figure 3) are presented in Table 2, where the volume of initial sample r to construct the model includes data from the beginning of the sintering process up to 7.5 min (15 values). The parameters of the grey model, which were found by (7), differ significantly for each sample. This is due to the fact that each temperature curve was obtained under different initial conditions: the content of coke, phosphorite ore, the amount of return, moisture and other parameters of the charge, which are not directly taken to build a predictive model. Moreover, in production under real conditions, it is not possible to continuously control the composition of the charge, which makes it challenging to use a model that takes into account all the factors. Therefore, it is necessary to build a predictive model, which use only measured real-time factors and dynamically construct the predictive model for a certain batch of sintered ore. The results for the samples are shown in Figure 6 (data are provided in Appendix Table A2). Prediction error according to (11) for 3 samples, is shown in Table 2. The predictive results based on grey systems do not improve the accuracy in comparison with the other models, but allow to build an adequate prediction model of BTP in the absence of a large amount of historical temperature data. The additional advantage is the time saving for data collection and model training.

( ) ( ) ( ) ( ) ( ) ( ) 1

Control structure

Dynamic construction of the grey model uses only actual data, which represents realtime information about the sintering process, not depends on historical data and will make it possible to obtain the prediction of the charge temperature before the strand end. If the predictive temperature of the charge in the last point does not reach the setpoint, then it is necessary to control the sintering process. The control can be carried out by changing the amount of fuel in the initial charge, the strand speed, and the pressure created in wind boxes. The change in the amount of fuel affects only the charge that has not yet been fed to the sinter, therefore this effect is not considered in the current study. The proposed control structure for BTP is presented in Figure 7 and includes (1) data acquisition of temperature and pressure in wind boxes from the beginning of the process to a certain point, (2) construction of the grey predictive model GMC(1,n) based on the accumulated data, (3) prediction of the temperature up to the strand end, (4) optimization of process control parameters (speed and pressure in wind boxes) to achieve the desired temperature at the end of the process, (5) change of control parameters for the considered batch to obtain a good sinter quality and minimum return. The control structure is working in real-time and has the following algorithm: after the charge is passed under the horn, the system begins collecting data on temperature, pressure in the wind boxes and sinter machine speed. Based on the collected data, a forecast model is built on the basis of the grey model that predicts the temperature at the end of the sintering machine. If the temperature does not correspond to the BTP, a predictive optimization algorithm calculates the necessary values of the sinter speed and pressure in the wind boxes. The resulting values are fed to the appropriate controllers. After charge is reaching the end of sintering machine, the cycle is repeated for the next charge. The particle swarm is used [START_REF] Wu | Grey multivariable convolution model with new information priority accumulation[END_REF] as a method of predictive optimization. The particle swarm algorithm is a system of particles that move to optimal solutions, and each particle contains the coordinates of the found best solution (pbest) and the best solution from all the particles in the swarm (gbest). The following formula determines the direction and length of the particle velocity vector

( ) ( ) ( ) ( ) 1 2 . . . . i i i i i i a rnd pbest x a rnd gbest x ϑ ϑ = + - + - ( 12
)
where ϑ is particle speed vector, 1 a , 2 a are constant accelerations and x is the particle's current position. Particle current position includes two variables: number of samples that represents time of sinter process and gas velocity. As a criterion of optimality, the difference between the desired and predicted temperatures at the end of the sinter strand is used as follows

( ) ( ) 0 _ int ˆmin set po Y t Y - → (13)
subject to With the help of the obtained optimal sintering process time t value, the strand speed is determined, and through the optimum gas velocity value, the pressure in wind boxes is found according to the Ergun Equation ( 1). Modeling results of BTP control system for the samples are represented in Figure 8 (data are provided in Appendix Table A2). In the first sample, the sintering temperature of the charge is reached in 22 minutes. To increase line productivity, extended boundaries of inequalities ( 13) are set. Wherein, the optimization algorithm allows us to find such values of strand speed and pressure in wind boxes at which the BTP is reached in 19.5 minutes. The sample 1 results of forecast optimization are as follows: the speed values change from 3.5 m/min to 4.5 m/min and the pressure in wind boxes from 800 mmHg to 760 mmHg. In the second sample, the BTP is not reached. Therefore, as a result of predictive optimization, a new value is supplied to the pressure regulator, at which the sintering temperature is reached. In the third case, as a result of predictive optimization, the speed of the sinter strand and pressure in wind boxes is increased, which allows us to achieve the optimum temperature in 19 minutes.

Conclusion

The proposed control process structure of phosphorite ore sintering considered in this article is intended to improve the product quality and reduce the return. As an indicator responsible for the sintering quality, the BTP was chosen, i.e., the position at which the process reaches the highest temperature. Prediction of this variable was realized through the grey predictive model with some main contributions: (1) dynamic construction of the predictive model using small sample size, obtained from the beginning of the process, which reduces the time for data acquisition and system training;

(2) control of the sintering process not only based on the strand speed, but also on the pressure in the wind boxes; (3) use of a grey model with (n-1) influencing factors that take into account not only the effect of the predicted value but also other process variables; (4) use of predictive optimization algorithm to determine optimal process parameters. In the current study's framework, the initial amount of data for constructing the model was also determined, as a result of which the amount of costs for building the data acquisition system is reduced, while the predictive model error

Figure 1

 1 Figure 1 Technological chain of phosphorite ore sintering process

  (a) Under horn. (b) End of sintering machine.

Figure 2

 2 Figure 2 Sintering machine in the Novozhambul phosphorus plant

Figure 3

 3 Figure 3 Temperature curves of 3 samples in wind boxes

Figure 4

 4 Figure 4 Gas velocity of 3 samples

Figure 6

 6 Figure 6 Predictive results for the samples

ŶFigure 7

 7 Figure 7 Control structure for BTP

Figure 8

 8 Figure 8 Control results of BTP for the three samples

Table 1

 1 Correlation results between temperature and gas velocity

	Correlation type	Sample 1	Sample 2	Sample 3
	Spearman	-0.4072	-0.7715	-0.7430
	GRA	0.6690	0.6757	0.6839
	Bidirectional GRA	-0.7485	-0.7509	-0.7589

Table 2

 2

		GMC model of samples (n=2)
	No. of sample	GMC(1,n)	RMSPE, %

Ŷ 20,178 20,178 20,18 20,18 20,182 20,182 70,61841

135,1026 67,90837 130,5574 73,54634 135,7069 116,0574 125,1421 116,003 125,0854 123,7109 127,7107 156,3934 163,1588 158,421 164,5974 167,7012 170,1072 193,2281 197,9532 196,9186 200,6212 207,4161 208,4796 227,5997 230,4934 232,6748 234,2326 244,1281 244,0405

does not exceed 2%.

References Appendix

Table AErreur ! Document principal seulement. Initial data of temperature ( ) y and gas velocity ( ) x


Cousty

Bulai Livideanu
email: livideanu.c@chu-toulouse.fr

S Cousty

Sudhakar Seenivasan

Vascular Nd:YAG laser: a therapeutic alternative for large venous lakes of the oral mucosa

Vascular Nd:YAG laser: a therapeutic alternative for large venous lakes of the oral mucosa

Vascular Nd-YAG laser: a therapeutic alternative for large venous lakes of the oral mucosa Editor 4 Venous lakes are benign vascular anomalies often present on the lips and oral mucosa. [START_REF] Mlacker | Laser and light-based treatments of venous lakes: A literature review[END_REF] 5

Although different treatment modalities have been described, no standardized treatment is yet established, especially in the case of large venous lakes of the oral mucosa (≥10 mm). We report, here, two cases of patients successfully treated for intra-oral large venous lakes with a single session of long-pulsed Nd-YAG laser.

