Lionel Bombrun
email: lionel.bombrun@ims-bordeaux.fr

BISTATIC POLARIMETRIC SAR DECOMPOSITION IN TERMS OF ROLL-INVARIANT PARAMETERS

Keywords: Bistatic Polarimetry, Polarimetric Synthetic Aperture Radar, Roll-invariant decomposition, Target Scattering Vector Model

This paper introduces a new bistatic Polarimetric SAR decomposition in terms of roll-invariant parameters. The proposed decomposition is an extension of the Target Scattering Vector Model to the bistatic case, where the cross-polarization terms of the scattering matrix are not necessary equal.

INTRODUCTION

The polarimetric information has been widely used to interpret the Synthetic Aperture Radar (SAR) scene. Hence, many coherent and incoherent target decompositions have been proposed in the literature to extract polarimetric parameters with a physical meaning (1) [START_REF] Titin-Schnaider | Physical Meaning of Bistatic Polarimetric Parameters[END_REF]. Nevertheless, for most of them, the reciprocity assumption is assumed. For a bistatic Polarimetric SAR (Pol-SAR) sensor, the cross-polarization terms of the scattering matrix are generally not equal (S HV = S V H ). This paper presents a generalization of the Target Scattering Vector Model (TSVM) to the bistatic case: the bistatic TSVM [START_REF] Bombrun | Extension of the Target Scattering Vector Model to the Bistatic Case[END_REF]. Five roll-invariant parameters (independent of the orientation angles) are necessary for an unambiguous description of the target scattering mechanism: µ, α s , Φ αs , τ 1 and τ 2 . This paper is organized as follows. In Section 2, the extension of Target Scattering Vector Model to the bistatic case is first introduced. Then, a presentation of the bistatic incoherent target decomposition in terms of rollinvariant parameters and a study of the influence of the processing window size on the estimation of the bistatic TSVM parameters are achieved in Section 3. Next, some results are shown in Section 4. Finally, some conclusions of this work are discussed in Section 5.

THE TARGET SCATTERING VECTOR MODEL

The Kennaugh-Huynen con-diagonalization

Coherent targets are fully described by their scattering matrix S. In the context bistatic polarimetry, S is a com-

plex 2 × 2 matrix, S = S HH S HV S V H S V V
where the crosspolarization elements S HV and S V H are not equal in general.

Kennaugh and Huynen have proposed to apply the characteristic decomposition on the scattering matrix to retrieve physical parameters (4) [START_REF] Kennaugh | Effects of Type of Polarization on Echo Characteristics[END_REF]. The Kennaugh-Huynen decomposition is parametrized by means of 8 independent parameters: θ R , τ R , θ E , τ E , ν, µ, κ and γ by (4) (6) (7):

S = e -jθ R σ3 e -jτ R σ2 e jνσ1 S 0 e jνσ1 e -jτ E σ2 e jθ E σ3 (1) where:

S 0 = µe jκ 1 0 0 tan 2 γ
and e jασ k = σ 0 cos α+jσ k sin α.

(2) σ i are the spin Pauli matrices defined by:

σ 0 = 1 0 0 1 , σ 1 = 1 0 0 -1 , σ 2 = 0 1 1 0 , σ 2 = 0 -j j 0 . (3)
θ R and θ E are the tilt angles. τ R and τ E are the helicity. The subscript R and E stand respectively for reception and emission. µ is the maximum amplitude return. γ and ν are respectively referred as the characteristic and skip angles. κ is the absolute phase of the target, this term is generally ignored except for interferometric applications. Moreover, it can be shown that:

e jνσ1 S 0 e jνσ1 = µe 2j(ν+κ/2) 0 0 µ tan 2 γ e -2j(ν-κ/2) = λ 1 0 0 λ 2 , (4)
where λ 1 and λ 2 are the two complex con-eigenvalues of S.

The bistatic TSVM model

The TSVM consists in the projection in the Pauli basis of the scattering matrix con-diagonalized by the Takagi method. It yields that k

P = 1/ √ 2 S HH + S V V , S HH - S V V , S HV + S V H , j(S HV -S V H ) T .
After some mathematical manipulations, it yields:

k P = e jΦs    1 0 0 0 0 cos(θ 1 ) -sin(θ 1 ) 0 0 sin(θ 1 ) cos(θ 1 ) 0 0 0 0 1    ×    cos(θ 2 ) 0 0 -sin(θ 2 ) 0 1 0 0 0 0 1 0 -j sin(θ 2 ) 0 0 -j cos(θ 2 )    k roll-inv P , (5)
where the expression of the roll-invariant target vector k roll-inv P is given by ( 3):

k roll-inv P = µ    cos α s cos(τ 1 ) sin α s e jΦα s cos(τ 2 ) -j cos α s sin(τ 1 ) -j sin α s e jΦα s sin(τ 2 )    , (6)
where τ 1 = τ R + τ E and τ 2 = τ R -τ E . α s and Φ αs are the scattering type magnitude and phase parameters, given by:

tan(α s ) e jΦα s = λ 1 -λ 2 λ 1 + λ 2 . ( 7
)
It has been pointed out that Huynen's parameters are not unique and need to be reevaluated. If the tilts angles

(θ 1 = θ R + θ E , θ 2 = θ R -θ E ) are solution of (6), then (θ 1 ± π, θ 2 ± π), (θ 1 ± π, θ 2
) and (θ 1 , θ 2 ± π) are also solutions of [START_REF] Germond | Théorie de la Polarimétrie Radar en Bistatique[END_REF]. It yields the following three relations (3):

k P = k P (Φ s ± π, θ 1 ± π, θ 2 ± π, τ 1 , τ 2 , µ, α s , Φ αs ) = k P (Φ s , θ 1 ± π, θ 2 , -τ 1 , -τ 2 , µ, α s , Φ αs ± π) = k P (Φ s ± π, θ 1 , θ 2 ± π, -τ 1 , -τ 2 , µ, α s , Φ αs ± π). (8)
After this step, the tilt angles θ 1 and θ 2 belong to the interval [-π/2, π/2] and the decomposition is unique. In the context of bistatic polarimetry, five parameters (namely µ, τ 1 , τ 2 , α s and Φ αs ) are necessary for an unambiguous description of a coherent target. The scattering type magnitude α s and phase Φ αs contain information on the scattering type mechanism. The target helicity τ 1 is a measure of the target symmetry, i.e. τ 1 = 0 for a symmetrical target. The target helicity τ 2 contains information on the asymmetrical part of the scattering matrix, i.e. τ 2 = 0 corresponds to S HV = S V H .

BISTATIC INCOHERENT TARGET DECOM-POSITION IN TERMS OF ROLL-INVARIANT PARAMETERS

Principle

The roll-invariant bistatic incoherent target decomposition is based on the characteristic decomposition of the coherency matrix. For a bistatic polarimetric radar, the coherency matrix [T ] can be represented as the incoherent sum of four coherency matrix [T ] i of rank 1. The four coherency matrices [T ] i are weighted by their real positive eigenvalue µ i by:

[T ] = 4 i=1 µ i [T ] i . (9)
Each coherency matrix [T ] i of rank 1 is associated to one single scatterer. [T ] i can be rewritten as a function of the target scattering eigenvector k i as:

[T ] i = k i k H i . ( 10
)
The principle of the roll-invariant bistatic incoherent target decomposition can be decomposed into three steps as follows:

1. Estimation of the coherency matrix [T ] on a sliding window, denoted [ T ].

Application of the characteristic decomposition on [ T ]

, and extraction of the four eigenvectors k i with their respective eigenvalues µ i .

3. Application of the bistatic TSVM on each eigenvector k i and extraction of the five roll-invariant parameters (µ i , τ 1i , τ 2i , α si and Φ αs i ) to fully characterized the scatterers.

To apply the incoherent target decomposition, the covariance matrix [T ] should be estimated. For homogeneous regions, the target vector k is generally modeled by a zero-mean multivariate circular complex Gaussian vector. In this case, the maximum likelihood estimator of the polarimetric covariance matrix [T ] is the sample covariance matrix [ T ] SCM given by:

[ T ] SCM = 1 N N i=1 k i k H i . (11)

Influence of the processing window size

As PolSAR images are corrupted by the speckle noise, incoherent target decomposition parameters can be biased.

A study of the influence of the processing window size on the estimation of the bistatic TSVM parameters is necessary to find the minimum window size required for nearly unbiased parameter estimation.

Figure 1 shows the evolution of the scattering type magnitude α s parameter associated to the dominant scattering mechanism (of eigenvalue λ 1 ) as a function of the equivalent number of looks L. For this purpose, an homogeneous region containing fields located on the south west of Figure 2 has been extracted and bistatic TSVM parameters are computed on square window. As observed in Figure 1, αs1 is biased for a relatively small window size (7 × 7) which corresponds approximately to equivalent number of looks L of 18. For sufficiently large windows size (15 × 15, i.e. L ≈ 60), the bias vanishes and αs1 converges to α s1 for the sample covariance matrix estimator. A processing window containing at least 60 equivalent number of looks is therefore necessary to derive nearly unbiased incoherent decomposition parameters as discussed in (8; 9).

