Marwa El

Lucile Gamond

Laurence Conty

Julie Grèzes
email: julie.grezes@ens.fr

Selective attention effects on early integration of social signals: same timing, modulated neural sources

Keywords: Attentional influence, EEG, integration, self-relevance, social cues

Humans combine co-emitted social signals to predict other's immediate intentions and prepare an adapted response. However, little is known about whether attending to only one of co-emitted social signals impacts on its combination with other signals. Here, using electroencephalography, we address selective attention effects on early combination of social signals. We manipulated three visual cues: gaze direction, emotional expression, and pointing gesture, while participants performed either emotion or gaze direction judgments. Results showed that a temporal marker of social cues integration emerges 170 ms after the stimulus onset, even if the integration of the three visual cues was not required to perform the task, as only one feature at a time was task-relevant. Yet, in addition to common temporal regions, the relative contribution of specific neural sources of this integration changed as a function of the attended feature: integration during emotion judgments was mainly implemented in classical limbic areas but in the dorsal pathway during gaze direction judgments.

Together, these findings demonstrate that co-emitted social cues are integrated as long as they are relevant to the observer, even when they are irrelevant to the ongoing task.

A C C E P T E D M A N U S C R I P T A C C E P T E D M A N U S C R I P T INTRODUCTION

The quality of our social interactions depends on correctly detecting co-emitted social signals and adapting our behaviour accordingly. Of interest, once merged into a single percept, co-emitted social signals can take on new significance and certain combinations, notably those indicating the presence of threat, become more relevant than others. Typically, angry expressions are perceived as more threatening when associated with a direct gaze than with an averted gaze [START_REF] Sander | Interaction effects of perceived gaze direction and dynamic facial expression: Evidence for appraisal theories of emotion[END_REF];

N' Diaye et al. 2009;[START_REF] Sato | Amygdala integrates emotional expression and gaze direction in response to dynamic facial expressions[END_REF][START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF]. Despite the clear relevance of understanding the spatiotemporal characteristics of the mechanisms underlying the combination of social cues, the question of whether, when and how, directing one's attention towards a specific social signal impacts on its neural integration with other co-emitted social cues remains.

Indeed, the literature exploring the neural sources of gaze and expression integration reports incongruous results [START_REF] Graham | Neurocognitive mechanisms of gaze-expression interactions in face processing and social attention[END_REF]. One possible explanation is that the neural sources underlying social cues integration may be task demand-dependent [START_REF] Graham | Neurocognitive mechanisms of gaze-expression interactions in face processing and social attention[END_REF][START_REF] Dumas | MEG Evidence for Dynamic Amygdala Modulations by Gaze and Facial Emotions[END_REF]. While most of the functional Magnetic Resonance Imagery (fMRI) experiments revealed that the amygdala integrated emotion and gaze when participants were required to attend to the emotional content of the faces or their gender [START_REF] Sato | The amygdala processes the emotional significance of facial expressions: an fMRI investigation using the interaction between expression and face direction[END_REF][START_REF] Sato | Amygdala integrates emotional expression and gaze direction in response to dynamic facial expressions[END_REF][START_REF] Sander | Interaction effects of perceived gaze direction and dynamic facial expression: Evidence for appraisal theories of emotion[END_REF][START_REF] N'diaye | Self-relevance processing in the human amygdala: gaze direction, facial expression, and emotion intensity[END_REF][START_REF] Adams Rb | Amygdala responses to averted vs direct gaze fear vary as a function of presentation speed[END_REF], the premotor cortex was involved in gaze and expression combination when participants were requested to attend to gaze direction [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF].

Electroencephalography (EEG) results also suggest that the temporal marker of such integration is susceptible to task demand influences: it emerges around 170 ms after stimulus onset when participants attend emotional expressions [START_REF] Akechi | The effect of gaze direction on the processing of facial expressions in children with autism spectrum disorder: an ERP study[END_REF], at around 200 ms when participants attend gaze direction [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF], at 240 ms during passive viewing [START_REF] Rigato | The shared signal hypothesis and neural responses to expressions and gaze in infants and adults[END_REF], and later during an oddball task concerning gaze direction [START_REF] Klucharev | Interaction of gaze direction and facial expressions processing: ERP study[END_REF]. Finally, other studies in the literature have reported that when observers orient their attention to only one feature at a time as requested by the task (i.e. judging the emotion or the gaze of emitters), co-emitted facial

A C C E P T E D M A N U S C R I P T

signals are processed independently [START_REF] Bindemann | How do eye gaze and facial expression interact?[END_REF]) by anatomically and functionally segregated neural structures, at least initially [START_REF] Klucharev | Interaction of gaze direction and facial expressions processing: ERP study[END_REF][START_REF] Pourtois | Dissociable roles of the human somatosensory and superior temporal cortices for processing social face signals[END_REF]).

To directly address how selective attention affects the time course and neural bases of early combination of social signals, we implemented an electroencephalography (EEG) experiment (evoked potentials and source reconstruction analysis). To parametrically modulate the self-relevance of perceived social signals, we manipulated three visual cues: emotion, gaze direction and pointing gesture (as in [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF]. Participants performed two tasks: one which requested them to attend only to the gaze direction cue and one which requested them to attend only to the emotional cue. Based on our previous study using the same stimuli [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF], we expected an early combination (rather than parallel processing) of the social cues that clearly portrayed a relevant threat for the observer within the first 200 ms. Yet, how the precise temporality and the sources of this integration were influenced by task-demand was addressed in a hypotheses-free manner.

METHODS

Participants

Eighteen healthy subjects (10 females; mean age, 24.0 ± 0.5 years) participated in the EEG experiment. All participants were right handed, with a normal or corrected vision, and were free of current or past psychiatric or neurological disorders. The subjects gave their written informed consent and were paid for their participation. The study was approved by the local Ethics Committee and was conducted in accordance with the Declaration of Helsinki.

Stimuli

The stimuli used in the present experiment were developed by [START_REF] Conty | Look at me, I'll remember you: the perception of direct gaze enhances memory and right hippocampal activity[END_REF]. They consisted of 192 photographs of 12 actors (six females) seen under 8 conditions: 2 emotions (anger / neutral) * 2 gaze directions (head and eye gaze directed toward the participant or averted to the

A C C E P T E D M A N U S C R I P T
right and left side: direct/averted) * 2 gestures (pointing / no pointing) (Fig. 1a). An "initial position"

photograph depicts each of the actors with a neutral expression, arms by their sides, and an intermediate head and eye direction of 15°. More detailed description of the stimuli can be found in [START_REF] Conty | Look at me, I'll remember you: the perception of direct gaze enhances memory and right hippocampal activity[END_REF].

Procedure

Each trial started with a fixation screen (500 ms) consisting of a central red fixation point and four red angles, displayed on a uniform gray background. The participant was instructed to fixate the central point and to keep his/her attention inside the fixation area at the level of the central point throughout the trial, avoiding eye blinks and saccades. Because dynamic social displays are more ecologically valid [START_REF] Sato | Amygdala integrates emotional expression and gaze direction in response to dynamic facial expressions[END_REF][START_REF] Schilbach | A second-person approach to other minds[END_REF], we created an apparent movement by presenting two photographs, one after the other [START_REF] Conty | When eye creates the contact! ERP evidence for early dissociation between direct and averted gaze motion processing[END_REF][START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF]. The first photograph always displayed the actor in the initial position during a random period of time, ranging from 1200 to 1500 ms. The second one immediately followed and displayed the same actor in one of the eight conditions of interest (Fig. 1b) for 1300 ms. Throughout the trial, the actor's face remained within the fixation area. Then, a response screen was presented for 1000 ms, followed by a black screen of 500 ms preceding the next trial. We delayed the responses to ensure that the participants responded at the end of the observation period.

The experiment was divided in 8 experimental blocks of 96 trials each. Two tasks alternated in separate blocks resulting in 4 blocks for each task. Participants were requested to focus either on the nature of the emotional expression (expression task) or the gaze direction of the actor (direction task). We chose to only include those two tasks based on the literature described in the introduction.

The expression task consisted in indicating the content of the actors' facial expressions during a response screen displaying the words "neutral" and "angry". In the direction task, participants had to indicate the gaze direction during a response screen now displaying the words "me" and "other". The location of the two words (on the right or left parts of the screen) was randomized (Fig. 1b). Varying

A C C E P T E D M A N U S C R I P T

the location of the words allowed preventing the participants from preparing their responses during the observation period. Therefore, our design was not appropriate for detecting any reaction time advantage in making judgments about gaze directions or emotions. During the EEG experiment, the participants perfectly performed the two tasks (Expression task: mean correct response = 96±0.8%

and Direction task: mean correct response = 98±0.4%), which assured that participants kept their attention on the stimuli.

To summarize, there were 16 conditions of interest in our experiment: 2 Tasks (Expression/Direction) * 2 Emotions (Anger/Neutral) * 2 Gaze directions (Direct/Averted) * 2 Gestures (Pointing/No pointing).

Post-test

On the same day, just after the EEG experiment, participants had to perform a behavioural post-test.

They were exposed to all stimuli using the same procedure described above. After each trial, they had to evaluate their felt self-involvement on a scale ranging from 0 to 9 (0, "not involved"; 9, "highly involved"). A repeated-measures ANOVA was performed on these subjective ratings, with emotion (anger/neutral), gaze direction (direct/averted) and gesture (pointing/no pointing) as within-subjects factors.

EEG data acquisition, processing and analyses

The recording of the EEG activity was held at Centre de NeuroImagerie de Recherche (CENIR at Institut du Cerveau et de la Moelle Epinière; ICM) at a sampling rate of 1000 Hz using a BRAINAMP amplifier (Brain Products, BRAINAMP MR PLUS). Participants were equipped with an EEG cap of 63 sintered Ag/AgCl ring electrodes (Easycap). The reference channel was placed on their nose and a forehead ground was used. Impedances were kept under a threshold of 10 kΩ. EEG signal was low pass filtered online at 250 Hz.

The raw EEG data was recalculated to average reference, down-sampled to 500 Hz, and low-pass filtered at 30 Hz (using EEGlab version 11 sccn.ucsd.edu/eeglab). Trials containing blinks and muscles artefacts were manually excluded. We computed the ERPs for each condition between 200 ms before and 800 ms after the onset of the second photograph and corrected using a baseline subtraction (from -200 ms to stimulus onset).