6

The first patient, a 67-year-old female, presented a 20 mm venous lake on the buccal mucosa and an 18 mm lesion on the dorsal surface of the tongue (Fig. 1). The second patient was a 68-year-old female with a 15 mm venous lake on the inner side of the upper lip. She had a history of major ballistic trauma with peri-oral scarring (Fig. 2). Treatment of these venous lakes was indicated because the patients experienced chronic biting and bleeding.

For both patients, we used a vascular long-pulsed Nd-YAG laser with the following parameters: 1064 nm wavelength, 7 mm spot size, 100 J/cm 2 energy and a pulse width of 20 ms. The laser beam was swept over the venous lakes for a few seconds, without overlapping. The end point was characterized by the hardening of the lesion, the whitening of its centre and an audible snap. No alteration of the mucosal surface was noted in the immediate postoperative period but diascopy showed a non-blanchable lesion. Local anaesthesia was not necessary, and the use of the laser's dynamic cooling device was sufficient to ensure the patients' comfort. The postoperative outcome was uneventful, and none of the patients experienced pain or bleeding. The first reassessment at 1 week showed a complete disappearance of the lesions for both patients. At 5 months and 1-year follow-ups, the results were stable: no relapse or scarring was noted.

The effectiveness of long-pulsed Nd-YAG laser in the treatment of venous lakes lies in the fact that its 1064 nm wavelength is preferentially absorbed by methemoglobin and has deep surface penetration of 4-7 mm. [START_REF] Asai | Effectiveness of photocoagulation using an Nd:YAG laser for the treatment of vascular malformations in the oral region[END_REF][START_REF] Crockett | Treatment of oral cavity venous malformations with the Nd:YAG laser using the underwater technique[END_REF][START_REF] Eivazi | Laser treatment of mucosal venous malformations of the upper aerodigestive tract in 50 patients[END_REF][START_REF] Medeiros | Nd:yAG laser photocoagulation of benign oral vascular lesions: a case series[END_REF] Its photocoagulating effect allows therefore the specific targeting of the venous tissue, decreasing the possibility of relapse, and presents sufficient penetration for the treatment of deep-seated lesions. Several types of lasers have been used for the treatment of venous lakes of the lips and vascular malformations of the oral mucosa, including diode laser, [START_REF] Bacci | Diode laser to treat small oral vascular malformations: a prospective case series study[END_REF] pulse-dye laser 7 and argon laser. [START_REF] Neumann | Venous lakes (Bean-Walsh) of the lipstreatment experience with the argon laser and 18 months follow-up[END_REF] Although these seem effective for superficial and small lesions, the longer wavelength of the Nd-YAG laser allows better and quicker results in the treatment of deeper and thicker lesions 1 : a single session is often sufficient for the treatment of venous lakes of the lips and oral mucosa and provides stable results over time. [START_REF] Eivazi | Laser treatment of mucosal venous malformations of the upper aerodigestive tract in 50 patients[END_REF][START_REF] Medeiros | Nd:yAG laser photocoagulation of benign oral vascular lesions: a case series[END_REF][START_REF] Yang | Long-pulsed Nd:YAG laser treatment in vascular lesions of the oral cavity[END_REF][START_REF] John | Treatment of venous lesions of the lips and perioral area with a long-pulsed Nd:YAG laser[END_REF] Nd-YAG seems also to be better tolerated than argon and diode lasers since these do not dissipate heat as well as the Nd-YAG laser, increasing the likelihood of tissue damage following treatment. [START_REF] Mlacker | Laser and light-based treatments of venous lakes: A literature review[END_REF] Finally, the procedure generates minimal discomfort peri-and postoperatively. Although several authors reported the use of topical or local anaesthetics, we found it was not necessary if a cooling device is used. Surgery or sclerotherapy is most commonly described for large venous lakes of the lips. However, these techniques are more invasive than laser treatment and can often leave residual scarring, which can be problematic in multioperated patients or patients presenting several vascular lesions, such as our second patient.

Long-pulsed Nd-YAG laser is therefore a simple, non-invasive and effective technique for the treatment of venous lakes of the oral mucosa that can be proposed at the first consultation.

  hal.archives-ouvertes.fr/hal-02967861 Submitted on 15 Oct 2020

Figure 1

 1 (a): 20 mm venous lake of the right buccal mucosa. The patient experienced recurrent biting and bleeding. (b): 18 mm venous lake on the dorsal surface of the tongue. (c): Outcome at 1year follow-up: complete disappearance of the buccal venous lake and stability of the results. (d): Outcome at 1-year follow-up: complete disappearance of the lingual venous lake, no relapse is noted.

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Figure 2

 2 Figure 2 (a): 15 mm venous lake on the inner side of the right upper lip. The patient complained of chronic biting and bleeding. (b): Result at 1-year postoperatively. No scarring is noted on the treated site.

  COLOR© 2019 European Academy of Dermatology and Venereology

	2	Letter to the Editor
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	JEADV 2019


Marion Clé

Jean-Baptiste Maranci

Sebastian Weyn Banningh

Jade Lanfranchi

Marie Vidailhet

Isabelle Arnulf
email: isabelle.arnulf@aphp.fr

Marion Cle

Sebastian Weyn Banningh

Smiling asleep: A study of happy emotional expressions during adult sleep

Keywords: rapid eye movement sleep behaviour disorder, sleepwalking, zygomatic, orbicularis oculi, smile EMG = electromyogram, NREM sleep = non-rapid eye movement sleep, REM sleep = rapid eye movement sleep, REMs = rapid eye movements, RBD = rapid eye movement sleep behaviour disorder

INTRODUCTION

The facial expressions of happiness (smiling, laughing), sadness, surprise, fear, anger, and disgust are recognized as a universal non-verbal language found in all human ethnicities but also in some non-human primates [START_REF] Ekman | The repertoire of nonverbal behavior: Categories, origins, usage, and coding[END_REF]. Darwin stipulated that some facial expressions were not learned but biologically determined, including specific inborn emotions that are expressed even in the neonate and may serve a basic survival function (Darwin, 1897(Darwin, /1965)). Among these expressions, smiling is an early social and emotional behaviour. An "endogenous" smile appears in utero, as early as during the 15 th week of gestation, with more consistent smiles between 18 and 20 weeks [START_REF] Piontelli | Development of normal fetal movements: the first 25 weeks of gestation[END_REF].

Sleep monitoring in premature infants and neonates indicates that smiling occurs during active sleep, the precursor of rapid eye movement (REM) sleep [START_REF] Emde | Neonatal smiling in REM states, IV. Premature study[END_REF][START_REF] Messinger | How sleeping neonates smile[END_REF]. After birth, smiles often occur during sleeping states without obvious external stimulation. The infant smile is a powerful tool to attract the attention of the caregivers, driving them to become involved in an interaction. Communicative smiles in the presence of the caregiver are observed.

