{'fraction_non_alphanumeric': 0.037582298974635726, 'fraction_numerical': 0.02316243928764166, 'mean_word_length': 5.069173326346129, 'pattern_counts': {'":': 0, '<': 23, '<?xml version=': 0, '>': 1, 'https://': 1, 'lorem ipsum': 0, 'www.': 1, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
I See Your Effort: Force-Related BOLD Effects in an Extended Action Execution–Observation Network Involving the Cerebellum

Abstract Action observation (AO) is crucial for motor planning, imitation learning, and social interaction, but it is not clear whether and how an action execution–observation network (AEON) processes the effort of others engaged in performing actions. In this functional magnetic resonance imaging (fMRI) study, we used a “squeeze ball” task involving different grip forces to investigate whether AEON activation showed similar patterns when executing the task or observing others performing it. Both in action execution, AE (subjects performed the visuomotor task) and action observation, AO (subjects watched a video of the task being performed by someone else), the fMRI signal was detected in cerebral and cerebellar regions. These responses showed various relationships with force mapping onto specific areas of the sensorimotor and cognitive systems. Conjunction analysis of AE and AO was repeated for the “0th” order and linear and nonlinear responses, and revealed multiple AEON nodes remapping the detection of actions, and also effort, of another person onto the observer’s own cerebrocerebellar system. This result implies that the AEON exploits the cerebellum, which is known to process sensorimotor predictions and simulations, performing an internal assessment of forces and integrating information into high-level schemes, providing a crucial substrate for action imitation.


Introduction
Social behavior is based on understanding the actions of others and predicting appropriate reactions and subsequent interactions. In this context, perceiving the force applied to objects by others is crucial for understanding their intentions, for predicting the success of self-generated actions, and for dynamic movement control in interactions. However, there is still debate over the question of whether, when observing someone else performing an action, we mirror the actual movement dynamics or simply its goals (Calvo-Merino et al. 2006;Filimon et al. 2007; Thompson et al. 2007;Hamilton and Grafton 2008;Caspers et al. 2010;Cavallo et al. 2015;Koul et al. 2018). Understanding, through observation, the force involved in movements performed by others can prime the force imparted during subsequent action executions (AE) (Salama et al. 2011). The achievement of a better understanding of how force is represented in observation could facilitate and improve the clinical application of action observation (AO) in neurorehabilitation (Porro et al. 2007;Garrison et al. 2013;Buccino 2014). Although AE and observation have been studied using several techniques (Munzert et al. 2009;Sevdalis and Keller 2011;Vanderwert et al. 2013;Naish et al. 2014;Valchev et al. 2015), the neuronal processes involved in mirroring the motor effort of others have still not been fully explored.
The most renowned imitation learning hypothesis claims that "mirror neurons" are activated by observation of actions performed by others (Rizzolatti and Craighero 2004) and that the brain simulates the observed action by using the motor system as a forward model (Buccino et al. 2001;Miall 2003;Kilner et al. 2007;Ito 2008;Turella et al. 2009), recruiting hierarchically organized brain circuits (Kilner 2011;D'Angelo and Gandini Wheeler-Kingshott 2017). On a broader perspective, the brain has been proposed to include a "mirroring system" which can understand the intentions of others from observing movements ("body" reading) and a "mentalizing system" which can infer the intentions of others reconstructing hypothetical events ("mind" reading) (Van Overwalle and Baetens 2009;Van Overwalle, D'aes et al. 2015). In this context, even though magnetic resonance imaging (MRI) does not allow neuronal populations to be studied directly, functional MRI (fMRI), thanks to the blood-oxygenation-level-dependent (BOLD) effect (Kim and Ogawa 2012), can be used to study neuronal activation during both execution and observation of actions. fMRI studies (Buccino et al. 2001;Caspers et al. 2010;Caligiore et al. 2013;McGregor and Gribble 2015) support the notion that, during observation of a complex motor task, the AE network (AEN) and the AO network (AON) combine to form an action executionobservation network (AEON), which provides the neural infrastructure for imitation learning. Although the "core AEON" structures are the premotor cortex and a limited number of parietal and temporal cortical areas (Grèzes and Decety 2001), it is now clear that the AEON also comprises the supplementary motor area and the inferior frontal gyrus, as well as large sections of the somatosensory and occipitotemporal cortices (Gatti et al. 2017). Furthermore, the cerebellum and basal ganglia have also been suggested to play a role in an extended circuit underlying action understanding (Caligiore et al. 2013), to the point that the cerebellum is now considered to play a role as an adaptive predictor in AO (Sokolov et al. 2017). This idea derives from the general theory of cerebellar functioning, wherein the cerebellum is seen as a forward controller in behavioral schemes that concern the interaction of the body with the external world, instructing the cerebral cortex in a predictive manner (Cotterill 2001;Llinás 2009;Diedrichsen et al. 2010;Shadmehr and Mussa-Ivaldi 2012;Callan et al. 2013). Moreover, a growing body of evidence from both lesion and fMRI studies (Gazzola and Keysers 2009;Molenberghs et al. 2012;Christensen et al. 2014;Van Overwalle et al. 2014;Caligiore et al. 2017) suggests that the cerebellum plays a crucial role in action-perception coupling, coordinating the application of an appropriate force and its timing to generate movement, and thus operating in a forward mode (D'Angelo and Casali 2012; Avanzino et al. 2015;D'Angelo and Gandini Wheeler-Kingshott 2017). On these bases, it can be hypothesized that predicting how to move by observation entails processing of force and involves an extended AEON that includes the cerebellum together with a complex set of cortical areas.
In the present study, aiming to identify the network involved in force perception, we exploited a paradigm that recently showed how a complex set of linear and nonlinear BOLD responses are elicited in several brain regions, including the cerebellum, when varying the force applied to an object Alahmadi et al. 2017). We used this grip-force (GF) squeeze ball paradigm to assess whether: 1) the AON presents both linear and nonlinear BOLD-GF associations during observation of the squeeze ball task; 2) the AEN and the AON share a common neural substrate, corresponding to the extended AEON; and 3) regions identified as part of the AEON exhibit linear and nonlinear BOLD-GF associations. The results of this work indeed support the existence of force-related BOLD effects not only in AE but also in the extended AEON, which includes the cerebellum.