Four classical ERP components were studied: the occipital P100, the temporal N170, the central P200 [START_REF] Ashley | Time course and specificity of event-related potentials to emotional expressions[END_REF][START_REF] Vlamings | Is the early modulation of brain activity by fearful facial expressions primarily mediated by coarse low spatial frequency information?[END_REF]) and a later component: the late positive potential (LPP) [START_REF] Cuthbert | Brain potentials in affective picture processing: covariation with autonomic arousal and affective report[END_REF][START_REF] Schupp | Affective picture processing: the late positive potential is modulated by motivational relevance[END_REF]. For each ERPs of interest, we selected specific electrodes and time range on the peak amplitude observed on mean ERPs computed on all trials. For the P100, average activity on two occipito-parietal electrodes around the peak, between 92 and 116 ms, in each hemisphere was selected (O1/PO7, O2/PO8). For the N170, average activity on three electrodes around the peak, between 162 and 186 ms, in each hemisphere was selected (P7/TP7/TP9, P8/ TP8/TP10). For the P200, average activity on six central electrodes around the peak, between 184 and 208 ms, was selected (C1/Cz/C2/CP1/CPZ/CP2). Finally, according to previous literature on the late positive potential (LPP; [START_REF] Schupp | Affective picture processing: the late positive potential is modulated by motivational relevance[END_REF][START_REF] Liu | Neural substrate of the late positive potential in emotional processing[END_REF], LPP related activity was measured by considering the mean activity averaged on five parietal electrodes (on which the LPP activity was maximal) between 300 and 700 ms (P3, P1, Pz, P2 et P4).

Repeated-measures ANOVA was performed on each ERP measure with task (expression/direction), emotion (anger/neutral), gaze direction (direct/averted), gesture (no pointing/pointing), ─ and for bilateral ERP components: P100, N170 ─ hemisphere (right/left), as within-subjects factors. Secondly, to address selective attention effects on the sources of early social cues integration, we performed the same masked analysis as described above, but for each task separately. We created a conjunction map to identify neural sources that were common to both tasks, and then used this conjunction image as an exclusive mask to identify the sources that were specific to one or the other task.

EEG source localization

Brainstorm

For both analyses, regions representing a surface area superior to 1.5 cm 2 (and thus included more than 15 contiguous vertices), following the self-relevance pattern are reported and labelled on the basis of the correspondence between the Tzourio-Mazoyer brain atlas [START_REF] Tzourio-Mazoyer | Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain[END_REF], the brainstorm generic brain and source model implemented in Brainstorm software. For each region, we reported the number of vertices observed (Table 1). We selected 3 regions: 1) one revealed across tasks, 2) one for the Direction task and 3) one for the Expression task, and plotted for

A C C E P T E D M A N U S C R I P T
comparison the data for one representative vertex of those regions, for each task independently (Fig. 3).

RESULTS

Behavioural post-test

As expected from our previous experiment [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF], stimuli were considered more selfinvolving in the angry condition as compared with the neutral condition (F (1,17) =32.8, p<0.001), in the direct gaze condition as compared with the averted gaze condition (F (1,17) =160.9, p<0.001), and in the pointing condition as compared with the no pointing condition (F (1,17) =69.7, p<0.001). Interestingly, an interaction between emotion, gaze, and gesture was observed (F (1,17) =10.3, p<0.01). Post-hoc comparisons revealed that the condition that was judged as more self-involving as compared to the other conditions (all t (1,17) >3, all p<0.001) was the condition where the 3 relevant cues were coemitted (angry expression, direct gaze and pointing gesture). Moreover, the self-involvement ratings increased with the number of self-directed social cues: it was higher when two self-directed social cues were present (direct gaze and anger or direct gaze and pointing) as compared to one selfdirected cue (direct gaze) (all t (1,17) >5.7, all p<0.001) whereas no difference was observed between the two conditions of two self-directed social cues (t (1,17) =0.09,p=0.92) (Fig. 2a).

Time course of social cues processing

We addressed when emotion, gaze, and gesture were integrated and whether this integration varied with task demand. On P100 activity, we observed main effects of emotion and gesture. Anger (F (1,17) =17.7, p<0.001) and pointing (F (1,17) =17,3, p<0.001) induced greater positive activity than neutral and no-pointing conditions, respectively (see Figure S1). No other main effects or interaction between factors were observed (all F<1, all p>0.2).

A C C E P T E D M A N U S C R I P T

On the temporal N170, main effects of hemisphere, emotion, gaze and gesture were detected. The activity was more important in the right than in the left hemisphere (F (1,17) =6.69, p<0.05). Anger (F (1,17) =128.04, p<0.001), direct gaze (F (1,17) =6.17, p<0.05), and pointing (F (1,17) =24.99, p<0.001) conditions generated greater negative peak amplitudes than, respectively, neutral, averted gaze, and no-pointing conditions. There was an interaction between emotion and gaze (F (1,17) =6.69, p<0.05), an interaction between emotion and gesture (F (1,17) =16.3 p<0.001), and more importantly, an interaction between emotion, gaze, and gesture (F (1,17) =4.59, p<0.05). This interaction was explained by an interaction between gaze and gesture only in the anger conditions (F (1,17) =4.537, p =0.048) but not in the neutral conditions (F (1,17) <0.001, p=0.991), strongly supporting the idea that there was integration between the three co-emitted cues rather than additive effects only. The peak amplitude of the most self-relevant condition (anger, direct gaze and pointing) was greater than all other conditions (all t (1,17) >3.3, all p<0.01) (Fig. 2c). In addition, just as in the post-test ratings, N170 activity increased with the number of self-directed social cues: activity was greater when two self-directed social cues were present (direct gaze and anger or direct gaze and pointing) as compared to one self-directed cue (direct gaze) (t (1,17) =6,p<0.001) whereas no difference was observed between the two conditions of two self-directed social cues (t (1,17) =0.47,p=0.65) (Fig. 2b).

Analysis ran on the central P200 revealed a main effect of emotion and gaze. Anger (F (1,17) =8.9, p<0.01) and averted gaze (F (1,17) =5.1, p<0.05) elicited greater positive activity than, respectively, neutral and direct gaze conditions (see Figure S1). No other main effects or interactions between factors were observed (all F<1, all p>0.2). Although [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF] found a triple interaction on the P200, our results are not surprising as the triple interaction in this study is already observed on the N170. Greater activity for averted gaze as compared to direct gaze on the P200 replicates the findings of [START_REF] Rigato | The shared signal hypothesis and neural responses to expressions and gaze in infants and adults[END_REF].

On the late positive potential (LPP), we observed main effects of task and emotion. Anger (F (1,17) =24, p<0.001) induced greater activity as compared to neutral condition. Expression task (F (1,17) =19.4, p<0.001) induced greater activity as compared to Direction task (see Figure S1). An interaction

A C C E P T E D M A N U S C R I P T

between gaze and task was also observed (F (1,17) =4.7, p<0.05) and was justified by a main effect of gaze only in the Direction task (F (1,17) =6, p<0.05). In this task, direct gaze induced greater activity as compared to averted gaze whereas no such difference was observed in the Expression task (see Figure S1). These results suggest that, at these later temporal stages, the emotional content of the faces may be always processed in both tasks whereas their gaze direction may only be processed in the Direction task. The present main effect of emotion on the late positive potential (LPP) is consistent with previous results that involve the LPP in explicit emotional processing [START_REF] Cuthbert | Brain potentials in affective picture processing: covariation with autonomic arousal and affective report[END_REF] and task switching [START_REF] Rushworth | Components of switching intentional set[END_REF][START_REF] Astle | Fractionating the cognitive control required to bring about a change in task: a dense-sensor event-related potential study[END_REF]).

Crucially, there was no main effect of task before the LPP (all F<1.52, all p>0.23) nor interaction of the task with the other factors (all F<4.2, all p>0.05), suggesting at first view that the integration between gaze, emotion and gesture during the first 200 ms after stimulus onset are independent of selective attention related to the task.

Finally, we tested whether there were between-subjects correlations between the peak amplitudes of the N170 and the behavioral self-involvement ratings (for all the different conditions separately as well as for the differences of interest between conditions). No significant effects emerged (all r<0.4, all p>0.1).

Sources reconstruction

We then explored the brain sources of early integration of emotion, gaze and gesture observed on the N170 (see Fig. 2c) and whether the sources of this integration were influenced by task-demand.

Firstly, we estimated these sources of early social cues integration across tasks. The masked source reconstruction analysis revealed that both structures of the limbic system (such as the amygdala, the hippocampus, the cingulate cortex as well as the ventromedial prefrontal cortex), previously reported in experiments using explicit emotional tasks [START_REF] Sato | The amygdala processes the emotional significance of facial expressions: an fMRI investigation using the interaction between expression and face direction[END_REF][START_REF] Sato | Amygdala integrates emotional expression and gaze direction in response to dynamic facial expressions[END_REF][START_REF] Sander | Interaction effects of perceived gaze direction and dynamic facial expression: Evidence for appraisal theories of emotion[END_REF][START_REF] N'diaye | Self-relevance processing in the human amygdala: gaze direction, facial expression, and emotion intensity[END_REF][START_REF] Adams Rb | Amygdala responses to averted vs direct gaze fear vary as a function of presentation speed[END_REF], and the dorsal pathway including the parietal and premotor

A C C E P T E D M A N U S C R I P T

cortex, reported by [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF] that used a gaze direction task, are involved in the early integration of emotion, gaze and gesture and showed an increase of activity with the increase of selfrelevant social cues (same pattern as observed on the N170).