Degree of coherence for the assessment of target scattering phase

As observed in ( 6), the target scattering type phase Φ αs is the trihedral-dihedral channel phase difference. This rollinvariant parameter can be exploited only under coherence conditions. By following the same procedure as described in [START_REF] Touzi | Phase of Target Scattering for Wetland Characterization Using Polarimetric C-band SAR[END_REF], the degree of coherence of Φ αs (denoted p Φα s ) is therefore introduced. Its expression is given by:

p Φα s = |a| 2 -|b| 2 2 + 4| a • b * | 2 a| 2 + |b| 2 , ( 12
)
where a = cos α s cos τ 1 and b = sin α s e jΦα s cos τ 2 for a bistatic polarimetric radar. Therefore, a partially coherent scatterer is represented as a point inside the Poincaré sphere at a distance p Φα s from the sphere center.

RESULTS

To illustrate the roll-invariant bistatic target scattering vector model, a PolSAR RAMSES X-band data-set acquired over Brétigny, France is analyzed. This data-set is composed by three buildings surrounded by agricultural fields. A colored composition of the target vector in the Pauli basis is given in Figure 2. This PolSAR data-set has been acquired in a monostatic mode. As the four polarimetric SAR channel are recorded by the sensor, the incoherent bistatic TSVM parameters can be computed. Nevertheless, the usefulness of the proposed method will not be fully emphasized as S HV and S V H are quite similar in the monostatic case. To evaluate the influence of the processing window size on the roll-invariant parameters, three different window size (7 × 7, 15 × 15 and 31 × 31) are analyzed. Figure 3 shows the dominant target scattering type magnitude α s issued from the first eigenvector of the estimated coherency matrix. Moreover, for relatively small window size (7 × 7, i.e. L ≈ 18), the estimated parameters are biased. An unbiased estimation of target scattering parameters is achieved for a sufficiently large window (31 × 31 pixels, i.e. L ≈ 137) as shown in Figure 1. This yields to a blur effect. Nevertheless, for such window size, the region might involve scatterers having different polarimetric responses and might lead to a misinterpretation of the bistatic TSVM parameters. In the following, a window size of 15 × 15 pixels will be considered as a good trade-off.

Figure 4 shows the five roll-invariant bistatic target scattering target vector parameters (µ, α s , Φ αs , τ 1 and τ 2 ) issued from the first eigenvector of the sample covariance matrix estimator [ T ] SCM computed on a 15 × 15 window. The degree of coherence p Φα s is also computed and shown in Figure 4(f). The maximum amplitude return µ characterizes the power of the dominant scattering mechanism. This parameter is equal to the largest eigenvalue λ 1 of the covariance matrix [ T ] SCM . The α s quantity describes the type of scattering mechanism (1). It varies from 0 for surface scattering (see fields on the bottom left of Figure 4(b)) to π/2 for double bounce scattering as observed on the three buildings. Φ αs is the target scattering type phase. This term can be exploited only under coherence conditions. For this purpose, the degree of coherence p Φα s is computed. For high values of p Φα s (near 1), the target scattering type phase can be used as an additional parameter to interpret PolSAR data. The target helicity τ 1 = τ R + τ E is a measure of the target symmetry. It allows to separate symmetric (τ 1 = 0) from asymmetric (τ 1 = 0) scatterers that have the same scattering type magnitude and phase. For natural media, the target helicity τ 1 is relatively low (τ 1 ≈ 0) as observed on fields (see Figure 4(c)). The target helicity τ 2 characterizes the asymmetrical part of the scattering matrix. This term indicates if the reciprocity assumption holds (for τ 2 = 0) or not (for τ 2 = 0). As the studied PolSAR data-set has been acquired under monostatic condition, the cross-polarization terms S HV and S V H are expected to be similar, which will lead to τ 2 ≈ 0. This is confirmed by Figure 4(d) where the target helicity τ 2 is very low.

CONCLUSION

This paper has presented a roll-invariant target decomposition in the context of bistatic PolSAR imagery: the bistatic target scattering vector model. Based on the Kennaugh-Huynen characteristic decomposition, five parameters, namely α s , Φ αs , τ 1 , τ 2 and µ, are necessary for an unambiguous description of a coherent target. This new PolSAR model is an extension of the TSVM, introduced by Touzi in 2007 (1), to the general case of bistatic polarimetry where the cross-polarization elements S HV and S V H are not equal. A new parameter has been introduced: the target helicity τ 2 , which contains information on the asymmetrical part of the scattering matrix.

Figure 1 .

 1 Figure 1. Influence of the number of looks L on the estimation of the dominant scattering type magnitude parameter α s .

Figure 2 .

 2 Figure 2. RAMSES X-band PolSAR data over Brétigny, France (501 × 501 pixels). Colored composition of the target vector in the Pauli basis [k] 2 -[k] 3 -[k] 1 .

Figure 3 .

 3 Figure 3. Dominant target scattering type magnitude α s1 , issued from the Sample Covariance Matrix estimator [ T ] SCM on a (a) 7 × 7 window (L ≈ 18), (b) 15 × 15 window (L ≈ 60) and (c) 31 × 31 window (L ≈ 137).

ACKNOWLEDGMENT

The author wish to thank the French Research Agency (ANR) for supporting this work through the EFIDIR project (ANR-2007-MDCO-004-03, http://www.efidir.fr).


Anne-Marie Argenti
email: anne-marie.argenti@ens.fr

Michel Charolles

The Effect of Position on Understanding : Preposed vs Inserted ` selon X ´(according to X)

Centering theory (Grosz et al., 1983, Walker et al., 1998) establishes a structural relationship between the form of referential expressions and attentional focus. It predicts specifically that highly focused entities tend to be realized with less marked forms (e.g. pronouns) and that factors such as grammatical status or surface position affect prominence. The experiments reported here aimed to test a claim put forward in linguistic studies on French evidential adverbials (Schrepfer, 2005) concerning the functioning of the preposed position as a potential frame influencing the following pronominal resolutions : a preposed prepositionnal phrase (PP), but not an inserted one, frames an informational bloc in which antecedents are easily accessed compared to antecedents located outside the bloc

Counterbalanced Factors

Interpr

Interpré étation tation

In Preposed Position  no Reading time difference of Target sentence whatever the Pronoun Possibly due to the first mention effect reported by Gernsbacher et al. (1989) In our first experiment, results were similar to those obtained by Gordon et al. (1993) in their 5th test with the Repeated Name Penalty Paradigm, results they interpreted as indicating that "an initial and non subject" or a "noninitial and subject" entity equally provides prominence. Our second experiment, however, suggests that the rather robust effect obtained with our material was probably not only a question of surface order. Our third experiment shows the importance of the verbal phrase in our preceding results. Altogether, these experiments confirm the importance of antecedent prominence in pronominal resolution as pointed out by Centering Theory and suggest a new factor of prominence, besides surface order and grammatical status, nameky the semantic affinity between Evidential Preposition and subsequent Verb Phrases whose Subject pronoun is the mentioned Speaker. The Speaker's point of view signaled by the PP seems to prime opinion VP, possibly changing the narrative from an objective story about the previous Grammatical Subject to a story concerning the subjectivity of the Speaker. This last result shows that Preposed PPs fulfil a specific framing function (Charolles, 1987) in certain conditions which further studies will focus on and develop

Methodology:

  Self Paced Reading Paradigm with P2 as Target + Comprehension task Participants : 24 students (University of Paris III) Same material with two introductory sentences added P-2 : Vincent/Francine prépare un master de gestion à Paris-Dauphine. (Vincent/Francine is taking a Master in Management at Paris-Dauphine. ) P-1 : Les programmes comprennent des enseignements théoriques et des mises en situation… (The syllabus includes theorical knowledge and applied skills…) introduction  Same results in Expt. 1 The Subject in introduction  In the Preposed Position, shorter Reading time for Subject Target sentences of Expt. 2 stimuli are replaced P2 : Il/Elle a mis à contribution proches et relations du secteur en début d'année… (He/She asked some friends and colleagues for help early this year…)Hypothesis HypothesisExpected Effect of antecedent Prominence on the Pronoun resolution of Target sentence as predicted in ExptShorter Reading time of Target sentence for Subject's Gender Pronoun (F(1,23)=7, p=0.01)Interaction : Shorter Reading time for Inserted Position x Subject's Gender Pronoun condition than for others(F(1,23)= 4.45, p=0.046)

Material P1 : Selon Francine, Vincent a trouvé un stage dans une agence de publicité. (According to Francine, Vincent found an advertising agency internship.) P2 : Il/Elle apprécie que les cursus étudiants incluent une expérience professionnelle… (He/She appreciates the fact that the curriculum includes a work experience…) P1 : Vincent a trouvé, selon Francine, un stage dans une agence de publicité. (Vincent found, according to Francine, an advertising agency internship.) P2 : Il/Elle apprécie que les cursus étudiants incluent une expérience professionnelle… (He/She appreciates the fact that the curriculum includes a work experience…) Hypothesis Hypothesis

	Prepositional Phrase Position  Preposed or Inserted Target Pronoun Gender  Gender of the NP complement of the evidential PP (here the Speaker)
	or Previous Grammatical Subject Gender