In parallel, the frequency of sleep-associated smiles decreases between the 3 rd and 6 th months, but a few sleeping smiles are observed after 1 year (Kawakami et al., 2009a).

In adults, zygomatic activity is highly correlated with positive affect in awake subjects [START_REF] Brown | Relationships between facial electromyography and subjective experience during affective imagery[END_REF]. However, the activity of facial muscles during sleep has rarely been studied through electromyography [START_REF] Bliwise | Facial muscle tonus during REM and NREM sleep[END_REF]. In six healthy subjects, the phasic activity of facial muscles, including the corrugator (involved in negative emotional expression), zygomatic (involved in positive emotional expression), masseter, orbicularis oculi, depressor anguli oris and frontalis muscles, persisted while asleep, with a higher frequency during REM than NREM sleep [START_REF] Rivera-Garcia | Facial muscle activation during sleep and its relation to the rapid eye movements of REM sleep[END_REF]. In addition, some facial muscles tended to co-contract during REM sleep, producing a pattern consistent with emotional expression during waking [START_REF] Rivera-Garcia | Facial muscle activation during sleep and its relation to the rapid eye movements of REM sleep[END_REF]. However, these studies did not include concomitant video monitoring. Consequently, they could not evaluate the presence of visually observable emotional expressions during sleep.

We aimed to examine whether visible smiling and laughing would persist during normal adult sleep, using a large group of subjects and combined video, sleep and EMG monitoring. In addition, we aimed to measure whether smiling and laughing would have the characteristics of emotional expressions, as indicated by the concomitant autonomic reactions, association with rapid eye movements and presence of Duchenne (genuine) smiles (Duchenne de Boulogne, 1862Boulogne, -1990)).

Furthermore, we studied smiles and laughs in models of enacted dreaming, including REM sleep behaviour disorder (RBD) and NREM parasomnias (sleepwalking). We hypothesized that facial expressions would be more frequent in these parasomnias due to imperfect normal muscle atonia in RBD and to complex behaviours in sleepwalkers and that some of the concomitant behaviours would help to determine whether there is a concomitant pleasant dream scenario.

METHODS

Participants

The 174 consecutive participants (men, N = 94; women, N = 80) were recruited in the Sleep Disorders Unit of the Pitié-Salpêtrière university hospital between February and June 2016. All adults referred to the unit for a sleep study and consenting to take part in the study (i.e., to have facial EMG in addition to the routine sleep and video recording) were included, except those with untreated sleep apnoea and with sleep-related motor disorders. Please note that video monitoring during the night is a routine, consistent procedure in our sleep unit, meaning that all subjects are videotaped, even those with no movement disorder or parasomnia. The sleep disorders were defined in accordance with the International Classification of Sleep Disorders-3 (American Academy of Sleep Medicine, 2014). The participants were split into two groups, with and without parasomnia. In the parasomnia group, the patients with RBD had to meet the international criteria, including i) repeated episodes of sleep-related vocalization and/or complex motor behaviours; ii) that these behaviours were documented by polysomnography to occur during REM sleep or, based on clinical history of dream enactment, were presumed to occur during REM sleep; iii) that polysomnographic recording demonstrated REM sleep without atonia (defined here as the presence of enhanced tonic chin muscle tone during more than 18% of REM sleep epochs [START_REF] Frauscher | Normative EMG values during REM sleep for the diagnosis of REM sleep behavior disorder[END_REF]; and iv) that the disturbance was not better explained by another sleep disorder, mental disorder, medication, or substance use. Idiopathic RBD was defined by the absence of any neurological disorder at time of inclusion, after an interview, a neurological examination and cognitive tests. The patients with NREM parasomnia had to meet the international criteria of arousal disorders, including i) recurrent episodes of incomplete awakening from sleep; ii) inappropriate or absent responsiveness to efforts of others to intervene or redirect the person during the episode; iii) limited or no associated cognition or dream imagery; iv) partial or complete amnesia for the episode; and v) that the disturbance was not better explained by another sleep disorder, mental disorder, medical condition, medication, or substance use. Patients with sleepwalking (same criteria plus ambulation and other complex behaviours out of bed), night terrors (with episodes typically beginning with an alarming vocalization, intense fear and signs of autonomic arousal) or both (as the two phenomena are frequently associated in adults) were grouped in a single group labelled "sleepwalking". The non-parasomnia group included all subjects without REM and NREM parasomnia (none of the above criteria) and without sleep-related motor disorders. There were healthy subjects (no sleep complaint or sleep disorders, recruited and paid to take part in another study), patients with a complaint of insomnia, patients with adequately treated sleep apnoea referred for controlling the treatment efficacy, patients with Parkinson's disease and no RBD or sleep complaint who volunteered for another research trial, patients with narcolepsy (but without RBD), and patients with idiopathic hypersomnia. All participants provided written or oral informed consent (after the study was explained to them by the research assistant and physicians) for this study, depending on their groups. In patients referred for exploring their sleep disorders, this study consisted of adding surface EMG of two facial muscles to the routine recording and completing a test on facial expression, which was considered a non-invasive, mild supplementary exploration, for which the local ethics committee (Comité de Protection des Personnes Ile-de-France VI) waived written consent but asked for verbal non-opposition of patients, consigned in the subject file. Healthy volunteers, patients with PD (with and without RBD), with idiopathic RBD and with sleepwalking/night terrors provided written consent for various studies approved by the local ethics committee (Comité de Protection des Personnes Ile-de-France VI), including the ICEBERG (NCT02305147), HYPNOSOM (NCT02648568) and AEP programs and consented to the additional study of their facial expression during sleep. Only healthy volunteers were paid for participation. All participants provided consent for their face to be studied on video by researchers, but not to be shown in a medical journal, except for a few participants, but they provided consent for a scientific illustrator (Juliette Rey) to draw their face (without changing its expression) for illustration purposes, with changes rendering it unrecognizable.

Questionnaires

The participants were interviewed by a sleep neurologist who performed the diagnosis of their disorder (if any) following the international criteria after interview, clinical examination and review of the sleep tests (American Academy of Sleep Medicine, 2014). Participants completed the Epworth sleepiness scale [START_REF] Johns | A new method for measuring daytime sleepiness: the Epworth Sleepiness Scale[END_REF] in the evening and a dream report the next morning (a free, written report of any dream mentation that they would recall upon final awakening), plus a general question about the pleasantness of their dream recall ("was your dreaming pleasant, unpleasant, neutral?"). Only the answers about the pleasant/unpleasant aspect of the recalled dreams were analysed here. Participants then underwent the condensed Ekman test for emotion recognition [START_REF] Ekman | Pictures of facial affect[END_REF]; they were required to choose one among seven expressions (anger, happiness, fear, sadness, disgust, surprise or neutral emotion, 5 pictures per expression) when looking at 35 black-and-white face pictures issued from 5 different characters. The score corresponded to the number of correctly identified emotions (0-35). This test allowed to determine whether no participant was deficient in recognising emotions, and to roughly check whether they displayed facial emotions (and especially smiling) in mirror during wakefulness.