Secondly, as the literature pointed toward inconsistent neural sources of a) gaze and emotion combination, and b) of the N170 [START_REF] Itier | Source analysis of the N170 to faces and objects[END_REF][START_REF] Eimer | The Face-Sensitive N170 Component of the Event-Related Brain Potential[END_REF], and even though there was no statistical interaction on the N170 activity (evoked potential analysis) between the three manipulated social cues (emotion, gaze and gesture) and the task factor, we tested whether the sources of the N170 varied as a function of the ongoing task. To do so, we performed the abovementioned masked analysis for each task separately. When participants attended to the emotional expressions, the amygdala, the hippocampus and the subgenual cingulate area were involved in the integration of social cues (see Table 1 for a full description of the results) whereas the post-central gyrus and the inferior and superior parietal cortex were detected when participants attended to gaze direction. In addition to these task-specific sources, the fusiform gyrus, middle occipital gyrus, inferior occipital gyrus and middle temporal gyrus which most probably involved the superior temporal sulcus (STS) were involved in both tasks (as revealed by the conjunction analysis).

DISCUSSION

The aim of the present study was to address whether, when and how, directing one's own attention towards a specific social signal emitted by another person impacts on its neural integration with other co-emitted social signals. Our critical finding was that the early integration of social visual cues is indexed by a temporal marker (N170) that is independent of the attended feature, yet being dependent on the relevance of the combination. While the underlying neural sources of the N170 included both limbic and dorsal pathway structures, their relative contribution was modulated as a function of the attended feature: integration during emotion judgments was mainly implemented in classical limbic areas but in the dorsal pathway during gaze direction judgments.

A C C E P T E D M A N U S C R I P T

The amplitude of the N170 and associated neural sources, as well as of the self-involvement ratings, are maximum when the combination of the co-emitted social cues clearly portrayed a threat for the observer, i.e. when the actor expressed anger, looked, and pointed toward the participant, in agreement with previous findings [START_REF] Klucharev | Interaction of gaze direction and facial expressions processing: ERP study[END_REF][START_REF] Akechi | The effect of gaze direction on the processing of facial expressions in children with autism spectrum disorder: an ERP study[END_REF][START_REF] Rigato | The shared signal hypothesis and neural responses to expressions and gaze in infants and adults[END_REF][START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF]. The statistical interactions between, in one hand, the three cues, and on the other hand, gaze and gesture within anger conditions only, suggest that the three co-emitted cues are merged into a single percept rather than triggering additive effects only. These results substantiate that our sensory system is not globally adapted to the statistics of all natural stimuli, but rather evolution has tailored our brain to be specifically optimized to biologically relevant stimuli [START_REF] Machens | Testing the efficiency of sensory coding with optimal stimulus ensembles[END_REF].

The temporal marker of the integration of emotion, gaze and gesture emerges 170 ms after stimulus onset. Importantly, this temporal marker emerges even if the integration of the three visual cues was not required to perform the task, as only one feature at a time was task-relevant. To our knowledge, this is the first study that directly compares the impact of two tasks on the spatiotemporal course of early integration of social cues. This allowed to reveal that early integration appears to be temporally task-related attention independent and thus contradicts the view that orienting attention to only one feature at a time results in processing co-emitted facial signals independently (Pourtois et al. 2004, Klucharev and[START_REF] Klucharev | Interaction of gaze direction and facial expressions processing: ERP study[END_REF][START_REF] Bindemann | How do eye gaze and facial expression interact?[END_REF]. A general attention effect (rather than a selective attention effect) may explain whether this marker emerges within the first 200 ms or later:

indeed, when participants are requested to attend to the stimuli by judging either the emotional expressions (present study, [START_REF] Akechi | The effect of gaze direction on the processing of facial expressions in children with autism spectrum disorder: an ERP study[END_REF] or the gaze direction [START_REF] Conty | Early binding of gaze, gesture, and emotion: neural time course and correlates[END_REF], the temporal marker of social cues integration emerges earlier (between 170 and 200 ms) than when participants observe passively [START_REF] Rigato | The shared signal hypothesis and neural responses to expressions and gaze in infants and adults[END_REF] or perform an oddball task (starting at 190 and lasting till 350 ms [START_REF] Dumas | MEG Evidence for Dynamic Amygdala Modulations by Gaze and Facial Emotions[END_REF]-but see exception by [START_REF] Klucharev | Interaction of gaze direction and facial expressions processing: ERP study[END_REF].

The integration of social visual cues recruited the posterior occipital cortex, the fusiform gyrus (FG)

and the superior temporal sulcus (STS) independently of task-demand. In functional imaging studies,

A C C E P T E D M A N U S C R I P T

those areas have been frequently associated with face perception [START_REF] Kanwisher | The fusiform face area: a module in human extrastriate cortex specialized for face perception[END_REF][START_REF] Puce | Temporal cortex activation in humans viewing eye and mouth movements[END_REF][START_REF] George | Contrast polarity and face recognition in the human fusiform gyrus[END_REF], notably, the FG preferentially processes the invariant aspects of the face while the STS processes changeable aspects such as the gaze and the mouth [START_REF] Haxby | The distributed human neural system for face perception[END_REF][START_REF] Hoffman | Distinct representations of eye gaze and identity in the distributed human neural system for face perception[END_REF]. Moreover, EEG source analyses have either reported the STS [START_REF] Batty | Early processing of the six basic facial emotional expressions[END_REF][START_REF] Henson | Electrophysiological and haemodynamic correlates of face perception, recognition and priming[END_REF][START_REF] Itier | Face, eye and object early processing: what is the face specificity?[END_REF][START_REF] Itier | Source analysis of the N170 to faces and objects[END_REF][START_REF] Watanabe | The spatiotemporal dynamics of the face inversion effect: A magneto-and electro-encephalographic study[END_REF] or the FG [START_REF] Itier | Inversion and contrast polarity reversal affect both encoding and recognition processes of unfamiliar faces: a repetition study using ERPs[END_REF][START_REF] Rossion | Early lateralization and orientation tuning for face, word, and object processing in the visual cortex[END_REF][START_REF] Watanabe | The spatiotemporal dynamics of the face inversion effect: A magneto-and electro-encephalographic study[END_REF] as the main source of the N170.

Here, we further showed that these classical neural sources of the N170 [START_REF] Bötzel | Scalp topography and analysis of intracranial sources of faceevoked potentials[END_REF][START_REF] Rossion | Early lateralization and orientation tuning for face, word, and object processing in the visual cortex[END_REF][START_REF] Conty | When eye creates the contact! ERP evidence for early dissociation between direct and averted gaze motion processing[END_REF]) are involved in the early integration of facial expression with coemitted gaze direction and gesture, independently of the attended social cue.

Several limbic areas as well as dorsal pathway structures were also found to be engaged during the early integration of relevant social cues. Yet, in contrast to the above-mentioned areas, the contribution of these specific neural sources appears to be modulated as a function of the attended feature: predominantly sustained by classical limbic areas during emotion judgments, the integration of social cues involved the dorsal pathway during gaze direction judgments. Although most of the brain regions were revealed in previous fMRI studies on gaze-emotion integration [START_REF] Hadjikhani | Pointing with the eyes: the role of gaze in communicating danger[END_REF][START_REF] N'diaye | Self-relevance processing in the human amygdala: gaze direction, facial expression, and emotion intensity[END_REF][START_REF] Sato | Amygdala integrates emotional expression and gaze direction in response to dynamic facial expressions[END_REF], we further demonstrated, using two tasks, that when participants were requested to attend to the emotional content of the faces, the early integration of emotion, gaze and gesture took mainly place in the temporal pole including amygdala-hippocampal region and the subgenual orbital cortex, brain areas known to be involved in emotional processing [START_REF] Phillips | Neurobiology of emotion perception I: The neural basis of normal emotion perception[END_REF][START_REF] Höistad | Sequence of information processing for emotions through pathways linking temporal and insular cortices with the amygdala[END_REF][START_REF] Fusar-Poli | Functional atlas of emotional faces processing: a voxel-based meta-analysis of 105 functional magnetic resonance imaging studies[END_REF], notably explicit processing [START_REF] Gur | Brain activation during facial emotion processing[END_REF][START_REF] Keightley | An fMRI study investigating cognitive modulation of brain regions associated with emotional processing of visual stimuli[END_REF][START_REF] Habel | Amygdala activation and facial expressions: explicit emotion discrimination versus implicit emotion processing[END_REF]). Nonetheless, these regions were less evidenced in the direction task mainly associated with the postcentral and the parietal cortex involved in gaze perception [START_REF] Puce | Temporal cortex activation in humans viewing eye and mouth movements[END_REF][START_REF] Hoffman | Distinct representations of eye gaze and identity in the distributed human neural system for face perception[END_REF]. Of interest, using fMRI, [START_REF] Zaki | Task-dependent neural bases of perceiving emotionally expressive targets[END_REF] similarly showed the involvement of specific neural networks as a function of the perceiver's goals, i.e. to attend to the gaze direction or to the emotional state of the actor. Here, we further revealed that the contribution of the limbic system to the integration of social cues was enhanced when

A C C E P T E D M A N U S C R I P T

participants explicitly paid attention to emotional cues but decreased when they paid attention to gaze direction while the contribution of the dorsal pathway increased.

The present study thus reveals that the integration of social cues and not simply the perception of one or the other cues recruits a large brain network around 170 ms after stimulus onset, which activity is partly modulated by task-demand. Still, the question remains as to whether and how biologically relevant information flows within the whole network at a more fine-grained time scale.

From macaque monkeys data, one could speculate that the amygdala may initiate the integration and enhance sensory processing of biologically relevant signals thanks to direct projections to the ventral visual pathway including the FG and the STS (Hadj-Bouziane et al. 2012) and premotor cortex in the dorsal pathway [START_REF] Avendano | Evidence for an amygdaloid projection to premotor cortex but not to motor cortex in the monkey[END_REF]). To conclude, by addressing selective attention effects on the spatiotemporal course of social cues integration, we were able to show an influence of taskdemand on the "where" component rather than on the "when" component. Moreover, our results demonstrate that all social cues are encoded even when they are irrelevant to the task, as long as they are relevant to the observer.

Figure 1 .

 1 FIGURE LEGENDS

Figure 2 .

 2 Figure 2. Social cues interaction on the N170 as a function of self-relevance. a) Post-test self-

Figure 3 .