Preposed Position x Subject's Gender Pronoun  Quick « Inside Frame » Reading Preposed Position x Speaker's Gender Pronoun  Slow « Outside Frame » Reading Inserted Position x Speaker's Gender Pronoun  Slow Reading due to inaccessibility of antecedent Inserted Position x Subject's Gender Pronoun  Quickest Reading consistent with Centering Theory

ms) Speaker Subject Expt. 3 : Position X Pronoun

	INTRODUCTION INTRODUCTION
		EXPERIMENT 1 EXPERIMENT 1
			Expt. 1 :Position X Pronoun
		Reading Times (ms)	3400 3600 3800 4000 4200 4400 4600	Speaker Subject
			Preposed	Inserted
			Position
	EXPERIMENT 2 EXPERIMENT 2	EXPERIMENT 3 EXPERIMENT 3
			3800
			3700
			3600
			3500
			3400
			3300
	Expt. 2 : Position X Pronoun Reading Times (3200 3600 3700 3800 3900 4000 4100 4200 4300
	3500
	Preposed	Inserted
	Position
	SUMMARY SUMMARY

Participants : 64 students (University of Paris III)

Results

Main effect : Shorter Reading of Target sentence for Subject Gender Pronoun (F1(1,63)= 7.6, p=0.007)

Interaction

Longer Reading for Inserted Position x Speaker Gender Pronoun condition than for others (F1(1,252)=4.3, p=0.

Interpretation Interpretation

No effect of the Prominence manipulated factor Possibly due to interaction between the meaning of the evidential PP and opinion verbs such as « appreciate, find, think, hope… » systematically used in Target sentences

Replacement of the opinion verbs of Target sentences by verbs describing the Subject's action

Adjunction of a new factor to manipulate protagonist Prominence

Two introductory sentences are added to the previous texts : the first sentence starts with the mention of one of the protagonists, the Speaker or the Subject Participants : 48 students (University of Paris III)

Results

Main effect : as previously (F1(1,47)= 16, p < 0.001)

No longer any Position x Pronoun Interaction

(F1(1,188)= 0.65, p= 0.8)

Prominence x Pronoun Interaction

Longer Reading for Subject in introduction x Speaker Gender Pronoun condition (F1(1,188)= 6.96, p < 0.01)

Interpretation Interpretation

Without opinion verbs, Reading of Target utterances depends on antecedents' prominence given by their grammatical status and their number of occurences Gender Pronoun than for Speaker Gender Pronoun


Ya-Huei Wu
email: yahuei.wu@brc.aphp.fr

Mohamed Chetouani

Victoria Cristancho-Lacroix

Jade Le Maître

Céline Jost

Brigitte Le Pevedic

Dominique Duhaut

Consuelo Granata

Anne-Sophie Rigaud

ROBADOM: The Impact of a Domestic Robot on Psychological and Cognitive State of the Elderly with Mild Cognitive Impairment

Keywords: assistive robot, elder care, ethical issue, mild cognitive impairment

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In the last years, many projects have addressed the use of robots for supporting elderly people aging in place. Research in the technical community has begun to identify specific needs and values future robotic technologies might support for the aged population. Some of these include support in managing the home; maintaining personal and household supply; monitoring and providing ambulatory support; and providing communication and social interaction [START_REF] Kawamura | Design philosophy for service robots[END_REF], [START_REF] Schraft | Care-O-botTM: the concept of a system for assisting elderly or disabled persons in home environments[END_REF], [START_REF] Forlizzi | Assistive robotics and ecology of elders living independently in their homes[END_REF]. According to Broekens et al. [START_REF] Broekens | Assistive social robots in elderly care: a review[END_REF], robot research in eldercare concerning assistive robots comprises both rehabilitation robots and social robots. The first ones emphasize physical assistive technology. The second ones concern systems that can be perceived as social entities with communication capacities. Furthermore, studies on assistive social robots in eldercare feature either pet-like companionship robot whose main function is to enhance health and psychological well-being or service type robots whose main function is to support daily activities related to independent living.

Recent research, such as Nursebot project [START_REF] Pollack | Pearl: a mobile robotic assistant for the elderly[END_REF], Robocare project [START_REF] Bahadori | RoboCare: an integrated robotic system for the domestic care of the elderly[END_REF], Care-o-bot [START_REF] Graf | Care-O-bot II -development of a next generation robotics home assistant[END_REF], CompanionAble project [START_REF]CompanionAble project[END_REF], and MOBISERV project [START_REF]MOBISERV project[END_REF] has been increasingly focusing on service type assistive social robots to support the elderly to live independently at home. The rationale for the development of this kind of robots is that the aged population experience different degree of cognitive decline (ranging from aged-related cognitive decline, mild cognitive impairment to dementia) which might lead to difficulties in performing complex daily activities and in some case to a loss of autonomy. In this context, this kind of robots are conceived to assist the elderly with cognitive impairment in the following ways: by providing assurance that the elder is safe and is performing necessary daily activities, and, if not, alerting a caregiver; by helping the elder compensate for their impairment, assisting in the performance of daily activities; and by assessing the elder's cognitive status [START_REF] Pollack | Intelligent technology for an aging population: the use of AI to assist elders with cognitive impairment[END_REF].

In the same line with the recent researches, the ROBADOM project is devoted to the design of a robot-based solution, a "robot butler", for assisting daily living of the elderly: reminder of appointments and of medicines intake, management of shopping lists and cognitive stimulation. The specificity of our project lies in developing a robot capable of providing verbal and non-verbal interactions and feedbacks and therefore coaching the elder users during cognitive stimulation exercises.

Project objectives

The ROBADOM project addresses the following issues:

1. Social context for designing social robots: 1) define the robot appearance acceptable by the elderly and 2) investigate the perceptions, attitudes and preferences of the elderly toward an assistive robot at home 2. Develop the robot's behaviors to provide natural interaction with the elderly:

1) first technological solutions for an expressive robot and 2) verbal and nonverbal communication between elderly people and the robot 3. Study the issue of robot acceptance in the elderly 4. Study the impact of robot on the elderly users (e.g., emotion and cognitive states, quality of life…)

System design

In order to design appropriate robot behaviors, interactions between the elderly and a psychologist are studied. The study will bring out specific signals, which will be characterized, in order to build a robust model. These signals will then be integrated in a complex architecture, MIIRE, which is specifically created to manage the interactions between the robot and a user.

Triadic Interaction: detecting verbal and non-verbal signals

The interaction between an older person, a psychologist and cognitive stimulation exercises is a triadic interaction situation, as shown in Figure 1. In this situation, the psychologist explains to the older person how to do the exercise, how to correct or erase an answer, or just encourages him. Backchannels of the psychologist were important for the elderly to build self-confidence and therefore to do these exercises correctly. An older person sits in front of the touch screen with the psychologist at his right. A video camera is placed in a corner, in order not to disturb the older person. To establish interaction between the robot and the user, the robot needs to detect verbal and non-verbal signals, and send a feedback to the user. These social signals are fundamental for the regulation and the success of cognitive exercises.

To monitor the engagement/attention and to detect when the user requires encouragement and help, we propose a multi-modal system described in Figure 2

Engagement monitoring

To estimate where the user is looking at, and thus to monitor his attention and engagement, two cameras are placed on top of the touch screen and on top of the Nabaztag1 to record user's movements. We want to detect if the user is talking/interacting or looking at the touch screen or Nabaztag. The algorithm consists of the following steps:

1. Detection of the face using the standard Viola-Jones detector [START_REF] Viola | Robust real-time face detection[END_REF] on each camera (touch screen and robot).

2. Double camera tracking with the Camshift algorithm with re-initializations.

3. Similar to face detection, eyes can be identified using a cascade of boosted tree classifiers with Haar-like features. Eye-contact estimation is based on the combination of face and eye classifiers. The robustness of the eye-contact detector can be improved by thresholding the output of the eye-detector. The eye-contact detection system developed in this paper doesn't require calibration of the cameras but only the presence of the same user. Future works will be carried out on the extraction on more features such as movement analysis: head nod/shake detection as done in [START_REF] Al Moubayed | Generating Robot/Agent Backchannels During a Storytelling Experiment[END_REF].

The eye-contact signal is used to monitor the attention/engagement of the user during cognitive exercises and further to adapt the robot's behaviors.

KeyWords spotting

The key idea here is to infer the intention of an older user by detecting some predefined keywords. After analyses of recorded sessions, we defined 5 principal intentions: greeting, validating, clarification (e.g., cancel, type… These are clarifications the user needs in order to process through the exercise), user being lost, asking for instructions. The study of the user's behaviors gave number of specific words the robot has to pay attention to -the KeyWords that are in fact essential to recognize what the user is really saying. A recognized KeyWord uttered by the user will trigger verbal and non-verbal responses that can differ depending on context: type of exercises, level of user's engagement and actions.

MIIRE: Interaction and Individualization Modules in Emotional Robotic

A complete architecture will be created to manage human-robot interaction. MIIRE takes input data from the multi-modal system and precedes them to different behaviors that the robot can express as output data. Indeed, the robot will have the possibility to express different kind of behaviors when triggered by a single input, in order to avoid repetitions of similar movements, which might bore users and thus break the interaction. This architecture is a base for the cognitive modeling of humanrobot relationships. The applications of human-robot interaction field are very important. Moreover, robot has to perceive its environment and to build dynamic model of it.