Sleep evaluation

All participants underwent one or two successive video-polysomnographies, including Fp1-A2, C3-A2 and O1-A2 electro-encephalographic derivations (EEG), bilateral electrooculography (EOG), nasal pressure and respiratory effort monitoring, tracheal sound recording, electrocardiography, pulse oximetry, EMG recording of the levator menti and bilateral tibialis anterior muscles (Compumedics Ltd, Australia). In addition, 4 surface electrodes were placed on orbicularis oculi and zygomatic muscles with a bipolar montage (Figure 1). The facial muscle calibration was performed in awake subjects during the Ekman test and a free conversation with the research assistant in order to evoke some expressions of happiness (smiles and laughs). The night behaviours and facial expression were filmed via infrared video cameras (one camera allowed a general view of the sleeper's full body, and a second was focused on the face), and a microphone captured the ambient sounds. The sleep stages, arousals, and respiratory and motor events were scored based on visual inspections of 30-s epochs according to standard criteria. [START_REF] Iber | The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications[END_REF] A REM sleep epoch was considered REM sleep without atonia if more than 50% of the epoch contained an enhanced EMG activity of the levator menti that was at least two times greater than the corresponding lowest activity during NREM sleep [START_REF] Iber | The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications[END_REF].

Evaluation of facial expression during sleep

The video observations were driven by the visual inspection of the zygomatic muscle activity on the EMG, which was measured in all subjects during the full night. An activation of the zygomatic muscle was defined as any waveform exceeding the baseline activity by 500% and lasting longer than 0.1 sec [START_REF] Rivera-Garcia | Facial muscle activation during sleep and its relation to the rapid eye movements of REM sleep[END_REF], a sub-clinical threshold that was found sufficient to catch any movement of the lips. The concomitant video was visually inspected during any muscle activation, which allowed to recognise unilateral lip raising, bilateral lip raising, and bilateral lip raising with an active closure of the eyelids. EMG activations without any observable event were discarded. Because smiles are defined by bilateral lip corner raising, a unilateral zygomatic EMG activation was sufficient to look at the concomitant face on the video and observe whether this EMG activity resulted in a smile or not. The video could not be fully examined in some patients sleeping face down or under the sheets. One may note that applying 6 additional EMG electrodes to the face (in addition to the electrodes of the mentalis muscle, of electrooculography, of the Fp1 and ground EEG electrodes on the forehead, the pressure sensor plus oral thermistor within the nostrils and in front of the mouth) was sometimes perceived as uncomfortable by the sleeper and could blur the visualization of the facial expression. Consequently, we first monitored the left and right zygomatic muscles in the same patient and night (N = 12), then monitored the left (N = 52) or right (N = 78) zygomatic muscle in the next series of patients, and eventually monitored a combination of the zygomatic and orbicularis oculi muscles on opposite sides of the face (N = 88). The objective of monitoring the orbicularis oculi muscles was to catch concomitant proofs of Duchenne genuine smiles. The video and concomitant polysomnography signals were stored together. The video clips were scored using the following rating scale (Figure 1): i) compared to an absence of mouth movement, the unilateral raising of a lip corner (without concomitant raising of the contralateral lip corner) was scored as E1, a smile with raising of both lip corners as E2, a smile with raising both lip corners plus opening of the mouth as E3, and a full laugh as E4 (laugh markers included a shrug of the shoulder, a recognizable vocalization of breaking into a peal, and a belly contraction, visible on the abdominal belt). Simple twitches refer to E1 events. Most E1 events were short lasting (< 0.5 sec), whereas the majority of happy expressions lasted from 0.5 to 6 sec. The video clips were scored by two independent scorers. The video clips were discarded from the analysis when no consensus between the scorers could be reached. The Facial Action Coding System was not used here because it has not been developed for sleeping subjects with eyes closed [START_REF] Ekman | Emotional Facial Action Coding System. Manual and Investigators Guide[END_REF]. The number of each of the 4 types of events was divided by the time asleep, as was the time spent in the sleep stage (N1, N2, N3 of NREM sleep, and REM sleep) in which it occurred, in order to develop an index of events per hour slept. We also measured the concordance between rapid eye movements (isolated and in bursts) and smiles. Because we needed to illustrate the scoring methods and findings but could not always display identifiable faces (to preserve the anonymity of the patients), a scientific illustrator (Juliette Rey, Estienne Art School, Paris) drew the facial expression asleep (without the electrodes) but rendered the faces unidentifiable without losing the expression. The two patients in the Video Clip#1 and #2 have expressly given their authorization for their video-clips to be published.

Correlates of happy emotional expressions during sleep

We indirectly investigated whether or not these visible smiles and laughs reflected an inner emotion, as it was not possible to awaken the subjects immediately after the smiles or laughs to get their mental recall, due to the rare and unpredictable occurrence of smiles and laughs. For this purpose, we looked for Duchenne smiles, which include smiling plus raising the upper part of the cheeks, produced by a contraction of the orbicularis oculi muscles. During wakefulness, Duchenne smiles are proposed to carry a true feeling of happiness [START_REF] Johnson | Smile to see the forest: Facially expressed positive emotions broaden cognition[END_REF], in opposition to isolated raising of bilateral lip corners (which may correspond to 'polite' smiles). For this purpose, we measured the frequency of bilateral raising of the lip corners associated with concomitant EMG activation of the zygomatic and orbicularis oculi muscles or, in subjects without monitored EMG of the orbicularis oculi, with bagging or wrinkling the skin below the eye as well an active closure of the eyes (a dimple was visible in the lower eyelid and the basis of the eyelashes dug in, causing crows' feet). This aspect of the Duchenne smile was doublechecked by two independent scorers, and only smiles scored as clear Duchenne smiles by both scorers were kept in the analysis.

In addition, we looked for autonomic activity concomitant with smiles and laughs while asleep in order to estimate whether those behaviours would be associated with changes in the orthosympathetic vs. parasympathetic tone. Indeed, some strong negative emotions are associated with increased heart frequency and skin temperature, although this is less consistent for happiness than for anger [START_REF] Ekman | Autonomic nervous system activity distinguishes among emotions[END_REF]. We measured the heart rate on the ECG and the pulse wave amplitude (vasoconstriction vs. vasodilatation, an indicator of the sympathetic vs. parasympathetic tone) before vs. during zygomatic muscle contraction. The measure started 5 seconds before the event, as this is a common time window for a baseline analysis of heart rate changes before and after motor events such as periodic leg movements [START_REF] Pennestri | Blood pressure changes associated with periodic leg movements during sleep in healthy subjects[END_REF]. Because rapid eye movements (REMs) in REM sleep are temporally locked with the activity in the amygdala [START_REF] Calvo | Phasic activity of the basolateral amygdala, cingulate gyrus, and hippocampus during REM sleep in the cat[END_REF][START_REF] Miyauchi | Human brain activity time-locked to rapid eye movements during REM sleep[END_REF][START_REF] Andrillon | Single-neuron activity and eye movements during human REM sleep and awake vision[END_REF][START_REF] Corsi-Cabrera | Human amygdala activation during rapid eye movements of rapid eye movement sleep: an intracranial study[END_REF], we measured how frequently REMs exactly overlapped the zygomatic muscle activity in REM sleep. Eventually, we looked for behaviours associated with smiles and laughs to find scenic behaviours directly indicative of pleasant or unpleasant mental scenarios.