 3 Figure 3. Neural sources of the N170 interaction. Regions that reflect the parametric increase of self-

Figure 1 A

 1 Figure 1

  polhemus of 4 subjects. Computation of the forward model of EEG was done using the OpenMEEG BEM model[START_REF] Kybic | A common formalism for the integral formulations of the forward EEG problem[END_REF][START_REF] Gramfort | OpenMEEG: opensource software for quasistatic bioelectromagnetics[END_REF]. For each subject and each condition, cortical current maps were computed from the ERPs of interest using the weighted minimum norm current estimate (WMNE).First, to estimate the source of the integration of emotion, gaze and gesture observed on the N170, irrespective of the tasks, we averaged the sources data on the time window of the N170 (162-186 ms) for each subject and condition, and across tasks. Then, we applied a statistical mask on every vertex of the 15028 vertices of the model that reflects our parametric increase of self-relevance as a

	was	used	for	source	reconstruction	(Tadel	et	al.	2011	-
	http://neuroimage.usc.edu/brainstorm). A source model that consisted in 15028 current dipoles was
	used to obtain a cortical current source density mapping per subject and condition. Dipole
	orientations were loosely constrained to the cortical mantle of a generic brain model taken from the

standard Montreal Neurological Institute (MNI) template brain provided in Brainstorm. This head model was warped to the standard geometry of the EEG sensor cap taking into account a mean A C C E P T E D M A N U S C R I P T function of the number of self-oriented social cues. A vertex was thus considered as significant if: 1) the activity of the most self-relevant condition (Anger, Direct and Pointing) was statistically different (t-tests) from the activity in all the other conditions; and if 2) the activity in the two conditions with two self-directed cues (Anger, Direct, no Pointing and Neutral, Direct, Pointing) were statically different (t-tests) from the activity in the condition with one self-directed cue (Neutral, Direct, no Pointing).

Table 1 .

 1 Number of vertices for each region reported as integrating emotion, gaze and gesture.

	Task	Hemisphere	Brain regions	Vertices
	E/D	R	Fusiform	21
	E/D	R	Middle occipital	36
	E/D	R	Middle temporal	103
	E/D	R	Inferior occipital	36
	D	L	Postcentral	18
	D	L	Inferior/superior parietal	36
	E	R/L	Subgenual cingulate	34/23
	E	R/L	Rectus	16/35
	E	R/L	Hippocampus	41/38
	E	R/L	Amygdala	23/26
	E	R/L	Caudate	80/64
	E	L	Inferior frontal	23
	E	L	Thalamus	16
	E	L	Superior Temporal Pole	16
	E	L	Calcarine fissure	16

ACKNOWLEDGEMENTS

We wish to warmly thank Florence Bouchet and Laurent Hugueville for their useful technical help. The research was supported by ANR-11-EMCO-00902, ANR-11-0001-02 PSL*, ANR-10-LABX-0087 and by INSERM.

A C C E P T E D M A N U S C R I P T


Florent Mehdi Benallegue

Keywords:

Humanoid Flexibility Deformation Can Be Efficiently Estimated Using Only Inertial Measurement Units and Contact Information

Mehdi Benallegue 1,2 and Florent Lamiraux 1,2 Abstract-Most robots are today controlled as being entirely rigid. But often, as for HRP-2 robot, there are flexible parts, intended for example to absorb impacts. The deformation of this flexibility changes the configuration of the robot, particularly in orientation. Nevertheless, robots have usually inertial sensors (IMUs) to reconstruct their orientation based on gravity and inertial effects. Moreover, humanoids have usually to ensure a firm contact with the ground, which provides reliable information on the surrounding environment. We show in this study, how important it is to take into account these information to improve IMU-based position/orientation reconstruction. We use an extended Kalman filter to rebuild the deformation, making the fusion between IMU and contact information, and without making any assumption on the dynamics of the flexibility. We show how, with this simple setting, we are able to compensate for perturbations and to stabilize the end-effector's position/orientation in the world reference frame.

I. PROBLEM STATEMENT

Many current humanoid robots are controlled as rigid systems, even if there are compliant and flexible parts in it. A good example of such a system is the robot HRP-2. Between the ankle and the sole of the robot, there lies a flexible bush (see Fig 1), designed to absorb foot impacts in order to protect force sensors and leg actuators [START_REF] Kanehira | Design and experiments of advanced leg module (hrp-2l) for humanoid robot (hrp-2) development[END_REF]. However, this flexible part acts also as an angular spring and generates important deviation of the whole body, including the center of mass (CoM), which is not modeled in the rigid system.

Therefore, this flexibility can threaten the balance of the robot, for example if the deformation deviates the CoM enough. Moreover, it also may jeopardize environment-related tasks. For example, in the case of drilling a wall, a robot has to apply forces on the wall. These forces will create a deformation of the compliant material and will deviate the robot's tool from its reference position and/or orientation.

Fig. 1. The foot of HRP-2. Between the ankle joint and the sole of the robot, there is a rubber bush.

The problem of HRP-2 flexibility is currently tackled by a robot stabilizer. The stabilizer drives the deformation of the flexible *This work was partially funded by the French Romeo-2 project Mehdi Benallegue (mehdi@benallegue.com) and Florent Lamiraux (florent@laas.fr) are with: 1 CNRS, LAAS, 7 avenue du colonel Roche, F-31400 Toulouse, France 2 Univ de Toulouse, LAAS, F-31400 Toulouse, France material to produce the desired forces and moments at feet, using a model of elasticity of the flexible material [START_REF] Kajita | Balancing a humanoid robot using backdrive concerned torque control and direct angular momentum feedback[END_REF], [START_REF] Kajita | A running controller of humanoid biped hrp-2lr[END_REF]. At the same time, the upper-body orientation is maintained vertical, in order to minimize unwanted angular momentum and to enable to respect orientation-related upper-body tasks (manipulation, gaze, etc.). The orientation of the upper body is obtained using an inertial measurement unit at the chest of the robot. However, with this stabilizer, in the case of upper-body tasks, even if the torso is maintained upright, there is no guarantee that upper-body limbs are at their reference position, which is usually important when the robot is interacting with environment.

Moreover, the use of controllers based on force/torque sensors raises two main issues. First, these solutions are sensitive to sensors' calibration errors [START_REF] Voyles | The shape from motion approach to rapid and precise force/torque sensor calibration[END_REF], which can even appear during operation of the robot (e.g. due to impacts, under constraints, etc). Second, these approaches can obviously not apply to robots which are not equipped with these expensive force sensors at contact points, such as the future Aldebaran's Romeo robot [START_REF]Aldebaran Robotics. Romeo[END_REF].

By contrast, inertial measurement sensors are cheap, relatively reliable and more robust. In addition, they provide important data on the real kinematics of the robot in the inertial frame. We show in this paper that, if we couple these sensors with contact point positions, we can afford a real-time fine estimation of the flexibility state, without any model of its compliance dynamics. We show also that these measurements can enable a stabilization of the robot's end-effector in the presence of external perturbations.

This study aims at proving the efficiency of inertial sensors for whole body pose estimation, and perturbations detection. In the next section we describe the theoretical guarantees and improvements provided by contact information to IMU measurements. The section III presents the demonstrative example of an implementation of such an observer with minimum prior knowledge. The section IV presents an experimental setting where we use our method for endeffector stabilization and compensation of perturbations. Finally the section V concludes the paper.

II. THEORETICAL GROUNDING

In the case of humanoid locomotion, the contact forces have usually to respect center of pressure and friction cone constraints in order to maintain balance [START_REF] Wieber | On the stability of walking systems[END_REF]. That means that the contacts are firmly fixed to the environment. However, most methods for humanoid-robots attitude-estimation using inertial measurements do not consider contacts information, even for stabilizing the robots on their feet [START_REF] Perrin | Compliant attitude control and stepping strategy for balance recovery with the humanoid coman[END_REF], [START_REF] Kajita | Biped walking stabilization based on linear inverted pendulum tracking[END_REF]. Fixed contact positions provide coupling between the rotations and translations, transforming the inertial measurement unit (IMU) into a much more efficient sensor for reconstructing position/orientation. We show next a simple example of what this coupling provides to a simple pendulum.

A. The inverted pendulum

Let's consider a simple 3D inverted pendulum of 1m length, connected to the ground with a 3 DoF ball joint, and with an inertial measurements unit (IMU), rigidly aligned at the top of the pendulum (see Figure 2). The configuration of the pendulum is the rotation matrix R. This orientation defines the position p of the IMU in the global frame:

p = Rez (1)
where ez = 0 0 1 t is the unit vector along vertical z axis.

If we consider that an unknown external source u provides the control of the pendulum's acceleration, we can write the following state dynamics:

ẋ = ([ω]×R) t ωt 0 t + 0 0 I t u (2)
where x = R t ω t ωt t is the state vector formed by orientation, the angular velocity vector and the angular acceleration 1 , and [•]× is the skew symmetric operator such that

x y z × = 0 -z y z 0 -x -y x 0 Fig. 2.
On the left, 3D inverted pendulum. On the right, 2D inverted pendulum

The IMU at the top is composed of a gyrometer providing the angular rate at local reference frame yg and an accelerometer providing the gravity and the linear acceleration at the local frame ya. Let y = y t g y t a t be the whole measurements vector:

y = R t ω R t (p + g0ez) (3)
with g0 the standard gravity constant. This measurement provides partial information on the configuration, but we show next that depending on whether we consider translations-orientations coupling or not, the observable parts of the vector differ significantly.

B. Without translations-rotations coupling

In the case we do not take into account the coupling, we have to consider that the linear acceleration p is a free input to the system for which we do not have any model. So, let's consider the case of an input acceleration p = -gez, we have then y t a = 0, and the measurements provide only angular velocities, which are insufficient to reconstruct the orientation. Therefore, the configuration of the pendulum itself is not observable with these hypotheses.

Indeed, most today's approaches to reconstruct orientations with a gyrometer/accelerometer sensors without contact information, have to put an erroneous model on the linear acceleration, for example considered as Gaussian white noise for Kalman Filtering [START_REF] Crassidis | Survey of nonlinear attitude estimation methods[END_REF] or as high-frequency signal for complementary filtering [START_REF] Kubelka | Complementary filtering approach to orientation estimation using inertial sensors only[END_REF].

These method lead to ignore translation accelerations, which may carry important and redundant information on the dynamics of the pendulum.