Human-robot interaction is an emerging area of interest in which development and research are very active in many fields. The field we are working on needs new theoretical models, on one hand for the robotics scientists to improve the robot utility, and on the other hand to evaluate the risks and benefits of this new "friend" for our modern society. The table 1 shows several architectures currently used by the robotic community, with their application areas, as a state-of-the-art reference. This list is not exhaustive but is representative of the diversity of the suggested solutions. It seems that a single architecture, which manages several kinds of output (robot, avatar, others...) does not exist. Moreover, each architecture deals with a specific domain so it is possible to find a general model as none of the implementations is general. That is why we want to suggest a new architecture which will not have these constraints.

The MIIRE architecture is an organization to manage a human-robot interaction. The input of the system is composed of several sensors which allow the robot to possess the knowledge of the human state and of the situation. MIIRE merges all collected information and computes the answer that the robot will express (the output).

Fig. 3 shows the first release of the implementation of MIIRE in our context. The input is composed of a set of modules which analyze signals from sensors and send relevant information to the Input Coordinator. These modules can be:

 an attention manager, which checks if the person is concentrated on the exercises,  an agenda which manages the different appointments,  a news module which indicates which important event happens recently,  a motivation module which allows to help and to encourage the user, The Input Coordinator is in charge of sorting sensor data to avoid noise or wrong data. The relevant data is sent to the Interaction Manager which is the conductor of the architecture. Some modules can be implemented as:

 Event Analyzer: this module supervises data concerning human, environment, context, news, machine, etc. Information concerning current situation is acquired and analyzed and if a new event happens, the Event Analyzer warns the Interaction Manager.

 Dialogue Manager: this module manages the dialogue with the user.  Knowledge Manager: this module stores past actions, relevant information about the user, the situation, some news and so on.  Scenario Manager: this module represents interaction scenarios (which action to do, when to do ...) and the interaction ritual. It knows how to initiate an interaction; it knows communication rules, such as the timing to speak, etc.  Planner: it manages the Scenario Manager and suggests which action or behavior the robot will express. Then it transmits information to the Interaction Manager which decides what the robot has to do.  Cognition Manager: it adds an affective value in the architecture. It is in charge of giving the emotional state of the robot according to the situation and the emotional state of the user.

The Interaction Manager decides the action to do according to each module. If the person has a trouble, it is obvious that the current interaction will be broken and that the robot will do something to help her/him (for example, calling for help). The Interaction Manager provides the behavior to be executed of the robot to the Output Coordinator, which sorts data, if needed, and provides the answer to the output. Three types of answers are possible:  Reflex answer: this is the answer to a situation which does not require any reflection or decision making.  Coaching answer: it allows the robot to encourage and assist the user during the execution of a collaborative task, for example, in the case of cognitive stimulation exercises.  Emotional answer: allows the robot to express emotions and to send verbal or non verbal messages to the user. Emotions play an important role in the interaction on three aspects: they initiate, maintain and reinforce the interaction. Finally, MIIRE computes the final answer to express and provides as an output the behavior the robot has to adopt, directly referring to the answer. The output can be gestures, postures, facial expressions, speech, eye gaze, body language, sounds, music, light, impulsive movements, and even biological or physiological signs, such as breathing patterns.

The suggested architecture, MIIRE, is a modular architecture. It means that a set of modules, in fact computing programs, evolve autonomously and independently but with the knowledge of each other and with the capability of working together if necessary. The system works even if only few numbers of modules are activated. It allows an exprimenter to enable or to disable some modules according to expectations and needs of the older user. For example, if some users are disturbed by intensive light or fast movements, the MIIRE offers the possibility to completely disable modules or to set intensity of the light or the speed of movements, etc.

Finally, an asset of MIIRE is to infer more affective states, encompassing emotional reactions and non-verbal messages.

Preliminary results

Define the robot appearance

Three focus groups were conducted in order to investigate how the elderly perceive a robot's appearance. A total of 15 older adults over the age of 65 (range from 66 to 89 years old) participated in this study. Seven participants suffered from mild cognitive impairment, according to definition criteria of Petersen et al. [START_REF] Petersen | Current concepts in mild cognitive impairment[END_REF] while eight participants were healthy elderly without cognitive impairment. For more detailed descriptions, refer to Wu et al. [START_REF] Wu | Designing robot for the elderly: Appearance issue and beyond[END_REF].

The criteria of attractive robot appearance that we can get from our findings are as follows. First, robots appreciated by the elderly share some features: they are small (in comparison to human-size) and have some traits between human/animal and machine. According to Duffy [START_REF] Duffy | Anthropomorphism and the social robot[END_REF], anthropomorphic or life-like features should be carefully designed with the aim to make the interaction with the robot more intuitive, pleasant, and easy. Second, the elderly seem to prefer a robot which looks like a familiar object in a home setting. This point corresponds to the design guidelines of robotic products proposed by Forlizzi et al. [START_REF] Forlizzi | Assistive robotics and ecology of elders living independently in their homes[END_REF]. They suggest familiar product forms with augmented product functionalities will fit the system and maximize early product adoption. Further, elders seem to emphasize on the creativity in the design of robot appearance.

It is worth noting that many social and ethical issues were also raised during these focus group sessions. Participants expressed reluctance toward some humanoid robots which have inauthentic expressions and offer ersatz interactions and companionships. This invites us to open a dialog engineers in order to foster solutions which take into account the variety of social contexts in which the elderly lives. This invites us also to bring into question the way elderly users are implicitly considered and imagined by designers of assistive devices. Finally, we should consider elderly people not only as recipients of care, but also users whose needs have to be carefully identified, with their active participation.

Perceptions, attitudes and preferences of the elderly toward robots

In this study, we conducted semi-structured in-depth interviews with 15 communitydwelling older people with MCI. Their age ranges from 64 to 87 years old. They are 3 males and 12 females.

A guide consisted of three axis of questions was constructed and developped to provide a framework for interviews. The first axis aimes to explore the problems and difficulties experienced in their daily life and the strategies uesd to compensate for them. Second, we asked the elderly to give their opinions on how technologies could enhance their well-being. Third, we explore the elderly's representations, attitudes and opinions towards robots and a number of robots' functionalities conceived to assist them. In addition, sociodemographic data and information on the use of technology were collected. Our findings indicated that although the elderly with MCI experience discreet difficulties in their daily activities, they could compensate them with self developed strategies.

Most of the elderly interviewed use technological products (mobile phone, computer, GPS...) but they didn't consider that technologies could enhance their quality of life.

As for the representations of robots, most of the elderly perceived robots as automatic/autonomous machine, capable of assisting or replacing peoples for executing repetitive or dangerous tasks. Some mentioned robots as electronic appliances. Most of them didn't think robots useful for them for the moment. For those who found robots might be useful, they thought that they could be beneficial for fragile and handicapped people.

When we presented some functionalities of robots considered useful to assist them in their daily activities, most of the elderly were not enthusiastic about these functionalities. However, their appreciations toward some functionality, such as cognitive stimulation, reminder and object localization were rather positive. They were reluctant toward the idea of the "robot companion". They insisted on human contact and criticized that robots are inauthentic which could only offer ersatz companionship for those who are very fragile and lonely, for those who don't like human contact or for themselves in a future date.

Engagement detection of robot

A pilot experiment was conducted with some young adults to evaluate the relevance of the proposed interactive model described in section 3. The experimental setting requires a user in front of the touch screen and Nabaztag closely located as shown in Figure 4. The cognitive exercices can be started verbally by the user, after greeting the robot and asking for instructions. Then, the robot introduces the exercices by providing instructions. The user is only asked to follow instructions and to do the exercices. The proposed system is continously monitoring user's behaviors and provides feedbacks/helps/encouragements if necessary. Figure 3 reports the social signals exchanged in triadic interaction situation during cognitive stimulation exercises. As we can see, the user looks mostly at the touch screen, but this behavior is completely normal as the user is doing exercises on the screen. Consequently, most of the eye contacts are detected from the camera of the touch screen. Interestingly, when the user asks for information and/or helps from Nabaztag (KeyWord: How to), eye-contact detection with the Nabaztag is increased, which allows the system to efficiently trigger non-verbal behaviors and helps.

Figure 1 .

 1 Figure 1. Triadic situation either with a robot or a psychologist

  , using:  A Dialog system aiming to provide instructions and recognizing commands of the user during cognitive stimulation exercises.  An Eye-contact detection aiming to detect where the user is looking at (the touch screen or the robot) as a signal of engagement/attention.

Figure 2 .

 2 Figure 2. Multi-modal interactive system for on-line coaching

Figure 3 .

 3 Figure 3. The first MIIRE project

Figure 4 .