Statistical analysis

The clinical and sleep measures were compared between groups using chi-square tests for qualitative measures and analysis of variance for quantitative measures adjusted for age (because it was different between groups), using the software R (R Core [START_REF] Team | A language and environment for statistical computing[END_REF]. If significant (P < 0.05), post hoc tests with the Bonferroni correction were performed between two groups using a P level below 0.0166 (0.05/3). As the analysis of face expression required 20 comparisons (within groups and between sleep stages, between simple twitches and happy expressions, and then between groups), we considered that P<0.0025 was significant (0.05/20, to avoid type A error). Statistics were performed with subjects as units of analysis (Table 1 and2) and with nights as units of analysis (Table 3, which means that the subjects having slept two nights produced two values). with RBD were older than non-parasomniac subjects, who were themselves older than sleepwalkers, but the sex ratio did not differ among the three groups (Table 1). The sleepiness scores were globally different between the three groups, with no further between-pairs significant differences. The ability to assess emotion on the Ekman test of 35 faces was similar across groups.

RESULTS

Characteristics of the sample

Smiles and laughs

In the whole sample, 173 happy expressions were found, including 43 (24.8%) mild smiles, 51 (29.5%) open-mouth smiles and 79 (45.7%) laughs. In 76.8% of the 173 smiles and laughs, concomitantly enhanced EMG activity in the chin muscle was noted. In the non-parasomnia group, smiles while asleep were rare and mostly restricted to REM sleep (8% of subjects, but one healthy volunteer smiled in N2 sleep, Figure 2) and laughs were absent (Table 2). In the sleepwalking group, rare smiles were observed during N2 sleep and REM sleep (Figure 2), and one patient laughed, both in N3 sleep (during a parasomnia event)

and in REM sleep. The frequency of happy expressions per time asleep did not differ between NREM and REM sleep (Table 3; P = 0.35). Because this laugh during an N3 parasomniac event was unexpected, we later paid attention to this phenomenon among all adults with NREM parasomnia undergoing videopolysomnography during the next 18 months and found 5 patients among 120 (for a total of 6/142, i.e., 4%) with sleepwalking who smiled while "half-asleep" during the N3 parasomnia (Video clip 1). These new 5 patients were not included in the present analysed sample and were not equipped with zygomatic EMG. In the RBD group (Table 3), the full expressions of happiness, including mild smiles (Figure 2), open-mouth smiles and laughs (Video clip 2) were frequent, whereas unilateral lip raising was rarer (P = 0.0001 when compared with E2+E3+E4 events), even when hypothesizing that half of the unilateral lip raising was missed in patients with unilateral EMG sensor (P = 0.0009 when compared with E2+E3+E4 events). The frequency of all happy expressions per sleep time (unlike unilateral lip raising) was higher in REM than in NREM sleep. The index of unilateral lip raising was not different between groups, regardless of the sleep stage. In contrast, patients with RBD had a greater index of happy expressions during REM sleep than sleepwalkers and non-parasomniac subjects had. They also had a greater index of happy faces during NREM sleep than nonparasomniac subjects but not compared to sleepwalkers. There were no differences in the joyful events index during REM sleep (P = 0.49) and NREM sleep (P = 0.17) between the 26 patients with idiopathic RBD and the 19 patients with Parkinson disease and RBD.

Evidence suggesting that happy faces reflect happiness

Half (52.5%) of smiles were "Duchenne" smiles (Table 1 and2). During 79 laughs, 41 (51.9%) were associated with shrugging of shoulders and 45 (57%) with either the characteristic sound of a peal of laughter or, more rarely, with concomitant verbal (non-intelligible, but with a joyful affective prosody) utterances. Smiles and laughs were concomitant with REMs in REM sleep, with 70.5% occurring in the same 30-second epoch and with exactly simultaneous rapid eye movements in 57.7%. The heart rate frequency did not change from 5 seconds before the beginning of smiles and laughs to 5 seconds after, whether in patients with RBD (who may have an autonomic dysfunction) or in the other groups (who had no autonomic dysfunction). For the scenario associated with happy faces asleep, it was obvious (due to scenic concomitant behaviour) only in a patient smiling and laughing during an N3 arousal (Video-clip 1: a story of a cake placed in a basket, with potential candidates to eat it, at 2 AM). A patient with RBD first smiled and spoke, then laughed, and then sent a kiss, which suggested a pleasant associated dream. In the other cases, there was no speech or moaning, so it was not possible to infer the inner scenario. There was no smiling or laughing during visibly unpleasant scenic behaviours (including fighting, fracases, or fear shouting).

Among 113 questionnaires collected on dream recall the following morning, 37 included dream stories, and 64 included recalls of emotion (including the recollection of having dreamt, having forgotten the content). The recalled emotions were pleasant (N =19), unpleasant (N = 18) and neutral (N = 27), according to the subjects, with no between-groups differences (Table 3). The presence of happy emotional faces during sleep was not associated with more pleasant dream recalls in the morning than their absence (P = 0.58).

DISCUSSION

General finding

This study indicates that smiles are not restricted to neonate sleep but persist during adult human sleep. Indeed, 8% of 100 subjects without parasomnia smiled asleep, 7% in REM sleep and 1% in N2 sleep. Rare patients with sleepwalking also smiled and laughed during N2, REM sleep and during N3 parasomnia. Half of patients with RBD smiled, mostly but not exclusively during REM sleep, and onethird laughed during REM sleep. The 173 happy facial expressions collected here included mild smiles (24.8%), open-mouth smiles (29.5%) and laughs (45.7%).

More than half of smiles were Duchenne type, including an active closure of the eyelids. Approximately half of smiles and laughs were temporally associated with REMs. There was no increase in heart rate variability during smiles and laughs.

Two scenic behaviours (during sleepwalking and during RBD) concomitant with smiles and laughs suggested that happy facial expressions were associated with pleasant dream scenarios.

Smiling and laughing in RBD

Smiles and laughs were expected in patients with RBD, as non-violent and pleasant behaviours exist during REM sleep in these patients, although they are less frequent than violent and aggressive behaviours (Oudiette et al., 2009a). Indeed, two patients with RBD laughed in the video clips of this series, showing scenic, pleasant behaviours during REM sleep: a man whistled, said, "Show a leg!", laughed and concluded "Nobody, as usual!"; whereas a woman with RBD chatted with a neighbour and laughed. In addition, 4 spouses among 60 patients with Parkinson's disease reported that their spouses occasionally laughed during RBD (Oudiette et al., 2009a). Among 67 patients with RBD and a video camera focused on the face, 21% laughed during REM sleep, despite most having concomitant depression and facial parkinsonian hypomimia during wakefulness [START_REF] Siclari | Laughing as a manifestation of rapid eye movement sleep behavior disorder[END_REF]. In this direction, we previously observed in 47% of 55 patients with Parkinson's disease that their awake parkinsonian hypomimia disappeared during RBD with a restoration of various facial expressions, in parallel with a similar restoration of speed, strength and smoothness of limb movements [START_REF] De Cock | Restoration of normal motor control in Parkinson's disease during REM sleep[END_REF]. Here, the frequency of joyful expressions was similar in patients with idiopathic RBD (who have not yet any hypomimia during wake), and in patients with Parkinson's disease plus RBD, who have a severe movement disorder and a reduced facial expression awake. This result supports previous works having suggested that the motor signature of RBD is the same across disorders [START_REF] Oudiette | A motor signature of REM sleep behavior disorder[END_REF], and that movements and face expressions are produced by different networks asleep than awake [START_REF] Arnulf | REM sleep behavior disorder: motor manifestations and pathophysiology[END_REF]. Several lines of evidence (provided by movement analysis, functional imaging and deep brain recordings) suggest that during RBD, the activation of muscles is driven by the motor cortex and bypasses the basal ganglia [START_REF] De Cock | Restoration of normal motor control in Parkinson's disease during REM sleep[END_REF][START_REF] Mayer | Ictal SPECT in patients with rapid eye movement sleep behaviour disorder[END_REF][START_REF] Hackius | Electrophysiological evidence for alternative motor networks in REM sleep behavior disorder[END_REF].