C. With translations/rotations coupling

If we use the rotations/translations coupling provided by Equation (1), we have then

y = R t ω [R t ω]×ez + [R t ω] 2 × ez + g0R t ez (4)
and let's consider the first derivative of the gyrometer measurements

ẏg = R t ω (5)
with these three vectors, yg, ya and ẏg, we can reconstruct R t ez and then the roll and pitch components of the configuration R. The yaw is unfortunately not observable with these sensors when there is only one contact with environment, since the system is invariant with respect to rotations around the z axis.

D. The case of multiple contacts

If the number of contacts between the sensor and the environment is 3 or more, the sensor is fully constrained and cannot move. So let's consider the 2 contacts situation. There remains only one degree of freedom, which is the rotation around the axis (c1c2) passing by the two contact points. The system is equivalent to a 2D pendulum for which the configuration is defined only by one angle θ, and the state becomes x = θ θ θ (see Figure 2). There are two possibilities, (i) the axis (c1c2) is vertical, and in that case, the sensors can observe only angular velocities and accelerations around the axis, or (ii) the contact points are not vertically aligned and, without loss of generality, we can consider them at the same height and that the IMU is at 1 meter from the axis. If it is not the case, we only need to project the dynamics on the plane orthogonal to the axis (c1c2) with minor adaptations to find the same developments.

The measurements vector is three-dimensional: angular velocity around the axis (c1c2), and bi-dimensional accelerations orthogonal to it. All other measurements have constant values, the new measurement vector becomes:

y =   θ θ + g0 sin(θ) θ2 + g0 cos(θ)   (6)
which can straightforwardly reconstruct all the state vector. We see with the pendulum example that rotations/translation coupling, deduced from contact points information, can be taken into account to observe the sensor's attitude and position, without resorting to erroneous modeling of the state dynamics. In the next section, we show how we use this idea to reconstruct the state of the flexible part of the robot.

III. FLEXIBILITY DEFORMATION OBSERVATION

A. Modeling the flexibility HRP-2 is a 30+6 DoF robot controlled as being perfectly rigid. The configuration q is supposed to define perfectly for each limb i the position/orientation in the world, represented by a homogeneous transformation matrix C Mi (C superscript is for "control").

However, there is a flexible part in HRP-2 which is a small compliant material between the sole and the ankle joint of the robot. It can be compressed, bent and twisted according to applied forces/moments. Therefore, when the robot is on its feet, the compliance modifies the configuration of the robot in rotations and translations, even when the contacts are balanced and immobile. We depict the flexibility deformation by a 6 DoF transformation represented by a homogeneous transformation matrix

W MC = W RC W pC 0 0 0 1 (7)
with W RC and W pC are the rotation matrix and translation vector associated to the flexibility deformation.

Any limb i at position/orientation C Mi in the "control" reference lies in fact at position/orientation W Mi = W MC C Mi in the world actual reference frame (see Figure 3). Therefore, W MC is not the matrix associated to a sole-ankle joint, but as a virtual joint between the world and the free-flier root joint of the robot. The choice of this representation enables to remain adapted to any number of supports and to guarantee continuity regardless of changes in contacts. On the left the rigid robot model in the "control" reference frame and the head position at C M . On the right, the flexibility W M C transforms the configuration of the robot and the real position of the head W M = W M C C M (in red) in the world reference frame. We see that W M C is composed of a rotation and a translation.

To simplify notations, we omit the world frame W upper left superscript for next developments. Let's then define the 18 dimensional second order state vector

x = p t C Ω t C ṗt C ω t C pt C ωt C t
where ΩC is the rotation vector representation of RC, such that exp([ΩC]×) = RC, (i.e. ΩC is the angle or rotation and Ω C Ω C is the axis) and ωC is the vector of angular velocity.

Our study aims at showing that the measurements alone are able to provide accurate estimation of the flexibility state. Hence, we do not model the response of the flexibility to external forces. Instead we take the model of constant acceleration MC, which is a classical choice for pose and attitude estimation [START_REF] Barshan | Inertial navigation systems for mobile robots[END_REF], [START_REF] Lin | Sensor data fusion for body state estimation in a hexapod robot with dynamical gaits[END_REF], [START_REF] Gür | Model-based proprioceptive state estimation for spring-mass running[END_REF]. The discretetime model of the state dynamics is then:

x k+1 = f (x k ) + v k ( 8
)
where f is a simple integrator with constant accelerations and v k is Gaussian white noise which is used to model the differences between the real dynamics of the state and the constant-acceleration model.

It is important to note that this dynamical system is chosen only for demonstration purposes, so it is deliberately erroneous and unstable. In fact, for a real use of the proposed observer, we suggest to replace this dynamical model by a model that is closer to the natural dynamics of the studied system, for example by a spring/damper or an inverted pendulum dynamical models. This would increase the precision of the estimation as modeling error is reduced.

B. The sensors system

This system is not stable and relies entirely on the measurements to correct it. We use the stock IMU sensor in HRP-2 which is located at the chest of the robot, and is composed of an accelerometer and a gyrometer. The measurement vector is then classically:

y = yg ya = R t s ωs R t s (ps + g0ez) (9)
where yg and ya are gyrometer and accelerometer measurements, and Rs, ωs and ps are respectively the rotation matrix, the angular velocity vector and the position of the IMU in the world reference frame.

We suppose that we know perfectly the robot's configuration q and its derivatives, we know then the position C Rs, the angular velocity C ωs, the position C ps of the IMU, and their derivatives, in the control reference frame. On the other hand, we have the relationships due to flexibility: Rs = RC C Rs and ps = RC C ps + pC. All that leads to:

yg = C R t s C ωs + C R t s R t C ωC (10)
ya = C R t s R t C (([ ωC]× + [ωC] 2 × )RC C ps + 2[ωC]×RC C ṗs) + C R t s ( C ps + R t C pC) + g0 C R t s R t C ez (11)
But because the measurements are noisy and our dynamics is discretized, we model the sensors dynamics as following

y k = g(x k , q k , qk , qk ) + ws k ( 12
)
Where g is the measurement function summarizing equations ( 10) and ( 11) and ws k is a Gaussian white noise.

C. The contact points

We have seen that the flexibility provides six supplementary degrees of freedom to the robot. However, the size of the flexible bush and the magnitude of the linear forces exerted on it make linear translations of the compliance almost negligible. In other words, we can consider that globally the contact point positions in the world and in the control reference frame are almost identical: MC C pc i ≃ C pc i , where C pc i is the position of the i-th contact in the control reference frame, which is considered as perfectly known for all the contacts. We put then an approximation instead of an equality constraint. This enables to leave some freedom to violate the constraint and to detect for example sideways perturbations during double support. Thus, instead of constraining the contact points to be fixed to environment, we add fake measurements to our dynamical system. These measurement claim that the contacts are fixed in environment MC C pc i k -C pc i k = 0, but we model these measurements as being noisy to allow some freedom. So for each contact ci, the sensors model is:

r ik = MC k C pc i k -C pc i k + w ik ( 13
)
where w ik is a Gaussian white noise. We can gather then the measurements of a n contacts configuration in a 6 + (3 × n) dimensional vector:

z k = h(x k , q k , qk , qk , C pc 1 k , ..., C pc n k ) + w k ( 14
)
where h stacks all the measurements described earlier (IMU + fake measurements) and w k stacks all the measurement noises.

It is worth mentioning that, for the continuous-time system, the measurements described here provide the same observability properties as the inverted pendulum example of the previous section.

In the case of one contact, the orientation is observable except in yaw, which leads to a partial observability of the position pC (constrained to a circle around the vertical line passing by the contact point). In the case of multiple contacts, everything is observable.

D. Extended Kalman Filtering

We use for the estimation of the state vector a classical Extended Kalman Filter (EKF). This observer works in two steps for each time sample: the prediction and the update.

1) Prediction: Let's suppose that at instant k + 1, we have already an estimation of x k which we denote xk . We model the error e k = x k -xk as a random variable following a centered Gaussian distribution for which we suppose that we know the covariance matrix P k . The prediction consists in simulating the modeled dynamics of the system if it were neither noisy nor perturbed. We define:

xk+1 =f (x k ) ( 15
)
where xk+1 is the predicted state. This prediction commits also an error ēk+1 = x k+1 -xk+1 which is due to the transport of e k by f in addition to the process noise v k+1 . We model also the error ēk+1 as a Gaussian random variable and we linearize f to approximate its covariance matrix:

Pk+1 = F k+1 P k F t k+1 + Q k+1 ( 16
)
where Q k+1 is the covariance matrix of v k+1 , and

F k+1 = ∂f ∂x x=x k (17)
This prediction enables to estimate the measurements obtained if the state was equal to the prediction: zk+1 = h(x k+1 , q k+1 , qk+1 , qk+1 , C pc 1 k+1 , . . . , C pc n k+1 ) (18) where zk+1 is the predicted measurement vector.

2) Update: The update consists in using the actual measurements to correct, to some extent, the prediction of the previous step. The actual measurements are in our case the vector z k+1 = y t g k+1 y t ak+1 01×3n

t . We define the measurements innovation:

ez k+1 = z k+1 -zk+1 (19)
Again, this error is modeled as a Gaussian random variable, and the covariance matrix is approximated as follows:

Pz k+1 = H k+1 Pk+1 H t k+1 + R k+1 ( 20
)
where R k+1 is the covariance matrix of w k+1 , and

H k+1 = ∂h ∂x x = xk+1 , q = q k+1 , q = qk+1 , q = qk+1 , C pc 1 = C pc 1 k+1 , . . . , C pc n = C pc n k+1 (21)
This enables to compute the near-optimal gain K k+1 minimizing the quadratic error expectation for the estimation error e k+1 = x k+1 -xk+1 , where

xk+1 = xk+1 + K k+1 ez k+1 (22)
The near-optimal gain K k+1 is obtained as follows:

K k+1 = Pk+1 H t k+1 Pz -1 k+1 ( 23
)
And the corresponding covariance matrix of e k+1 is then

P k+1 = (I -K k+1 H k+1 ) Pk+1 (24)
The size of the measurements vector z k may change if a contact on environment is removed or added, but this does not change the state value nor the extended Kalman filter developments.

We have now an estimator of the flexibility deformation in its 6DoF and its derivatives. This estimation can be directly used for example in order to correct the position of the end effector as we show in the next section.