 4 Figure 4. Interaction Loop while solving a cognitive stimulation exercise

Table 1 :

 1 Several architectures

	Architecture name	Owner	Year	Context
	SAIBA [13] [14]	Lot of authors	2005	Communication of ACA
	GRETA [14]	Pelachaud et al	2002	Expressive ACA
	BDI [15]	Wooldridge et al	1999	Intelligent agents Model
	PAT [15]	Jaques	2002	E-learning
	Baghera [16]	Pesty et al	2003	E-learning
	HRI Framework [17]	Lee et al	2005	Human-Robot Interaction
	MEPAA [18]	Soueina	2003	Personality Model
	Robovie [19]	Kanda et al	2005	Expressive robot
	iGrace [20]	Saint-Aimé et al	2010	Expressive robot

Nabaztag is used in this human-robot interaction experiment because its appearance might be well accepted by the elderly. Refer to section 5.1 for detailed results from our focus groups concerning the design of robot appearance.

Acknowledgements

This work has been supported by the French National Research Agency (ANR) through TECSAN programme (project TECSAN n8ANR-09-TECS-012).


Anne-Claude Tabet

Marion Pilorge

Richard Delorme

Frédérique Amsellem

Jean-Marc Pinard

Marion Leboyer

Alain Verloes

Brigitte Benzacken

Catalina Betancur
email: catalina.betancur@inserm.fr

Autism multiplex family with 16p11.2p12.2 microduplication syndrome in monozygotic twins and distal 16p11.2 deletion in their brother

Keywords: duplication 16p11.2p12.2, deletion 16p11.2, autism, intellectual disability, SH2B1, SNP array

INTRODUCTION

Autism spectrum disorders (ASD) are neurodevelopmental disorders characterized by impairments in social communication and by restricted and stereotyped behaviors and interests, with an onset in the first three years of life and a sex ratio heavily skewed towards males (4:1). ASD are etiologically heterogeneous [START_REF] Betancur | Etiological heterogeneity in autism spectrum disorders: More than 100 genetic and genomic disorders and still counting[END_REF] . About 10%-20% of individuals have an identified genetic etiology, including chromosomal rearrangements, Mendelian disorders (e.g. fragile X syndrome, tuberous sclerosis, Rett syndrome), rare mutations in synaptic genes (e.g. NLGN4X, SHANK3, SHANK2), and copy number variations (CNVs). Microscopically visible chromosomal aberrations are observed in about 5% of individuals with autism [START_REF] Kielinen | Associated medical disorders and disabilities in children with autistic disorder: a population-based study[END_REF] . The most frequent cytogenetic abnormality is maternal duplication 15q11q13;

other recurrent abnormalities include deletions of 2q37, 22q11.2 and 22q13. Some of these recurrent rearrangements arise through non allelic homologous recombination (NAHR) between paired segmental duplications [START_REF] Lupski | Genomic disorders: molecular mechanisms for rearrangements and conveyed phenotypes[END_REF] .

As the short arm of chromosome 16 is rich in intrachromosomal segmental duplications, several microdeletion and microduplication syndromes have been described arising through NAHR. Recurrent ~600 kb deletions and duplications in the 16p11.2 region (29.5-30.1 Mb) are associated with a wide spectrum of neurobehavioral abnormalities, including ASD, intellectual disability (ID), attention deficit hyperactivity disorder (ADHD), seizures and schizophrenia [START_REF] Kumar | Recurrent 16p11.2 microdeletions in autism[END_REF][START_REF] Weiss | Association between microdeletion and microduplication at 16p11.2 and autism[END_REF][START_REF] Shinawi | Recurrent reciprocal 16p11.2 rearrangements associated with global developmental delay, behavioral problems, dysmorphism, epilepsy, and abnormal head size[END_REF][START_REF] Bijlsma | Extending the phenotype of recurrent rearrangements of 16p11.2: deletions in mentally retarded patients without autism and in normal individuals[END_REF][START_REF] Fernandez | Phenotypic spectrum associated with de novo and inherited deletions and duplications at 16p11.2 in individuals ascertained for diagnosis of autism spectrum disorder[END_REF][START_REF] Mccarthy | Microduplications of 16p11.2 are associated with schizophrenia[END_REF] . Dysmorphic features and congenital anomalies are also observed frequently [START_REF] Shinawi | Recurrent reciprocal 16p11.2 rearrangements associated with global developmental delay, behavioral problems, dysmorphism, epilepsy, and abnormal head size[END_REF][START_REF] Bijlsma | Extending the phenotype of recurrent rearrangements of 16p11.2: deletions in mentally retarded patients without autism and in normal individuals[END_REF] . In addition, 16p11.2 deletions and duplications increase the risk of obesity and being underweight, respectively [START_REF] Walters | A new highly penetrant form of obesity due to deletions on chromosome 16p11.2[END_REF][START_REF] Jacquemont | Mirror extreme BMI phenotypes associated with gene dosage at the chromosome 16p11.2 locus[END_REF] . Another microdeletion syndrome in 16p11.2p12.2 involving a ~7-9 Mb region (with a common distal breakpoint at 21.4 Mb and proximal breakpoints varying between 28.5 and 30.1 Mb) was identified recently in six patients with common dysmorphic features and developmental delay without autism [START_REF] Ballif | Discovery of a previously unrecognized microdeletion syndrome of 16p11.2-p12.2[END_REF][START_REF] Battaglia | Further characterization of the new microdeletion syndrome of 16p11.2-p12.2[END_REF][START_REF] Hempel | Microdeletion syndrome 16p11.2-p12.2: clinical and molecular characterization[END_REF] . Three patients carrying a 16p11.2p12.2 duplication had been described earlier [START_REF] Engelen | Duplication of chromosome region (16)(p11.2 -->p12.1) in a mother and daughter with mild mental retardation[END_REF][START_REF] Finelli | FISH characterisation of an identical (16)(p11.2p12.2) tandem duplication in two unrelated patients with autistic behaviour[END_REF] , but as these cases were studied by standard cytogenetic and fluorescence in situ hybridization (FISH) techniques, it is difficult to prove that they are the reciprocal duplication product of the 16p11.2p12.2 microdeletion syndrome. The three patients had ASD and short stature, but only one had ID and dysmorphic features [START_REF] Engelen | Duplication of chromosome region (16)(p11.2 -->p12.1) in a mother and daughter with mild mental retardation[END_REF][START_REF] Finelli | FISH characterisation of an identical (16)(p11.2p12.2) tandem duplication in two unrelated patients with autistic behaviour[END_REF] . A 16p11.2p12.2 duplication identified prenatally was also reported [START_REF] Bourthoumieu | First prenatally diagnosed case of 16p11.2p12.1 duplication[END_REF] . Thus, the phenotype of the 16p11.2p12 duplication is not well defined.

Here, we report a multiplex family with three boys with autism, including two monozygotic twins with severe ID and dysmorphic features carrying a de novo 16p11.2p12.2 duplication encompassing both the region implicated in the 16p11.2p12 microdeletion syndrome and the 16p11.2 region predisposing to ASD. The eldest brother carried a smaller, overlapping paternally-inherited microdeletion in the distal 16p11.2 region recently involved in early onset obesity [START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF] . We present the phenotype, cytogenetic and molecular findings in the three patients and discuss the genetic heterogeneity observed in this multiplex family.

CLINICAL REPORTS Patient 1

Patient 1 is a 21-year-old male, the first child of non-consanguineous parents. The father is Caucasian, the mother is from Mauritius. The father declined neuropsychological evaluation but was described by his wife as being non talkative, introverted and having few social relationships. When examined at 17 years of age, he was 173 cm tall (mean), weighed 49 kg (-2 SD) and had an OFC of 55 cm (-1 SD). He had a triangular face, with broad forehead and prominent orbital ridge (Figure 1B). The eyebrows were thick on the outer part, with a marked upslant; the eyes were deep set, the palpebral fissures were wide, almond shaped and upslanted and he had alternating strabismus. The nose had a prominent and large bridge, a wide, bulbous tip, and anteverted nares. The philtrum was tented, with a wide philtral groove and a wide cupid's bow, a thin vermillion border and everted lower lip.

There was marked overbite and retrognathia despite the presence of a marked chin. The ears were tilted backward. He had a very slender habitus, poor muscle mass in limbs, hypotrophic thenar muscles, cubitus valgus, and mild scoliosis. An asymmetric sternal deformity was noted, with increased Louis angle, bulge of the upper part of the sternum, and depression of the lower part (Figure 1D). He had long fingers and toes, with hypermobile small joints, bilateral single palmar creases and sandal gap.

Acanthosis nigricans was present in the neck. Neurological examination was normal, except for absent knee, bicipital and achillean reflexes, and pes cavus, without pyramidal signs. Further evaluations to rule out a peripheral neuropathy could not be performed because of non-compliance.

High-resolution karyotype showed an interstitial duplication on chromosome 16p. Fragile X testing, uric, lactic and pyruvic acid, plasma organic acids and amino acids were all normal except for isolated increase in cysteine in the latter. Brain MRI at 30 months showed white matter hyperintensities with moderate cortical atrophy and thin corpus callosum. An abdominal ultrasound and electroencephalogram were normal.