In 65 patients with RBD, apparently positive emotions were observed on the faces of 5% of the patients, compared with 30% displaying apparently negative emotions [START_REF] Oudiette | A motor signature of REM sleep behavior disorder[END_REF]. The present study indicates that among patients with RBD, half of nights contain smiles and laughs, which is more frequent than reported during the previous observational studies of patients with RBD. The monitoring of zygomatic muscle activity combined with a video focused on the face may explain this difference, given that brief smiles can be missed during the video-clip observation. All in all, it suggests that happy expressions are displayed by a majority of patients with RBD.

Smiling and laughing during normal REM sleep

Subjects without RBD (including non-parasomniac subjects and sleepwalkers) also displayed happy emotional expressions during sleep in our study. However, these events were rare, since only 9 smiles and laughs were observed during 121 nights in non-parasomniac subjects and 4 during 38 nights in sleepwalkers. This low (0.012 events/h) frequency contrasts with the high frequency of smiles recorded in human neonates. The frequency of smiles is 1.6 smiles/h of apparent REM sleep (no concomitant sleep monitoring) in 5-8-month-old foetuses as observed using ultrasound echography (Kawakami et al., 2009b), 4-30/h of apparent REM sleep in preterm neonates (Emde andHarmon, 1972, Messinger et al., 2002), and 4-19 smiles/h in full-term neonates [START_REF] Messinger | How sleeping neonates smile[END_REF], Kawakami et al., 2009a), i.e., at least one hundred times more frequent than found here in normal adult REM sleep. However, patients with RBD reached a smile/laugh frequency (1.75/h of REM sleep) close to that of foetuses but lower than that of neonates, suggesting that the frequency difference between neonates and normal adults is likely to be caused (in part) by increased REM sleep atonia during post-term development. Their neural correlates might be however different.

Smiling and laughing during non-REM sleep

Notably, we observed 11 smiles in N2 sleep and 1 in N3 sleep, plus 5 episodes of smiles and laughs during N3 sleep. These happy faces were mostly observed in patients with parasomnia, including sleepwalking and RBD. We are not aware of any previous description of sleepwalkers smiling and laughing during NREM parasomniac events, as most patients with arousal disorders display behaviours suggestive of surprise, fear or confusion, often in link with brief unpleasant dreaming scenario (Oudiette et al., 2009b). However, it is possible that many sleepwalkers do smile or laugh during N3 arousal, but that such phenomena had been unnoticed because they did not disturb the partner's sleep. Surprisingly, the patients with RBD had a higher frequency of smiling during NREM sleep than did the non-parasomniac subjects and sleepwalkers, which suggests that their motor dyscontrol during sleep may extend to eliciting phasic motor activity in NREM sleep or that the central pattern generator producing happy emotional expressions is also enhanced in NREM sleep. Phasic motor activity may occasionally occur during NREM sleep in patients with RBD [START_REF] Miguel | Phasic activity during non REM sleep[END_REF], although this is as frequent as in healthy controls [START_REF] Mayer | Quantification of tonic and phasic muscle activity in REM sleep behavior disorder[END_REF]. Eventually, one healthy control smiled during NREM N2 sleep. This result was unexpected but suggests that some phasic, coordinated motor activity occurs, although rarely, during NREM sleep.

Do sleep-associated smiles and laughs result from automatic muscle twitching?

The question of whether these numerous smiles and laughs performed asleep reflects an internal pleasant emotion or whether they are automatic, non-emotional expressions is crucial. Foetuses and neonates cannot verbally report any emotion after having smiled while asleep. Moreover, they may smile while asleep not because they are happy but as a way to train and develop this patterned behaviour underlying an important non-verbal language competence, useful for attaching to and interacting with adults when awake. Similarly, neonates, unlike adults, display abundant muscle twitches during REM sleep (including abundant twitching of the whiskers in rats), which are brainstem generated and do not involve any concomitant activation of the motor cortex [START_REF] Blumberg | Spatiotemporal structure of REM sleep twitching reveals developmental origins of motor synergies[END_REF].

Twitching of facial muscles during adult REM sleep (independent of any emotional expression) is a common observation in adult sleep, especially on the mentalis muscle [START_REF] Bliwise | Facial muscle tonus during REM and NREM sleep[END_REF], which is routinely monitored in sleep units. Unilateral twitches of the zygomatic muscle during adult REM sleep have also been reported [START_REF] Rivera-Garcia | Facial muscle activation during sleep and its relation to the rapid eye movements of REM sleep[END_REF], although the absence of video monitoring did not allow determination of whether the twitches were associated with face expression.

Here, we observed that these unilateral twitches led to brief, unilateral lip corner raising, without any concomitant expression of emotion. These twitching events were (unlike smiles and laughs) as frequent in RBD patients as in controls, which suggests that emotional expressions and twitches are different features and may not be generated by the same structures.

Are sleep-associated smiles and laughs mirthful?

In adults, there were several lines of evidence that smiles and laughs were not automatic but reflected true mirth. First, open mouth smiles outnumbered closed mouth smiles. Open mouth smiles in babies are associated with situations of social engagement and with high levels of arousal and positive emotional valence in the infant [START_REF] Messinger | All smiles are positive, but some smiles are more positive than others[END_REF]. They are exceptional during REM sleep in new-borns, in sharp contrast with a high frequency during communicative wake [START_REF] Cecchini | Smiling in newborns during communicative wake and active sleep[END_REF]. In sleeping neonate, open mouth smiles are twenty times less frequent than closed mouth smiles are [START_REF] Messinger | How sleeping neonates smile[END_REF]. Second, half of sleep-associated smiles were Duchenne smiles, which include bilateral cheek raising and active eye closing (whether the mouth is open or not). In contrast, "non-Duchenne smiles" appear in the mouth but not the eyes and are recognized as non-genuine, often polite smiles. Duchenne smiles have been proposed as spontaneous and genuine expressions of positive emotions, such as happiness, pleasure and enjoyment (Duchenne de Boulogne, 1862Boulogne, -1990)). Numerous studies support the association between mirth and Duchenne smiles. They selectively appear when subjects report positive subjective experiences [START_REF] Ekman | The Duchenne smile: emotional expression and brain physiology[END_REF], when they watch a funny movie and "get the joke" [START_REF] Juckel | Is evaluation of humorous stimuli associated with frontal cortex morphology? A pilot study using facial micro-movement analysis and MRI[END_REF], and in association with the specific cerebral asymmetry (increased left temporal EEG activity) which characterizes happiness [START_REF] Ekman | The Duchenne smile: emotional expression and brain physiology[END_REF]. People producing Duchenne smiles are rated more positively (i.e., authentic, genuine, real, attractive, trustworthy) [START_REF] Gunnery | Perceptions of Duchenne and non-Duchenne smiles: A meta-analysis[END_REF], and while Duchenne smiling they increase psychological, social and spatial proximity, whereas a non-Duchenne smile is associated with psychological distance [START_REF] Bogodistov | Proximity Begins with a Smile, But Which One? Associating Non-duchenne Smiles with Higher Psychological Distance[END_REF]. In contrast to open mouth smiles, which are rare during new-born sleep, new-borns display Duchenne smiles [START_REF] Messinger | How sleeping neonates smile[END_REF]. It is tempting to associate Duchenne smiles, as well as open mouth smiles and laughs during sleep with true mirth, as they are strongly associated during wakefulness.