IV. HAND POSITION COMPENSATION

A. The hand position in the world frame

When a humanoid robot interacts with the environment, the endeffector has usually to follow trajectories in the control reference frame. We have seen that because of flexible parts of the robot, these trajectories may differ in the world reference frame. Moreover, if the robot has to exert forces on the environment in some tasks, such as drilling a wall, the reaction force will create a deformation of the flexible parts and will move the end effector from its reference position.

We propose here to show a direct use of the flexibility observer. We put HRP-2 on its feet, we ask the robot to keep the right hand at a given reference position/orientation, summarized in a homogeneous matrix Mr, and we push the robot to excite flexibility. However, the hand controller takes only references expressed in C. So, the classical solutions consists in working in the control reference frame C, giving a reference C Mr = Mr. Obviously the hand will swing with all the robot, and will not keep its reference position, when the flexibility is deformed. Instead, we propose to ask for another reference of hand position and orientation

C Mr = M -1
C Mr, with the flexibility deformation MC estimated using the extended Kalman filter described in the prevous section. If the flexibility is efficiently reconstructed, the hand will stay at the same position in the world reference frame (see Figure 4).

B. Experimental setting

To achieve this setting, we use the Stack of Tasks framework [START_REF] Mansard | A versatile generalized inverted kinematics implementation for collaborative working humanoid robots: The stack of tasks[END_REF], which is a task-based hierarchical inverse kinematics solver. The tasks were set, in a decreasing priority order, to (i) keep both feet on the ground and the center of mass above the middle of them, in the control reference frame (ii), keep the height C pt and the orientation C Rt of the trunk (waist, chest and head), (iii) keep the right hand at C Mr = W M -1 C Mr and (iv) reproduce with the left hand the motion of the right hand. The last task is just to play the role of counterweight and avoid unstable dynamical effects of hand compensation.

The stack of tasks (SoT) enables also to introduce a feed-forward term which is the desired velocity of the task in the control reference frame. We introduce then also the following desired hand linear and angular velocities

C ṗr =[R t C ωC ]×R t C (pC -pr) -R t C ṗC (25) C ωr = -R t C ωC ( 26
)
where pr is the reference position of the hand in the world reference frame.

To show the performances of the observer, three experiments were conducted:

1) the reference orientation of the trunk C Rt is constant at upright position, and the robot is pushed to excite flexibility. The expected result is that the hand stays at the reference position while the whole robot is displaced. 2) the reference orientation of the trunk C Rt oscillates in time.

The IMU is then excited and provides oscillating measurements. The flexibility is excited as well, due to torques that move the upper-body, but the excitation is of much smaller magnitude than when the robot is pushed. 3) the oscillation of the trunk and the external perturbations are combined. The estimator has to distinguish between the signals due to the oscillation and those due to flexibility deformation.

C. Results

During the first experiment, the external perturbations made the robot oscillate of up to 0.175 rad (about 10 • ). The hand position, being at 1.1 m distance to the contact point, if it was not compensated, would move by about 20 cm. Instead, the hand moves by less than 2.0 cm. During the second experiment, the flexibility was slightly excited and observed by the Kalman filter. However the oscillation of the upper-body created vibration, detected particularly by the gyrometer. which lead to small estimation error, the hand moved by about 1.5 cm. During the third experiment, the combination of oscillation and the perturbation did not degrade the performances and the hand moved still by less than 2.0 cm.

The results are summarized in Fig. 5, and the relevant signals and observations in Fig. 6. The video attachment presents also the performances under several angles, including the ankle of the robot, and shows responses to lateral perturbations. We remind that only the right hand is stabilized and the left hand is just a counterweight.

V. DISCUSSION AND CONCLUSION

We have seen through this paper that the contact with environment enables to take profit from the position-orientation coupling, in order to better distinguish between body accelerations and gravitational component in accelerometer measurements. The separation of these two signals have two benefits: it increases the precision in verticality estimation (pitch and roll), but also it provides information on the acceleration of the attitude and position.

The combination of the inertial measurements and legs kinematics is already a subject or active research, but almost exclusively on multi-legged robots for odometry and localization purposes [START_REF] Gassmann | Localization of walking robots[END_REF], [START_REF] Chitta | Proprioceptive localilzatilon for a quadrupedal robot on known terrain[END_REF], [START_REF] Cobano | Location of legged robots in outdoor environments[END_REF], [START_REF] Lin | Sensor data fusion for body state estimation in a hexapod robot with dynamical gaits[END_REF], [START_REF] Chilian | Multisensor data fusion for robust pose estimation of a six-legged walking robot[END_REF], [START_REF] Reinstein | Dead reckoning in a dynamic quadruped robot: Inertial navigation system aided by a legged odometer[END_REF]. These methods provide reliable information on the position in the world. However, none of them took profit of the accelerations-gravity decoupling, even when attitude reconstruction was an important component of the reconstructed state vector [START_REF] Chilian | Multisensor data fusion for robust pose estimation of a six-legged walking robot[END_REF], [START_REF] Reinstein | Dead reckoning in a dynamic quadruped robot: Inertial navigation system aided by a legged odometer[END_REF].

To our best knowledge, only one method takes this advantage, which is presented by Bloesch et al. [START_REF] Bloesch | State estimation for legged robots -consistent fusion of leg kinematics and IMU[END_REF] for a multi-legged robot. They used the contact information provided by proprioceptive sensors and kinematics model and merged them with IMU signals in an multiplicative/additive extended Kalman filter. They could then constrain the dynamics of their state to respect contact kinematics, and use translations-rotation coupling to improve their estimation. However, their model considers the IMU signals as inputs to the system and not measurements. So their model of the dynamics is an integration of the measurements. This prevents having another model of the state dynamics (e.g. inverted pendulum, spring damper, etc) because this would remove IMU information from models. They also consider slipping contacts as measurements, which may be adapted to walking on uncertain environments, but which leads to the non-observability of the position as aknowledged by the authors. That means that the position may drift for long observation periods. This would lead for example the hand compensation experiment to deviate eventually from the reference positions. This issue could possibly be partially solved by reducing the covariance of the noise model of the measurements, but Kalman filtering is likely to have numerical issues with too certain or perfect measurements [START_REF] Simon | Kalman filtering with state equality constraints[END_REF]. In fact, for humanoid robots in known environments, we can consider the contacts as firmly linked to the ground and this should be exploited to constrain the dynamics of the reconstructed attitude, as presented in our study. Finally, Bloesch et al. model a rigid contact with the ground while our model enables small deviation in translation from the contact point. This deviation may happen in the case of a flexibility in translation, but this is different from slipping contact because in average the contact position is assumed constant, as it is guaranteed by our observer. Some issues may raise and be considered as limitations of our approach. First, if there is more than one flexible part in the robot, one single IMU does not guarantee the observability of the flexibility. In that case, a solution may be to use several IMUs [START_REF] Traversaro | In situ calibration of six-axes force torque sensors using accelerometer measurements[END_REF]. Second, in the case the joint positions are not perfectly known, the estimations error would be proportional to errors in contact positions and to errors in the position/orientation of the IMU and their derivatives in the control frame. In middle, the second experiment (the robot's trunk is oscillating without external perturbations). In bottom, the third experiment (trunk oscillation and external perturbations are combined).

Finally, the main purpose of a flexibility-deformation stateobserver should go beyond simply stabilizing end-effectors. Indeed, estimating efficiently the flexibility deformation means that (i) we know the actual kinematics of the center of mass in the world reference frame and (ii) we have an estimation of the ground reaction forces if we have a model of the force-response to deformations of the flexible part of the robot. Both estimations are precious information on the dynamic balance of the humanoid robot. Therefore, the main objective of this study is to open the way to balancing and stabilizing techniques that would not only run on robots that are not equipped by force sensors, but also provide redundant sensing to stabilization methods relying on force/torque sensors.

Fig. 3 .

 3 Fig.3.On the left the rigid robot model in the "control" reference frame and the head position at C M . On the right, the flexibility W M C transforms the configuration of the robot and the real position of the head W M = W M C C M (in red) in the world reference frame. We see that W M C is composed of a rotation and a translation.

Fig. 4 .

 4 Fig. 4. On the left, the hand compensation in the world reference frame. On the right what happens at the same time in the control reference frame.

Fig. 5 .

 5 Fig. 5. In the top left, a screen capture of the robot's hand during the compensation experiment. In the top right a superimposition of the two pictures of the extreme points of hand stabilization during the excitation of the flexibility. In the bottom left, a superimposition of extreme positions during oscillation. And in the bottom right, a superimposition of extreme positions during combined oscillation and excitation of the flexibility. For each superimposition, the position displacement for the hand is shown.

Fig. 6 .

 6 Fig.6.Signals of accelerometer along x, the gyrometer around y, and flexibility orientation Ω C around y, in the case of the three experiments. In top, the first experiment (the external perturbations on the upright robot). In middle, the second experiment (the robot's trunk is oscillating without external perturbations). In bottom, the third experiment (trunk oscillation and external perturbations are combined).

For simplicity, we keep the matrix representation of the orientation despite the heterogeneous nature of this state vector, in the next section we use rotation vector representation for the actual implementation.


Richard Audoly
email: richard.audoly@polytechnique.edu

Adrien Vogt-Schilb
email: avogtschilb@worldbank.org

Céline Guivarch
email: guivarch@centre-cired.fr

Ruben Bibas

Laura Bonzanigo

Stéphane Hallegatte

Aurélie Méjean

Pathways toward Zero-Carbon Electricity Required for Climate Stabilization

Keywords: climate change mitigation, life cycle assessment, power supply, carbon intensity JEL: Q01, Q4, Q54, Q56

This paper covers three policy-relevant aspects of the carbon content of electricity that are well established among integrated assessment models but underdiscussed in the policy debate. First, climate stabilization at any level from 2 • C to 3 • C requires electricity to be almost carbon-free by the end of the century. As such, the question for policy makers is not whether to decarbonize electricity but when to do it. Second, decarbonization of electricity is still possible and required if some of the key zero-carbon technologies -such as nuclear power or carbon capture and storage -turn out to be unavailable. Third, progressive decarbonization of electricity is part of every country's cost-effective means of contributing to climate stabilization. In addition, this paper provides costeffective pathways of the carbon content of electricity -computed from the results of AMPERE, a recent integrated assessment model comparison study. These pathways may be used to benchmark existing decarbonization targets, such as those set by the European Energy Roadmap or the Clean Power Plan in the United States, or inform new policies in other countries. These pathways can also be used to assess the desirable uptake rates of electrification technologies, such as electric and plug-in hybrid vehicles, electric stoves and heat pumps, or industrial electric furnaces.