Patient 3

The clinical presentation of Patient 3 is very similar to that of his twin brother (Patient 2), but he had no heart defect. His development followed an identical course, with verbal regression at 24 months. His cognitive abilities were also similar (Supplementary Table 1), but his behavior was more problematic, with frequent bouts of self-injurious behavior, clastic crises, and severe sleep disturbances. At 18 years, he was 172 cm tall (mean), weighed 55 kg (-1 SD) and had an OFC of 55 cm (-1 SD). He had dysmorphic features similar to his twin brother (Figure 1C), including the sternum malformation. The results of the karyotype, fragile X, brain MRI and metabolic screening were the same as in his twin brother.

METHODS

Cytogenetic analysis and FISH

High-resolution karyotypes were performed on peripheral blood lymphocytes using RHG and GTG banding. FISH using a whole chromosome painting probe for chromosome 16 (Oncor, Gaithersburg, MD, USA) was performed on metaphase spreads of the twins. Bacterial artificial chromosomes (BACs)

ADELA-1G01 and APADA-2A01 (Integragen) were used to confirm the duplication.

Whole-genome SNP array

Genomic DNA was analyzed with the HumanCNV370-Duo DNA Analysis BeadChip (Illumina, San Diego, CA, USA) containing over 370000 markers, the majority of which are single nucleotide polymorphisms (SNPs). The mean resolution is ~20 kb. SNP copy numbers (log R ratio) and B allele frequencies were assessed using the Illumina BeadStudio software v3.2. CNV analysis was performed using CNV partition v3.1.1 (Illumina) and PennCNV algorithms (www.openbioinformatics.org). Genomic locations are based on NCBI Build 36 (hg18).

Real-time qPCR

Quantitative PCR (qPCR) with the Universal Probe Library (Roche, Indianapolis, USA) was used to confirm and map the CNVs, as described previously [START_REF] Tabet | Molecular characterization of a de novo 6q24.2q25.3 duplication interrupting UTRN in a patient with arthrogryposis[END_REF] . Data analysis was performed with the qBase software (http://medgen.ugent.be/qbase/). 2).

RESULTS

High

The microarray in the eldest brother (Patient 1) showed a 847 kb microdeletion in 16p11.2

(28401454-29249055) (Figures 2A and3). The same deletion was present in the father, whereas the mother had a normal profile (Figure 2A). The other CNVs identified in Patient 1 were reported in the Database of Genomic Variants (http://projects.tcag.ca/variation) (Supplementary Table 2).

The results of the SNP arrays were confirmed by qPCR (Figure 2B). In Patients 2 and 3, the qPCR confirmed the duplication of VWA3A located at 16p12. ID, severe language impairment, short stature, feeding difficulties and recurrent ear infections [START_REF] Ballif | Discovery of a previously unrecognized microdeletion syndrome of 16p11.2-p12.2[END_REF][START_REF] Battaglia | Further characterization of the new microdeletion syndrome of 16p11.2-p12.2[END_REF][START_REF] Hempel | Microdeletion syndrome 16p11.2-p12.2: clinical and molecular characterization[END_REF] . None was reported to have autism or autistic traits, although only one was assessed formally for ASD [START_REF] Battaglia | Further characterization of the new microdeletion syndrome of 16p11.2-p12.2[END_REF] .

These subjects share a common distal breakpoint around 21.4 Mb, but differ in the proximal breakpoint, ranging from 28.5 to 30.1 Mb 12 .

Our patients are the first with a molecularly characterized 16p11.2p12.2 duplication. Apparently reciprocal duplication of the 16p11.2p12.2 region has been reported in three patients [START_REF] Engelen | Duplication of chromosome region (16)(p11.2 -->p12.1) in a mother and daughter with mild mental retardation[END_REF][START_REF] Finelli | FISH characterisation of an identical (16)(p11.2p12.2) tandem duplication in two unrelated patients with autistic behaviour[END_REF] , as well as in a fetus diagnosed prenatally [START_REF] Bourthoumieu | First prenatally diagnosed case of 16p11.2p12.1 duplication[END_REF] ; all were studied by standard cytogenetic analysis and FISH. The clinical features of the twins and previously reported patients are summarized in Supplementary Table 3; the only shared feature is ASD. A woman with autism, anxiety disorder and ADHD transmitted the duplication to her daughter, who had ASD and limited language; neither one had ID or dysmorphic features [START_REF] Engelen | Duplication of chromosome region (16)(p11.2 -->p12.1) in a mother and daughter with mild mental retardation[END_REF][START_REF] Finelli | FISH characterisation of an identical (16)(p11.2p12.2) tandem duplication in two unrelated patients with autistic behaviour[END_REF] . The third case, a male, had a more severe phenotype, with autism, severe ID, epilepsy, and dysmorphic features including hypertelorism, broad nasal bridge and tip, wide mouth, short stature and club feet [START_REF] Finelli | FISH characterisation of an identical (16)(p11.2p12.2) tandem duplication in two unrelated patients with autistic behaviour[END_REF] . In addition, a girl carrying a complex 16p11.2p12.1 rearrangement involving a duplication and triplication had moderate ID, short stature and dysmorphic features with short palpebral fissures, and wide nasal bridge and tip; she was described as friendly and talkative [START_REF] Ballif | Discovery of a previously unrecognized microdeletion syndrome of 16p11.2-p12.2[END_REF] . The twins described here had autism, severe ID and dysmorphic features including deep-set eyes and large nasal bridge and tip. They had recurrent infections during childhood, like the boy described previously [START_REF] Finelli | FISH characterisation of an identical (16)(p11.2p12.2) tandem duplication in two unrelated patients with autistic behaviour[END_REF] .

Based on this limited number of patients, duplications of the 16p11.2p12.2 region appear to be associated with a more variable phenotype compared to deletions, with ASD being the only constant feature identified thus far. Other cases of molecularly defined 16p11.2p12.2 duplications are necessary in order to clarify the genotype-phenotype correlation.

The centromeric end of the 16p11.2p12.2 deletion can overlap the 600-kb region in 16p11.2 (29.5-30.1 Mb) associated with autism and other neurodevelopmental disorders [START_REF] Ballif | Discovery of a previously unrecognized microdeletion syndrome of 16p11.2-p12.2[END_REF] . The duplication in the twins also encompassed this 16p11.2 region. Initially reported in up to 1% of patients with ASD, this CNV was shown to occur in 0.3%-0.4% of ASD subjects in two recent large studies [START_REF] Glessner | Autism genome-wide copy number variation reveals ubiquitin and neuronal genes[END_REF][START_REF] Pinto | Functional impact of global rare copy number variation in autism spectrum disorders[END_REF] , and in 0.6% patients submitted for clinical array-CGH [START_REF] Shinawi | Recurrent reciprocal 16p11.2 rearrangements associated with global developmental delay, behavioral problems, dysmorphism, epilepsy, and abnormal head size[END_REF] . Both the deletion and the duplication are associated with phenotypic heterogeneity, ranging from ASD, ID and/or multiple congenital anomalies, learning and speech problems, to an apparently normal phenotype [START_REF] Shinawi | Recurrent reciprocal 16p11.2 rearrangements associated with global developmental delay, behavioral problems, dysmorphism, epilepsy, and abnormal head size[END_REF][START_REF] Bijlsma | Extending the phenotype of recurrent rearrangements of 16p11.2: deletions in mentally retarded patients without autism and in normal individuals[END_REF][START_REF] Fernandez | Phenotypic spectrum associated with de novo and inherited deletions and duplications at 16p11.2 in individuals ascertained for diagnosis of autism spectrum disorder[END_REF][START_REF] Hanson | Cognitive and behavioral characterization of 16p11.2 deletion syndrome[END_REF] , but the deletion seems to be more penetrant compared to the duplication [START_REF] Fernandez | Phenotypic spectrum associated with de novo and inherited deletions and duplications at 16p11.2 in individuals ascertained for diagnosis of autism spectrum disorder[END_REF] . In addition to cognitive impairment and language deficits, individuals with the 16p11.2 duplication can exhibit motor delay, behavioral problems including ASD, ADHD, aggression or outbursts, schizophrenia, epilepsy, dysmorphic features without a recognizable pattern, and rare congenital anomalies [START_REF] Weiss | Association between microdeletion and microduplication at 16p11.2 and autism[END_REF][START_REF] Shinawi | Recurrent reciprocal 16p11.2 rearrangements associated with global developmental delay, behavioral problems, dysmorphism, epilepsy, and abnormal head size[END_REF][START_REF] Bijlsma | Extending the phenotype of recurrent rearrangements of 16p11.2: deletions in mentally retarded patients without autism and in normal individuals[END_REF][START_REF] Fernandez | Phenotypic spectrum associated with de novo and inherited deletions and duplications at 16p11.2 in individuals ascertained for diagnosis of autism spectrum disorder[END_REF][START_REF] Rosenfeld | Speech delays and behavioral problems are the predominant features in individuals with developmental delays and 16p11.2 microdeletions and microduplications[END_REF] . Patients with microdeletion are at increased risk for obesity [START_REF] Bijlsma | Extending the phenotype of recurrent rearrangements of 16p11.2: deletions in mentally retarded patients without autism and in normal individuals[END_REF][START_REF] Walters | A new highly penetrant form of obesity due to deletions on chromosome 16p11.2[END_REF] , while the duplication is associated with being underweight [START_REF] Jacquemont | Mirror extreme BMI phenotypes associated with gene dosage at the chromosome 16p11.2 locus[END_REF] . In common with other 16p11.2 duplication carriers, the twins had autism, ID, lack of speech, severe behavioral problems with hyperactivity and clastic crises, dysmorphic features, and a tendency to being underweight (-1 to -2 SD). One of the twins had a ventricular septal defect; a microduplication carrier with a similar heart abnormality was reported previously [START_REF] Rosenfeld | Speech delays and behavioral problems are the predominant features in individuals with developmental delays and 16p11.2 microdeletions and microduplications[END_REF] . Other features found in Patients 2 and 3, such as the sternal deformity and the muscular hypotrophy with absent reflexes, suggestive of peripheral neuropathy, have not been described before, either in association with 16p11.2 duplications or the larger 16p11.2p12.2 duplications.