Subjects
A total of 14 right-handed healthy volunteers (9 females) were initially recruited for this study. However, 2 participants were excluded from further analysis: one who failed to follow the task instructions and another who presented head motion (translation in the z direction) >2 mm. The final sample thus comprised 12 subjects (7 females; mean age 26 ± 3.5 years). The handedness of each subject was evaluated using the Edinburgh handedness scaling questionnaire (Oldfield 1971); the mean laterality index was 82 (±16). All participants had normal or corrected-to-normal vision. No subject had a history of neurological or psychiatric disease. All the participants received a detailed explanation of the experimental procedures before participating in the experiment. The local research and ethics committee approved the study and all participants gave their written informed consent.

MRI Scanner and Scanning Sequences
A 3 T Philips Achieva MR scanner (Philips Healthcare, Best, The Netherlands) with a 32-channel head coil was used to perform a 3D T1-weighted anatomical scan and 3 T2*-weighted echoplanner imaging (EPI) fMRI scans. The 3D T1-weighted sequence acquisition parameters were as follows: 3D inversion-recovery prepared gradient-echo (fast field echo) sequence with inversion time (TI) 824 ms, echo time (TE)/repetition time (TR) 3.1/6.9 ms, flip angle 8°and voxel size 1 mm isotropic. The fMRI acquisition parameters were: TR/TE 2.5/35 ms, 2.7 mm thick slices with interslice gap of 0.3 mm positioned axial-oblique to include the cerebellum, 3 × 3 mm 2 in-plane resolution, field of view 192 × 192 mm 2 , SENSE factor 2, flip angle 90°and 200 repeated volumes.

Experimental Design
All the participants completed 3 randomized event-related fMRI sessions (Fig. 1): AE, AO, and AO with visual cue (AOvc). In all cases, all the stimuli were projected onto the same white screen, which was kept in the same position throughout; shortsighted participants used nonmagnetic visual aid goggles. The 3 experimental sessions are described below.

Squeeze Ball Event-Related Paradigm
This paradigm, previously described elsewhere Alahmadi et al. 2017), consisted of a visuomotor event-related power grip task, in which the order and timing of trials and rest periods was optimized to introduce temporal jittering and randomization of the applied GF strength (see below). The task was performed using an MR-compatible sphygmomanometer inflation bulb ("squeeze ball") connected to a computer suite (located outside the scanner room) running the fMRI paradigm presentation. Compression of the ball resulted in an air pressure measurement proportional to the force exerted, which was recorded at a sampling rate of 20 Hz. In all, 75 active trials were performed, divided equally into sets of 15 corresponding, respectively, to GF levels representing 20%, 30%, 40%, 50%, and 60% of the subject's maximum voluntary contraction (MVC). MVC had previously been measured in each subject using the same force device (i.e., by asking the subject to continuously squeeze the power ball) and this value was used to set the GF target for each trial.
Trials were performed in a counterbalanced and randomized order as obtained using the OptSeq optimization software (https://surfer.nmr.mgh.harvard.edu/optseq/). The rest time between squeezing trials-this lasted between a minimum of 2 s and a maximum of 12 s, and was cued by a black crosshair located at the center of the screen-was also randomized to introduce temporal jittering between the task and data acquisition. Rest time accounted for 55% of the whole fMRI session (500 s). The visual cue used in the trials was a black static horizontal bar (presented for 3 s), which indicated the target GF level to reach. This cue was projected onto an MR-compatible white screen and shown together with an interactive colored bar, indicating the actual force level reached and thus providing real-time feedback to the subject about his/her own performance. The GF task was performed with the right (dominant) hand during the AE session.
A female actor was also filmed while performing the task in the control room of the scanner suite. The resulting video showed her whole right hand and forearm, filmed against a plain colored background, with the palm facing up. While recording the task, the computer also recorded the visual feedback she received (i.e., the visual cue bar), which was used to create a further video (in which the cue bar was superimposed on the forearm and hand) to be used in the AOvc session. Premiere Pro CS5 (Adobe System Software, CA, USA) was used for video editing.