Power generation plays an important role in global warming, for at least two reasons. First, it is responsible for a large share of anthropogenic greenhouse gas (GHG) emissions: today's electricity accounts for 12 GtCO 2 /yr, about 28% of total annual greenhouse gas emissions. Reducing the carbon content of electricity would thus decrease significantly global GHG emissions. Second, electricity can be used as a substitute for carbon-intensive fossil fuels in many cases. For instance, today's road transportation and housing sectors account together for about 16% of total emissions; and industrial energy consumption, mainly used to produce heat or motion, accounts for an additional 18% (IEA, 2012;WRI, 2014). Technologies such as electric vehicles, heat pumps, electric furnaces, industrial motors and other electric equipment can in part replace fossil-fuel based counterparts in these sectors, reducing indirectly GHG emissions.

A well-established result from integrated assessment models (IAM) is that both decarbonization of electricity supply and electrification of the energy system play a decisive role in reaching climate stabilization (e.g., [START_REF] Luderer | The economics of decarbonizing the energy system-results and insights from the RECIPE model intercomparison[END_REF][START_REF] Sugiyama | Climate change mitigation and electrification[END_REF][START_REF] Williams | The technology path to deep greenhouse gas emissions cuts by 2050: The pivotal role of electricity[END_REF]IEA, 2014;IPCC, 2014;[START_REF] Krey | Getting from here to there -energy technology transformation pathways in the EMF27 scenarios[END_REF][START_REF] Mccollum | Transport electrification: A key element for energy system transformation and climate stabilization[END_REF][START_REF] Sachs | Pathways to deep decarbonization. Interim 2014 report, Deep decarbonization pathways project (United nations' sustainable development solutions network and Institute for sustainable development and international relations)[END_REF].1 Indeed, stabilizing climate change to any level (e.g. 2, 3 or 4 • C) requires reducing global emissions to nearzero levels [START_REF] Collins | Long-term climate change: projections, commitments and irreversibility[END_REF]IPCC, 2013). Moreover, switching from fossil fuel to low-carbon electricity is one of the only technical options to drastically reduce GHG emissions in energy-intensive sectors such as industry, transportation and buildings.

Despite this consensus and its importance to inform the policy debate, costeffective pathways of the future carbon content of electricity are not available to decision-makers, researchers in other disciplines, or the general public -in particular, none of the above-mentioned studies provides any pathway of the carbon content of electricity under climate stabilization targets. To fill this gap, we compute and report the carbon content of electricity in a set of existing prospective scenarios.

We focus on a set of 55 pathways generated with 10 different integrated assessment models (IAM) for the purpose of a recent IAM comparison study: AM-PERE [START_REF] Riahi | Locked into copenhagen pledges -implications of short-term emission targets for the cost and feasibility of long-term climate goals[END_REF].2 IAMs compute cost-effective pathways of the socioeconomic and energy systems under the constraint set by climate targets. They factor in a wide range of parameters, such as long-term demographic evolution; availability of natural resources; countries' participation to emission-reduction efforts. Technology costs and maximum penetration rates, in particular, are calibrated using a mix of historical uptake rates and assumptions on learning by doing and autonomous technical progress [START_REF] Wilson | Future capacity growth of energy technologies: are scenarios consistent with historical evidence?[END_REF][START_REF] Iyer | Diffusion of low-carbon technologies and the feasibility of long-term climate targets[END_REF]. IAMs are regularly peer-reviewed in comparison exercises [START_REF] Clarke | International climate policy architectures: Overview of the EMF 22 international scenarios[END_REF][START_REF] Van Vuuren | Comparison of top-down and bottom-up estimates of sectoral and regional greenhouse gas emission reduction potentials[END_REF][START_REF] Edenhofer | The economics of low stabilization: model comparison of mitigation strategies and costs[END_REF]Kriegler et al., 2014a,b) and occasionally evaluated against historical data [START_REF] Guivarch | The resilience of the indian economy to rising oil prices as a validation test for a global energy-environment-economy CGE model[END_REF][START_REF] Wilson | Future capacity growth of energy technologies: are scenarios consistent with historical evidence?[END_REF].

Unsurprisingly, the pathways of the carbon content of electricity from AM-PERE confirm the above-mentioned consensus. Specifically, the pathways show that (1) near-zero-carbon electricity is necessary to reach concentrations consistent with global warming anywhere from 2 • C to 3 • C; (2) near-zero-carbon electricity can be achieved even if some of the key low-carbon technologies (nuclear, carbon capture and storage, or renewable power) turn out to be unavailable; and (3) near-zero-carbon electricity can and should occur in every major country or region of the world.

We report pathways at the global level and the country/region level for China, the EU, India and the US, under a variety of assumptions concerning the state of technology and long-term climate targets. These pathways may be useful to planners and policymakers designing climate mitigation strategies. First, they provide a reference on the speed at which decarbonization of the power sector should happen to meet a given climate target in a cost-effective way. They may thus be used to benchmark existing milestones, such as the ones proposed by the European Commission's energy roadmap (EC, 2011) and the Clean Power Plan currently under discussion in the US; or inform new measures in other countries or jurisdictions.

Second, such pathways of the carbon content of electricity are useful to assess the desirability of specific electrification technologies. Indeed, existing studies have focused on the impact of electrification on today's GHG emissions, and concluded that it depends on the carbon intensity of power generation at the specific location where it takes place. For instance, electric vehicles may emit more GHG than conventional vehicles in countries where electricity is produced from coal [START_REF] Sioshansi | Emissions impacts and benefits of plug-in hybrid electric vehicles and vehicle-to-grid services[END_REF]Hawkins et al., 2012a,b;[START_REF] Richardson | Electric vehicles and the electric grid: A review of modeling approaches, impacts, and renewable energy integration[END_REF].3 However, since climate stabilization eventually requires near-zero carbon electricity, the relevant question for policymakers is not whether to electrify, but when to do it. The pathways reported make it possible to investigate this question, using what [START_REF] Hertwich | Integrated life-cycle assessment of electricity-supply scenarios confirms global environmental benefit of low-carbon technologies[END_REF] recently called an integrated life cycle analysis. 4The remainder of the paper is structured as follows. Section 1 reports pathways of the carbon content of electricity in the most technology-optimistic scenarios, where bio-energy combined with carbon capture and storage (CCS) al- lows for producing electricity with negative carbon emissions. Section 2 reports pathways in scenarios where either (i) both nuclear and CCS or (ii) renewable power are constrained. In both cases, the carbon content of electricity still decreases to near-zero levels. Section 3 and Appendix B detail pathways at the country/region level, for China, the EU, India and the US. They illustrate that the decrease to near-zero level can happen in every region of the world under a wide range of assumptions concerning technology availability, and is part of cost-effective strategies toward a range of different climate targets. Section 4 concludes.

Biomass combined with CCS could provide electricty with negative carbon content

During AMPERE, IAMs were run under the constraint that final GHG atmospheric concentration should not exceed 450 ppm CO 2 -eq -Meinshausen et al. ( 2009) estimate such concentration leads to 63-92% probability of remaining below +2 • C by 2100. Figure 1a presents the projected carbon intensity of the global electricity generation in this scenario. It shows that all models project a drastic decrease in carbon intensity by the end of the century.

Most trajectories in this scenario even fall below zero-carbon electricity. Indeed, this scenario assumes the technologies able to generate low-carbon electricity are widely available -these technologies include mainly wind, solar, hydro, biomass, nuclear and carbon capture and storage [START_REF] Smith | Clearing the air -Introduction to the special issue on Carbon Capture and Sequestration[END_REF].

Among them, bio-energy with carbon capture and storage (BECCS), the burning of biomass in power plants associated to the long-term storage of resulting CO 2 , allows to produce electricity with negative net GHG emissions [START_REF] Tavoni | Modeling meets science and technology: an introduction to a special issue on negative emissions[END_REF]Kriegler et al., 2014b). 5 When BECCS is available, the least-cost strategy to achieve global carbon neutrality is to produce negativeemission electricity and offset emissions from sectors of the economy that are more difficult to decarbonize. 6However, stabilizing GHG concentration around 450 ppm would require a fast intergovernmental coordination that may be difficult to achieve in time [START_REF] Guivarch | 2C or not 2C?[END_REF][START_REF] Stocker | The closing door of climate targets[END_REF][START_REF] Luderer | Economic mitigation challenges: how further delay closes the door for achieving climate targets[END_REF]. AMPERE considered the effect of a less stringent concentration target: 550 ppm CO 2 -eq -generally admitted to be consistent with a 3 • C warming, and still 15-51% probability of remaining below 2 • C according to [START_REF] Meinshausen | Greenhouse-gas emission targets for limiting global warming to 2[END_REF]. If low-carbon technologies are still assumed to be widely available, pathways to this easier climate target also entail a decrease of the global carbon intensity to negative levels (Figure 1b).

Near-zero-carbon electricity does not require all carbon-free technologies to be available

A third scenario in AMPERE sets a 550 ppmCO 2 -eq stabilization target and assumes no further deployment of nuclear power after existing plants are decommissioned (for instance for social acceptability reasons) and assuming CCS never reaches market deployment. The decrease in carbon intensity of electricity holds under these assumptions (Figure 2a). The trajectories in this sample exhibit an average of more than 95% reduction in carbon intensity, reaching less than 25 gCO 2 /kWh by 2100, while the most conservative pathway falls below 75 gCO 2 /kWh.