The duplicated segment in the twins encompasses 125 RefSeq genes, including numerous brainexpressed genes with potential roles in neurodevelopment. Increased dosage of one or more genes in the 16p11.2p12.2 or the 16p11.2 regions could contribute to their phenotype, given that ASD, ID and dysmorphic features have been reported in both.

SH2B1-containing distal 16p11.2 deletion

In the eldest brother (Patient 1) the oligonucleotide array revealed a deletion of 847 kb in the 16p11.2 region (28.40-29.25 Mb), inherited from his healthy father. This microdeletion does not overlap the proximal 16p11.2 locus associated with ASD and ID, and encompasses 19 RefSeq genes (Figure 3).

Interestingly, deletions in this region were recently implicated in early onset obesity, with a minimal overlapping region of 220 kb (28.73-28.95 Mb) [START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF] (Figure 3). Patients with longer deletions extending through the 600-kb region associated with ASD/ID exhibited developmental delay in addition to obesity.

The 220-kb deletion was also identified in 2 out of 7366 controls. The minimal deleted interval contains 9 genes (Supplementary Table 4), including SH2B1, which encodes an adaptor protein involved in leptin and insulin signaling. Sh2b1 disruption in mice results in obesity and insulin resistance, a phenotype rescued by neuron-specific expression of SH2B1 [START_REF] Ren | Neuronal SH2B1 is essential for controlling energy and glucose homeostasis[END_REF] . Patient 1 had childhood obesity, while his father showed a tendency to be overweight, supporting the role of the SH2B1-containing region in obesity. However, in contrast to the patients with 16p11.2 deletions reported by Bochukova et al. [START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF] , who rapidly gained weight in the first years of life and became severely obese, our patient first met criteria for obesity at the age of 7 years (BMI 20.6, >97 th centile) and when last examined at 19 years, he was mildly overweight, with a BMI of 26 (84 th centile).

The frequency of the SH2B1-containing 220-kb deletion in patients with severe obesity is 0.51% (7/1362) [START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF] , while the 600-kb 16p11.2 deletion has a frequency of 0.36% in individuals ascertained for obesity (15/4197) [START_REF] Walters | A new highly penetrant form of obesity due to deletions on chromosome 16p11.2[END_REF] . Thus, both CNVs are among the most frequent genetic causes of obesity, after melanocortin-4 receptor (MC4R) point mutations.

The SH2B1-containing 16p11.2 deletion was recently reported in 31 of 23084 patients with developmental disabilities referred for chromosomal microarray analysis [START_REF] Bachmann-Gagescu | Recurrent 200-kb deletions of 16p11.2 that include the SH2B1 gene are associated with developmental delay and obesity[END_REF] . Only deletions not overlapping the ASD/ID proximal 16p11.2 CNV were included. When compared to published control datasets, where a single 200-kb deletion was identified in 7700 subjects (0.013%), deletions in this region appeared to be significantly enriched in the patient population (0.13%). Among 13 patients in which inheritance was determined, five were de novo. Detailed clinical information was only available for six subjects; all had developmental delay of varying severity, two had ASD, three had dysmorphic features and four had BMI ≥95 th centile. Because the enrichment analysis was performed with control data generated on different microarray platforms with varying sensitivity and specificity, these findings need to be replicated. Future studies, comparing the frequency of 16p11.2 deletions that include the SH2B1 gene in large samples ascertained for obesity alone, ID/ASD alone or both phenotypes, will help clarify the impact of this CNV in neurodevelopmental disorders.

Additional reports of eleven individuals with overlapping 16p11.2 distal deletions have been published recently (Figure 3), associated with highly variable phenotypes, including developmental delay (n=5), learning difficulties (n=1), behavioral problems such as ASD (n=2) and ADHD (n=1), unusual facial features (n=6), obesity (n=4), diabetes (n=2), seizures (n=1), congenital anomalies of the kidney and urinary tract (n=2), and Hirschprung disease (n=2) [START_REF] Bijlsma | Extending the phenotype of recurrent rearrangements of 16p11.2: deletions in mentally retarded patients without autism and in normal individuals[END_REF][START_REF] Hanson | Cognitive and behavioral characterization of 16p11.2 deletion syndrome[END_REF][START_REF] Sampson | Evidence for a recurrent microdeletion at chromosome 16p11.2 associated with congenital anomalies of the kidney and urinary tract (CAKUT) and Hirschsprung disease[END_REF][START_REF] Barge-Schaapveld | The atypical 16p11.2 deletion: A not so atypical microdeletion syndrome?[END_REF] . Three of the deletions were de novo, five paternally inherited and three unknown. Two carrier relatives, a father and a sister, had obesity and diabetes, but were otherwise reportedly healthy [START_REF] Barge-Schaapveld | The atypical 16p11.2 deletion: A not so atypical microdeletion syndrome?[END_REF] .

Of the other eight genes contained in the minimal deleted region, three are involved in autosomal recessive disorders (TUFM, ATP2A, CD19), three are involved in immunity (NFATC2IP, LAT, ATXN2L), RABEP2 plays a role in membrane trafficking, and little is known about the function of SPNS1

(Supplementary Table 4). SH2B1 haploinsufficiency, already implicated in central nervous systemmediated obesity [START_REF] Ren | Neuronal SH2B1 is essential for controlling energy and glucose homeostasis[END_REF] , could also participate in neurodevelopmental and other phenotypes. The widely expressed scaffold protein SH2B1 binds to a variety of ligand-activated receptor tyrosine kinases, including the receptors for nerve growth factor (NGF), insulin and insulin-growth factor 1. SH2B1

facilitates glial-cell-line-derived neurotrophic factor (GDNF)-induced neurite outgrowth through RET receptor signaling [START_REF] Zhang | Interaction of SH2-Bbeta with RET is involved in signaling of GDNF-induced neurite outgrowth[END_REF] . Through its implication in the RET-GDNF signaling pathway, SH2B1 could also play a role in the abnormalities of renal morphogenesis and enteric innervation seen in patients with distal 16p11.2 deletions.

26

Potential molecular mechanisms

Most recurrent CNVs described in the short arm of chromosome 16 occur through NAHR [START_REF] Weiss | Association between microdeletion and microduplication at 16p11.2 and autism[END_REF][START_REF] Ballif | Discovery of a previously unrecognized microdeletion syndrome of 16p11.2-p12.2[END_REF][START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF] . A NAHR mechanism is also likely to be involved in the rearrangements observed in the present family, as the breakpoints of the 16p11.2p12.2 duplication and the 16p11.2 microdeletion were found to map within segmental duplications with a high degree of sequence identity (see Figure 3 and Supplementary Note).

Both the duplication and the deletion are from paternal origin. Analysis of genotypes and B allele frequency indicated that Patients 1 and 2 shared the same paternal allele in the telomeric part of the region encompassing the duplication in the twins, but they inherited different paternal alleles in the region overlapping the deletion and the distal part of the duplication (Supplementary Table 5). This suggests that during meiosis in the father, a crossing over between the two homologous chromosomes 16 occurred distal to the deleted region. Thus, Patient 1 inherited part of the normal allele and part of the deleted allele comprising the deleted region.

We hypothesize that the 16p11.2 deletion in the father might have facilitated the appearance of the duplication in his twin children because of the formation during meiotic pairing of a deletion loop in the normal chromosome 16, together with misalignment of segmental duplications in the same orientation sharing >98% sequence identity (Figure 4 and Supplementary Note). After an intrachromosomal crossing-over within the loop, the recombined allele carried a direct duplication of the segment comprised in the loop. Thus, based on the suggested mechanism, the distal 16p11.2 microdeletion implicated in obesity [START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF] could contribute to increased risk of rearrangements of the 16p pericentromeric region in the progeny, some of which can result in ASD or other neurodevelopmental disorders, like in the present family. Further cases are needed to confirm this hypothesis.