However, a definitive proof of this association (as in new-borns) is lacking. Non-Duchenne smiles, which represented one fourth of "happy" faces during sleep here, are more ambiguous in terms of emotional valence as people smiling awake may be happy (with a lower intensity than when displaying Duchenne smiles), but they may also try to hide embarrassment, uncertainty, or sadness.

Laughs were abundant during sleep too (N = 79) and were associated with shrugging of shoulders, peals of laughter or concomitant joyful utterances, all suggestive of true concomitant happiness. In addition, half of the smiles and laughs were temporally synchronized with REMs in REM sleep. Because REMs are associated with activation of the amygdala (the brain structure activated during awake emotions) in normal REM sleep [START_REF] Calvo | Phasic activity of the basolateral amygdala, cingulate gyrus, and hippocampus during REM sleep in the cat[END_REF][START_REF] Miyauchi | Human brain activity time-locked to rapid eye movements during REM sleep[END_REF][START_REF] Andrillon | Single-neuron activity and eye movements during human REM sleep and awake vision[END_REF][START_REF] Corsi-Cabrera | Human amygdala activation during rapid eye movements of rapid eye movement sleep: an intracranial study[END_REF], one may infer that many happy emotional expressions are associated with amygdala activation. Happy expressions were not associated with increased heart rate variability during sleep, as is sometimes observed when smiling while awake [START_REF] Ekman | Autonomic nervous system activity distinguishes among emotions[END_REF]. However, most of the smiles and laughs were displayed by patients with RBD. In patients with RBD, autonomic control is altered during REM sleep [START_REF] Pyatigorskaya | Medulla oblongata damage and cardiac autonomic dysfunction in Parkinson[END_REF], to the point that heart rate is not increased even during violent and active behaviours. The dysautonomia may blunt heart rate and vessel changes during a happy emotion. In addition, even in normal subjects, the autonomic system is modified during REM sleep, including selective reduction in somatic and sympathetic tone, which may block outward manifestations (e.g., tachycardia, sweating) of the emotional experience. Consequently, it cannot be determined whether the lack of change in heart rate during REM sleep smile is caused by absent emotion or by absent autonomic outward signs of these emotions. During NREM sleep, happy facial expressions were unfortunately too rare to conduct proper statistical analysis on heart rate variability.

We did not collect the dream/emotion recall immediately after laughs and smiles upon awakening, as this was an observational (not an interventional) study and as we did not want to disturb sleep. However, we collected the morning dream recalls, but, probably because they were collected several hours after the smiling/laughing behaviour, pleasant recalls were similarly frequent after smiling and non-smiling nights. However, on two occasions, we had the chance to observe scenic behaviour including smiles and laughs, in NREM and in REM sleep; both behaviours were highly suggestive of a concomitant pleasant scenario (the pleasure of eating a cake, and a scenario including a kiss). Conversely, there was no smiling or laughing during visibly unpleasant scenic behaviours (including fights, fracases, and fear shouting). All in all, several elements, although there are not definitive, suggest that many smiles and laughs reflect a pleasant concomitant inner emotion.

Limitations

Our study has several limitations. First, there were only 18 healthy subjects in the non-parasomniac group (having slept one or two nights in the laboratory), which makes the estimate of the percentage of spontaneous smiles and laughs asleep in normal adult sleep less certain here than if 100 healthy controls had been monitored. Other non-parasomniac subjects included patients with sleep disorders (insomnia, hypersomnia) that are normally not associated with abnormal movements during sleep, but also patients with narcolepsy and with Parkinson's disease, who had no RBD at time of this study, but may later develop some RBD. Moreover, even this small sample of healthy volunteers was sufficient to find smiles and laughs while asleep. The sleepwalking group was less than half the size of the RBD group, which may have limited the ability to show difference of prevalence of smiling expression between these two groups. Second, the scoring of happy emotional expressions did not follow the most frequently used Facial Activity Coding System, but that system was developed for awake subjects with their eyes open. Instead, we chose to use the scoring system developed for scoring smiles and laughs in sleeping neonates and babies (who have closed eyes). Another limitation is that most observations were performed in patients with RBD, as they had the highest number of happy facial expressions. On the other hand, the patients with RBD, as well as those with sleepwalking, provide a unique opportunity to study concomitant behaviours and try to determine whether happy facial expressions occur in the context of a visibly pleasant scenario.

Future research into the connection between the felt emotion and its emotional expression may be performed by collecting the recalled emotion, having awakened the subject in the seconds after she smiled while asleep. Additionally, one may use brain functional imaging in sleeping, video-monitored subjects, and look for neural correlates of their happy emotional expressions. Both experiences are complex and challenging because REM sleep is difficult to reach when sleeping in a functional magnetic resonance imaging system and because smiles and laughs are rare, unpredictable events in adult sleep.

CONCLUSIONS

Smiling and laughing (which is particular to humans) occasionally persist during adult sleep. There are several lines of evidence that these happy emotional expressions may reflect a true inner mirth. The high frequency of happy emotional expression during RBD and its putative isomorphism suggests that the RBD model could be a small but direct window into the emotional component of REM sleep dreams and could be used in the future to better understand the mood regulatory function and emotion desensitization during sleep. (English translation: Eh! but what…? You made some cake, that's good, that, that's good. Put the cake in the basket there. Tomorrow, it will be very, very good -perfect -... Hey are there some candidates there? (unintelligible words) Laughs, "Oh boy!".) (Shown with the permission of the patient).

Video-clip #2 -Patient with a mild form of REM sleep behaviour disorder associated with Parkinson's disease, laughing during REM sleep (Shown with the permission of the patient). She later reported that she dreamt of attending a happy wedding party.

  The non-parasomnia group (N = 100 subjects) included healthy subjects (N = 18) and patients with adequately treated sleep apnea referred for controlling the treatment efficacy (N = 29), with idiopathic hypersomnia (N = 18), with narcolepsy without RBD (N = 6), with insomnia (N = 3), with suspected parasomnia later ruled out (N = 11) and with Parkinson's disease without RBD (N = 15). No one had any sleep-related movement disorder, as checked by interview and video and sleep monitoring. Except the patients with Parkinson's disease, who took levodopa and dopamine agonists, no patients in the control group took any psychotropic drug. The sleepwalking group contained 22 adult patients, and the RBD group (N = 52) included patients with idiopathic RBD (N = 26) or narcolepsy (N = 7) and Parkinson's disease (N = 19). Patients slept one (n = 118) or two (n = 56) nights in the sleep disorder unit, yielding 230 nights studied for facial expressions. Patients

Figure legends Figure 1 -

 legends1 Figure legends

Figure 2 -

 2 Figure 2 -Illustrations (redrawn from real patients) of smiles and laughs observed

Table 1 -

 1 Clinical measures in non-parasomniac subjects, patients with sleepwalking and patients with REM sleep behaviour disorder Data are expressed as the mean ± SD or %. * Analyze of variance between the three groups. Post hoc test: p<0.01 for a difference between a non parasomnia and sleepwalking, b non parasomnia and RBD, and c sleepwalking and RBD groups. Tests are adjusted for age. RBD = REM sleep behaviour disorder.