Even in this scenario, decarbonization of power supply is sufficient to justify electrification. For instance, a conservative estimate of electric vehicles' (EV) consumption is 25 kWh/100km from the power plant to the wheel, that is accounting for losses when transmitting electricity over long distances and charging the battery.7 In this case, electric vehicles, or hybrid vehicles running on electricity, would emit between 0 and 19 gCO 2 /km by 2100. For comparison, the European target for new passenger vehicles sold in 2015 is 130 gCO 2 /km on average, and the proposed objective for vehicles sold in 2021 is 95 gCO 2 /km (ICCT, 2014). AMPERE also explored scenarios where CCS and nuclear are widely available, but biomass, wind and photovoltaic power are constrained. Figure 2b reports the pathways of the carbon content of electricity in this case -they can still decrease to near-zero or negative levels by the end of the century.

Every major country or region of the world can and should decarbonize its electricity

Finally, according to AMPERE, the decrease in the carbon content of electricity is feasible in every region of the world. Figure 3 reports the pathways towards carbon free electricity as simulated in AMPERE for China and India, two countries with high initial emissions from power generation, and for the EU and US, where electricity is less carbon-intensive. We consider the less favorable scenario both in terms of the concentration target (550 ppm) and in terms of technology availability (no replacement of nuclear capacities and no CCS allowed) -detailed pathways for these regions with different technology portfolios are displayed in the appendix (Figure B.4,Figure B.6,Figure B.7,and Figure B.5). In every region, the average carbon intensity decreases steadily during the 21st century, and falls below 100 gCO2/kWh in 2100 in every simulation.

These figures suggest that electrification is an effective option to reduce longterm emissions in every region. In other words, the policy-relevant question is not whether to electrify, but when to do it. For instance, indirect emissions from driving an electric vehicle would reach 100 gCO 2 /km between 2030-2060in China, 2010-2030in Europe, 2030-2055in India and 2020-2050 Europe, 2050-2070 in India and 2035-2060 in the US.

Conclusion

The work reported here has several limitations. We only analyzed scenarios where all countries participate in climate policies. In regions that do not participate or delay their participation in climate policies, the reduction in carbon intensity of power generation would not necessarily happen, or would be delayed (Kriegler et al., 2014a). Also, our analysis may overestimate the speed and/or potential of carbon intensity reduction in power generation. Indeed, IAMs may imperfectly represent real-world barriers that may hinder power generation decarbonization. Appendix A further discusses these limitations. Finally, the IAM comparison studied here does not investigate the consequences of simultaneous shortage of all the key low-carbon power generation technologies -CCS, nu-clear, biomass and intermittent renewable.8 In that case, stabilizing the climate would be made much more difficult, and would require a drastic reduction in global energy consumption.

The pathways towards clean electricity reported here should be interpreted cautiously. In particular, they do not entail any normative prescription of the level of efforts that any specific country should affect to climate change mitigation. What they show is a consensus among state-of-the-art integrated assessment models: cost-effective climate stabilization requires near-zero carbon electricity in every major country/region of the world. This very robust finding is a technical one, which disregards any consideration of the burden sharing of emission reductions: independently of who is or should be paying for it, the cheapest strategy to achieve climate stabilization includes decarbonization of the power supply.

The pathways of the carbon content of electricity that we report can be used outside the community of integrated assessment, for instance when assessing the relevance of electric vehicles as a means to reduce greenhouse gas emissions; or to benchmark policies aiming at reducing carbon emissions from power plants. Further work could report pathways for other countries or regions of the world, and extend this approach to sectors other than power supply.

Zabalza Bribián, I., Aranda Usón, A., Scarpellini, S., 2009. Life cycle assessment in buildings: State-of-the-art and simplified LCA methodology as a complement for building certification. Building and Environment 44 (12), 2510-2520.

Appendix A. Methods

Data

We reanalyzed a set of 55 IAM pathways from AMPERE, a study for which CO 2 emissions for electricity are reported separately, thus allowing to recover the projected carbon intensity at each point (2005,2010 and then every 10 years up to 2100).

We retain final energy as our measure of electricity production, that is, the total electric energy consumed by end-users, excluding that used by the power supply sector itself for transformation, transportation and distribution (including these losses would result in lower carbon intensities). As electricityrelated emissions at a given point in time are readily available in our sample, computing cumulative emissions is straightforward.

Limitations

The limitations in our analysis are of two kinds. First, we restricted our study to a subset of IAM trajectories by selecting only results reported in a recent model comparison study. This may introduce a selection bias. Second, IAMs may imperfectly represent real-life barriers to power generation decarbonization. We may therefore overestimate the speed and/or potential of power generation carbon intensity reductions.

Bias

We restricted our study to the results of a recent IAM comparison exercise, AMPERE, because the data are available online.

We are not aware of any published scenario that would reach a low or moderate atmospheric concentration target without featuring a decreasing carbonintensity trajectory similar to the consensus highlighted here. However, reducing the study sample can always introduce biases. In particular, the studies presented here do not explore the case where all renewable energies, carbon capture and storage, nuclear and bio-energies turn out not to be widely available.

Moreover, previous studies have documented the risk of selection bias in IAM reviews, as results are not always reported when targets are unachievable [START_REF] Tavoni | Counting only the hits? the risk of underestimating the costs of stringent climate policy[END_REF]. Our sample of trajectories may be affected by selection bias, given some models might not report their results with some generation technologies unavailable. When availability of some technologies is restricted, such as CCS and nuclear, the number of reported paths decreased, in particular when targeting 450 ppm CO 2 -eq (this effect is mitigated with the looser 550 ppm CO 2 -eq constraint). 9 This hints at the potential difficulty of reaching a stringent climatic target if the development of BECCS is constrained [START_REF] Tavoni | Modeling meets science and technology: an introduction to a special issue on negative emissions[END_REF][START_REF] Bibas | Potential and limitations of bioenergy for low carbon transitions[END_REF][START_REF] Rose | Bioenergy in energy transformation and climate management[END_REF].

Barriers to the decarbonization of power generation

IAMs might imperfectly account for several barriers to the decarbonization of power generation [START_REF] Iyer | Diffusion of low-carbon technologies and the feasibility of long-term climate targets[END_REF]. For instance, the capacity credit -the contribution of a given technology to meeting the demand -tends to be lower for intermittent renewable energy (mainly solar and wind) than for fossil fuel, nuclear, and bio-energy, due to potential mismatches between resource availability and demand peaks [START_REF] Sims | Carbon emission and mitigation cost comparisons between fossil fuel, nuclear and renewable energy resources for electricity generation[END_REF]. Also, some low-carbon technologies may require to build wider distribution and transmission networks to connect remote energy sources or production locations to end-users (renewable energies and nuclear) and transportation infrastructure to carbon sequestration sites (CCS).

Appendix B. Additional figures

9 Such evidence should be taken with caution, as participants were not required to run every scenario (scenarios were ranked as required, recommended, or optional). A smaller number of trajectories does not necessarily reflect selection.

Figure 1 :

 1 Figure 1: Carbon content of electricity at the global scale in two scenarios: (a) stringent GHG concentration target (consistent with 2 • C); (b) less stringent GHG concentration target (consistent with 3 • C). Each thin line corresponds to the pathway simulated by one integrated assessment model (the reported carbon intensity for 2005 and 2010 varies among IAMs because they use different scopes and sources of historical data for calibration). In both cases, bio-energy with carbon capture and storage (BECCS) allows to reduce the carbon content of electricity to below-zero levels by the end of the century.

  (a) 550 ppm -No nuclear, no CCS (b) 550 ppm -Low renewable

Figure 2 :

 2 Figure 2: Decarbonization of global electricity in two 550 ppm scenarios (consistent with 3 • C): (a) without new nuclear or carbon capture; (b) with low potential for renewable power. In both cases, the carbon content of electricity is reduced to nearzero levels by the end of the century.

  in the US; and would drop below 50 gCO 2 /km between2045 -2065 in China, 2045 -2060 in in

Figure 3 :

 3 Figure 3: Carbon intensity in China, Europe, India and the US in AMPERE's 550 ppm (consistent with +3 • C), technology-pessimistic (no nuclear, no CCS) scenario.

  Figure B.4: Carbon content of electricity in China.

  Figure B.5: Carbon content of electricity in the EU.

  Figure B.6: Carbon content of electricity in India.

  Figure B.7: Carbon content of electricity in the US.

  Figure B.8: Carbon intensity of electricity at the global level.

These and other studies offer in-depth analysis of the interlinked dynamics of electrification and decarbonization of electricity, and cover topics out of the scope of this paper, such as economic implications and the role of different technologies to produce zero-carbon electricity.

 2 We chose this study as it is freely available online(IIASA, 2014), other recent studies such as EMF27(Kriegler et al., 2014b) are of similar scope, use a broader variety of models and assumptions, and reach qualitatively and quantitatively similar results, but are unfortunately not publicly available online at the moment.

Such studies have been interpreted as showing that electrification is to be avoided (e.g., BBC, 2012). Similar results have been reported by[START_REF] Thomson | Control of greenhouse gas emissions from electric arc furnace steelmaking: evaluation methodology with case studies[END_REF] on industrial electric furnaces, and[START_REF] Gustavsson | Life cycle primary energy analysis of residential buildings[END_REF] Joelsson (2010), Zabalza Bribián et al. (2009) and[START_REF] Ramesh | Life cycle energy analysis of buildings: An overview[END_REF] on buildings.

As mentioned before, IAMs are sometimes used to assess optimal electrification of the economy. The pathways provided here can nonetheless be used by scholars outside the IAM community, for instance to evaluate the impact on GHG emissions of a technology or industrial process too specific to be explicitly represented in an IAM.

(a) 450 ppm -all carbon-free technologies (b) 550 ppm -all carbon-free technologies

"Plants" extract carbon dioxide from the atmosphere as they grow.

However, the large-scale feasibility and desirability of BECCs is controversial, given their potential impact on land use, food production, freshwater availability, and the uncertain availability of suitable geological storage sites -see[START_REF] Guivarch | 2C or not 2C?[END_REF] for an overview.

For instance, today's most sold electric car, the Nissan Leaf is rated between 18 and 21kWh/100km (battery to the wheel) by the US Environmental Protection Agency; and 20% is an accepted upper bound for transmission, distribution, and recharging losses.

During AMPERE, IAMs explored the consequences of limited availability of renewable, limited availability of nuclear, and limited availability of CCS separately (as reported in Appendix B); in all these cases, the carbon intensity still decreases drastically in every region, sometimes to below-zero levels.