Conclusion

This multiplex family highlights the profound genetic heterogeneity underlying autism, including instances of intrafamilial heterogeneity like the one reported here. While the de novo 16p11.2p12.2 duplication is the likely cause of ASD, ID and malformations in the twins, the contribution of the paternally-inherited SH2B1-containing 16p11.2 deletion to the neurological phenotype of the eldest

  -resolution karyotype (800 bands) in the twins (Patients 2 and 3) showed additional material on the short arm of one chromosome 16. The whole chromosome 16 painting probe completely painted both chromosomes 16, showing that the extra material was from chromosome 16. Parental karyotypes were normal, indicating that the interstitial 16p duplication occurred de novo. The karyotype of Patient 1 was also normal. FISH analysis using clones ADELA-1G01 (16p12.1) and APADA-2A01 (16p11.2) in one of the twins (Patient 2) demonstrated a direct tandem duplication and ruled out an inversion in the parents (data not shown). High-resolution SNP array in Patient 2 confirmed the presence of a ~8.95 Mb duplication at 16p11.2p12.2 flanked by segmental duplications; the minimal and maximal estimated sizes of the duplication are 21282605-30235818 and 21273056-30239704 (Figures 2A and 3). Analysis of genotypes and B allele frequency in the duplicated segment showed that the rearrangement arose on the paternal chromosome. No other rare CNVs were observed in Patient 2 (Supplementary Table

  1, and NUPR1, LAT, and ALDOA located at 16p11.2, with normal dosage of the genes flanking the rearranged region. In Patient 1 and the father, both NUPR1 and LAT were deleted. We report a family with three children with autism carrying different rearrangements on an overlapping region of chromosome 16p. The monozygotic twins carried a de novo 8.95 Mb duplication in 16p11.2p12.2 (21.28-30.23 Mb), encompassing the region associated with the novel 16p11.2p12.2 microdeletion syndrome 12 . The six deletion carriers described so far exhibit similar dysmorphic features, inserm-00661857, version 1 -20 Jan 2012

Figure 1 .

 1 Figure 1. Photos of Patients 1-3. A. Patient 1, showing some unusual facial features (deep-set eyes, thick supraorbital ridge with thick eyebrows, wide and prominent nasal bridge, receding chin and everted lower lip). B-C. Patient 2 (left) and 3 (right); note similar dysmorphic features with hypertelorism, upslanting palpebral fissures, broad nasal bridge and tip, everted lower lip and retrognathia with marked chin. D. Sternum deformity in Patient 2 (also present in his twin brother).

Figure 2 .

 2 Figure 2. Microarray and qPCR results. A. SNP array profiles of chromosome 16 showing a 16p11.2 deletion in Patient 1, inherited from his father (both highlighted in red), a de novo 16p11.2p12.1 duplication in Patient 2 (highlighted in blue), and a normal profile in the mother. B. Quantitative PCR probes confirmed the 16p11.2p12.2 duplication in the twins (Patients 2 and 3) and the 16p11.2 deletion in Patient 1 and the father compared with 3 controls. Data represent mean ± SEM.

Figure 3 .

 3 Figure 3. Map of the short arm of chromosome 16 with a summary of abnormalities identified in the 16p11.2-p12.2 region. Schematic representation of chromosome 16p showing the 16p11.2-p12.2 duplication in Patients 2 and 3 (thick blue line) and other overlapping rearrangements reported previously: four duplications (thin blue lines), six deletions (red lines) and one complex rearrangement involving a duplication and a triplication (purple line). The location of five recurrent microdeletion/microduplication syndromes is represented by blue rectangles on the ideogram. A detailed map of ~9 Mb (21177300-30296811, hg 18), comprising the duplication in Patients 2 and 3 (thick blue line) and the deletion in Patient 1 and the father (thick red line) is shown. Additional horizontal thin red lines indicate deletions described previously in individuals with obesity, developmental delay (DD), learning disability (LD), congenital anomalies of the kidney and urinary tract (CAKUT), or Hirschsprung disease (HSCR). The patient marked with an asterisk was too young to evaluate the manifestations reliably. qPCR probes are shown as vertical bars; black bars represent a normal copy number, blue bars indicate a duplication (in Patients 2 and 3) and red bars indicate a deletion (in Patient 1 and the father). Horizontal green lines indicate the location of structural variations identified in non-BAC studies according to the Database of Genomic Variants (DGV). The inset shows a simplified interpretation of the segmental duplications located in the 16p11.2-p12.2 region (UCSC genome browser). See Supplementary Note for a detailed description of these segmental duplications and their possible role in the observed rearrangements in the family described here.

Figure 4 .

 4 Figure 4. Proposed mechanism for the formation of the 16p11.2-p12.2 duplication in the twins. A. Chromosome 16p region comprising the duplication in the twins (blue line) and the 16p11.2 deletion in the father (red line). Blocks of segmental duplications in the same orientation with a high degree of identity overlapping the breakpoint regions are represented by green arrows (see Supplementary note for details). Letters A-E indicate the chromosomal regions represented in the panels below. B. One of the paternal chromosomes (orange) carries a deletion of the segment identified as C. During meiosis, the normal chromosome (blue) forms a deletion loop; the genome architecture of the region facilitates misalignment of directly oriented segmental duplications, followed by nonallelic homologous recombination (NAHR) within the loop. C. Interchromatid mispairing of direct repeats results in duplication (the recombinant product transmitted to the twins) and deletion.

  One of his brothers (among ten sibs) had severe ID with epilepsy; he died at age 42; no further details were available. The maternal personal and family history was negative. Assessment with the Autism Diagnostic Observation Schedule (ADOS) was difficult because of hyperactivity but confirmed the diagnosis of autism. He was unable to complete the Raven's Colored Progressive Matrices test. The scores on the Vineland Adaptive Behavior Scales II indicated severe to profound ID. Sleep difficulties, hyperactivity and impulsivity were treated with melatonin and risperidone.

	pictograms.
	This boy was born at 41 weeks after an uneventful pregnancy; prolonged labor required the use of
	forceps. Birth weight was 3450 g (44	th centile), length 51 cm (65	th centile), and occipitofrontal
	circumference (OFC) 36 cm (54	th centile). Apgar scores were 6 and 10 at 1 and 5 min. Early
	development was normal; he walked at 15 months. He had gastroesophageal reflux and was operated
	for adenoidectomy and orchidopexy during childhood. The parents reported hyperactivity, motor
	stereotypies (flapping) and noise intolerance at age 2 years. Speech was severely delayed, with first
	words at 10 years. At 4 years he was diagnosed with autism based on DSM-IV criteria. He met criteria
	for autism on the Autism Diagnostic Interview-Revised (ADI-R). (Supplementary Table 1 shows the
	scores of the behavioral evaluations in the three siblings.) Obesity appeared in childhood; at 7 years 6
	months, he was 135 cm tall and weighed 37.6 kg (body mass index [BMI] 20.6, >97	th centile). He
	attended a special school where he acquired basic skills in reading and writing. At 16 years, his IQ was
	47.
	When examined at the age of 19, he was 187 cm tall (+2.5 SD), weighed 91.5 kg (+4 SD) and had
	an OFC of 58.5 cm (+1.5 SD). He had mild troncular obesity (BMI 26), and some unusual facial features
	(deep-set eyes, thick supra-orbital ridge with thick eyebrows, wide and prominent nasal bridge, receding
	chin and everted lower lip), which were difficult to assess considering his mixed ethnic background
	(Figure 1A). He had extensive acanthosis nigricans, mainly in the neck, axillae, and groin. Neurological
	examination was normal. His expressive language remained limited to restrictive sentences, mostly
	dyssyntaxic, equivalent to a developmental age of 4 years.
	Karyotype, fragile X testing, telomere analysis by multiplex ligation probe amplification (MLPA) and
	metabolic screening (amino acids, mucopolysaccharides, organic acids, and uric acid) were normal.
	Brain MRI performed at 5 years was normal. At 12 years, sleep polysomnography to explore difficulties
	to fall asleep showed temporo-occipital and temporo-parietal hypersynchrony with rapid rhythmic
	waves, but no significant epileptic event.
	Patient 2
	Patient 2 was born at term from a monochorionic, monoamniotic twin pregnancy. Birth weigh was 2450
	g (4	th centile), length 47 cm (13	th centile) and OFC 33 cm (9	th centile), with Apgar scores of 10 at 1 and
	5 min. A small ventricular septal defect was diagnosed in the neonatal period and closed
	spontaneously. He wore glasses for myopia and strabismus since the first months of life. Recurrent ear,
	nose, and throat infections required adenoidectomy. Early development was considered normal, with
	walking at 15 months and first words before age 2. However, verbal communication and social
	interaction vanished completely in four months after the 26th month. Frequent outbursts and
	stereotypies such as auditory self-stimulation started at that time. At 3 years of age he was diagnosed
	with autism, according to DSM-IV criteria. He also met criteria for autism on the ADI-R. His behavioral
	difficulties made long-term schooling impossible until he was 14 years old, when he entered an inpatient
	clinic. Additional psychiatric evaluations were conducted at 18 years. The patient remained severely
	handicapped; he was not fully toilet-trained and required assistance for most basic needs, but was able
	to feed and dress himself. He was non-verbal, but had acquired basic communication skills using

brother is unclear at present, and further studies in large samples are needed to enable genotype/phenotype correlations.

ACKNOWLEDGEMENTS

We are grateful to the family for participating in this study. This research was supported by Fondation de France, INSERM and by a donation from Mr. Gabriel de Broglie of the Fondation Dehecq-Institut de France. M.P. is supported by a PhD fellowship from the French Ministry of Research.

CONFLICT OF INTEREST

The authors declare no conflict of interest.

Supplementary information is available at the European Journal of Human Genetics website.