	Groups	Non-	Sleepwalking	RBD	P*
		parasomniac
	Subjects, No.	100	22	52	NA
	Recorded nights, No.	121	38	71	NA
	Sex ratio, male %	53/47 (53)	10/12 (45.5)	31/21 (59.6)	0.5
	Age, y	49.8 ± 19.6 a,b	33.3 ± 9 c	59.7 ± 15.2	<0.0001
	Epworth sleepiness	10.5 ± 5.5	9.2 ± 4.4	9.7 ± 5.4	0.01
	score, 0-24
	Ekman 35 faces test
	Total score, 0-35	28.2 ± 3.8	29.4 ± 2.9	28.1 ± 3.5	0.62
	Neutral, 0-5	4.8 ± 0.7	4.9 ± 0.3	4.8 ± 0.6	0.79
	Sadness, 0-5	3.1 ± 1.2	3.2 ± 1.3	3.2 ± 1.3	0.61
	Happiness, 0-5	4.9 ± 0.3	4.9 ± 0.3	5 ± 0.2	0.29
	Anger, 0-5	4.1 ± 1.3	4.5 ± 1.1	3.9 ± 1.1	0.78
	Disgust, 0-5	3.9 ± 1.2	4 ± 0.3	3.9 ± 0.9	0.84
	Fear, 0-5	3 ± 1.3	3.3 ± 1.5	2.8 ± 1.2	0.33
	Surprise, 0-5	4.4 ± 1	4.8 ± 0.5	4.5 ± 0.9	0.36

Table 2 -

 2 Type and frequency of smiles and laughs during sleep in subjects

	Group	Non parasomniac	Sleepwalking	RBD	P
	No of subjects	100	22	52	NA
	Smiles (E2 + E3 types), N (%) of subjects with
	Sleep	8 (8)	2 (9)	27 (51.9) b,c	<0.0001
	NREM sleep	1 (1)	1 (4.5)	7 (13.5) b	0.004
	REM sleep	7 (7)	1 (4.5)	20 (38.5) b,c	<0.0001
	Laughs (E4), N (%) of subjects with
	Total sleep time	0 (0)	1 (4.5)	18 (39.6) b	<0.0001
	NREM sleep	0 (0)	1 (4.5)	0 (0)	NA
	REM sleep	0 (0)	1 (4.5)	18 (39.6) b	<0.0001
	Duchenne smiles, N (%) of subjects with
	Total sleep time	2 (2)	1 (4.5)	28 (53.8) b,c	<0.0001
	NREM sleep	1 (1)	1 (4.5)	4 (7.7)	0.15
	REM sleep	1 (1)	1 (4.5)	24 (46.1) b,c	<0.0001
	All happy emotional expressions (E2, E3, E4), N (%) of subjects with
	Total sleep time	8 (8)	3 (13.5)	30 (57.7) b,c	<0.0001
	NREM sleep	1 (1)	2 (9)	10 (19.2) b	0.0003
	REM sleep	7 (7)	2 (9)	20 (38.5) b	<0.0001
	Post hoc test: p<0.01 for a difference between a non-parasomnia and sleepwalking,

b non-parasomnia and RBD, and c sleepwalking and RBD.

Table 3 -

 3 Number and frequency of laughs and smiles during sleep in subjects with and without parasomnia. Results are expressed as numbers or means ± SD. See the Results section for statistics. NA = not applicable (small samples). NS: not significant. Post hoc test: p<0.01 for a difference between b non-parasomnia and RBD, and c sleepwalking and RBD groups. * Duchenne smiles occured in mild (E2) or in open mouth (E3) smiles.

	Group	Non parasomniac	Sleepwalking	RBD	P
	Subjects, N	100	22	52	NA
	Nights, N	122	38	75	NA
	All types of lip raising (unilateral lip corner raising, mild smile, open mouth
	smile, laugh), total number for the group; n/h of sleep
	Total sleep time 19; 0.023 ± 0.071 17; 0.072 ± 0.238 182; 0.382 ± 0.503 <0.0001
	NREM sleep	7; 0.011 ± 0.053 14; 0.071 ± 0.273 21; 0.059 ± 0.132	NS
	N1	0; 0 ± 0	0; 0 ± 0	3; 0.538 ± 3.614	NA
	N2	6; 0.017 ± 0.086	12; 0.095 ± 0.36	16; 0.078 ± 0.213	NS
	N3	1; 0.004 ± 0.044	2; 0.033 ± 0.142	2; 0.012 ± 0.075	NS
	REM sleep	12; 0.13 ± 0.615	3; 0.062 ± 0.225	161; 1.863 ±	<0.0001
				2.811 b,c
	Unilateral lip corner raising (E1), total number for the group; n/h of sleep
	Total sleep time 10; 0.013 ± 0.063 13; 0.056 ± 0.224	22; 0.051 ± 0.1	NS
	NREM sleep	6; 0.01 ± 0.052	12; 0.061 ± 0.25	12; 0.036 ± 0.1	NS
	N1	0; 0 ± 0	0; 0 ± 0	2; 0.116 ± 0.7	NA
	N2	5; 0.15 ± 0.082	11; 0.09 ± 0.4	8; 0.042 ± 0.15	NS
	N3	1; 0.004 ± 0;044	1; 0.016 ± 0.1	2; 0.012 ± 0.08	NS
	REM sleep	4; 0.028 ± 0.155	1; 0.026 ± 0.16	10; 0.109 ± 0.34	NS
	Mild smile (E2), total number for the group; n/h of sleep
	Total sleep time	6; 0.006 ± 0.029	1; 0.003 ± 0.02 36; 0.077 ± 0.156 b,c <0.0001
	NREM sleep	1; 0.001 ± 0.013	1; 0.004 ± 0.026	7; 0.018 ± 0.061	NS
	N1	0; 0 ± 0	0; 0 ± 0	0; 0 ± 0	NA
	N2	1; 0.002 ± 0.026	1; 0.005 ± 0.031	7; 0.031 ± 0.111	NS
	N3	0; 0 ± 0	0; 0 ± 0	0; 0 ± 0	NA
	REM sleep	5; 0.075 ± 0.569	0; 0 ± 0	29; 0.389 ± 0.911 <0.0001

ACKNOWLEDGMENTS

The authors thank Juliette Rey for the illustrations and Dr Pascal Rey-Herme for his financial support via the ADOREPS. The study was promoted by Assistance Publique -Hôpitaux de Paris for the arousal disorders part, and by INSERM for the RBD part.

Conflict of interest

All authors declare that they have no conflicts of interest related to this study.

AUTHORS' CONTRIBUTION

Participants were included by MC, who also placed the EMG electrodes and performed the Ekman test. Faces and muscles were evaluated by MC and doubledcontrolled by JBM. Autonomic changes were measured by JL. Data were collected by MC and JBM. The statistical analysis was performed by JBM. MC and IA drafted the first manuscript, which was amended by all co-authors. IA and MV obtained the funding.