AO (AO and AOvc) Behavioral Sessions
Before and after the fMRI sessions, subjects underwent behavioral sessions during which they were asked to watch the AO and AOvc videos (the order of presentation of the videos was randomized among subjects) and to verbally report their own perception of the GF, that is, 20%, 30%, 40%, 50%, or 60% of the MVC of the actor's hand shown squeezing the ball in the video (perceived GF). These sessions served to test their recognition of the GFs observed, to saturate any learning effect before the actual fMRI experiment, and to test possible differences in learning effects between the pre-and post-MRI behavioral sessions. The purpose of running 2 AO behavioral sessions, AO and AOvc, was to assess whether GFs can be appreciated from subtle (and natural) cues alone-as in the AO condition (e.g., changes in the color of the hand with increasing effort and accompanying tendon contraction)-or whether subjects also need to see symbolic visual feedback, as in the AOvc condition. Performance accuracy was assessed for each of the 5 GF levels by calculating the number of correct answers and the mean difference between the perceived GF (pGF) and the GF actually applied by the actor during the video recording (aGF).

AE Training Session
After the AO behavioral sessions, just before the fMRI one, subjects were trained using a 2-min paradigm having a design shown below the arrow. During fMRI, every session lasted 8:33 min and the trials were administered in a counterbalanced and randomized order. The active trials (each lasting 3 s) were repeated 75 times and were divided equally between the 5 grip forces. A rest time of 2-12 s was allowed between active trials. similar to the above-described event-related one, with GF levels ranging from 10% to 70% of their MVC. The training session involved practising the task outside the scanner bore.

AE Session
Subjects performed the AE task following the visual instructions described above. Their feedback was recorded at a sampling rate of 20 Hz during the task. The data collected served to include subject-specific performance in the statistical analysis.

AO Session
Subjects observed the video showing the right hand of the actor performing the squeeze ball task. They were asked to keep their gaze at the center of the projection screen indicated by a cross during rest periods, to relax, not to touch the squeeze ball, and to think about nothing throughout this fMRI recording session (as opposed to trying to guess the force or the next action).

AOvc Session
The subjects received the same instructions as in the AO session. The only difference, compared with the AO condition, concerned the stimuli: the video again showed the actor's right hand performing the squeeze ball task, but this time the image was overlaid with a translucent representation of the visual feedback that the actor had received during the recording of the video (thus an indication of her performance). This session was originally included as part of the behavioral study as it was unclear whether force perception demands some kind of visual feedback on the performance, such as that provided by the real-time bar (symbolic guided action observation). However, since the AO condition alone was found to be sufficient to disclose perception of force-related effects, the AOvc data were not considered further for the purposes of this study.

Behavioral Data Analysis
The group mean accuracy of the subjects' perceptions (pGF) was calculated overall by measuring all correct responses as a percentage of all perceived forces (at 20%, 30%, 40%, 50%, and 60% of MVC of the hand squeezing the ball in the video), and also separately for each of the following sessions: AO before MRI, AOvc before MRI, AO after MRI, and AOvc after MRI. A number of statistical tests were performed. First, we used paired sample t-tests to assess possible significant differences between ratings in the AO versus the AOvc sessions; that is, considering the mean accuracy of pGF in the 2 conditions (considering "AO before MRI" vs. "AOvc before MRI" and then "AO after MRI" vs. "AOvc after MRI"). Second, a repeated measures ANOVA with Bonferroni correction was implemented to investigate learning effects, that is, testing for different performances within the AO and the AOvc sessions ("AO before MRI" vs. "AO after MRI" and then "AOvc before MRI" vs. "AOvc after MRI"). A statistical threshold of P < 0.001 was considered significant. Finally, to characterize the challenging nature of the AO task, we assessed the correlation between the actor's actual performance (i.e., the GF applied by the actor performing the task and recorded while filming) and the subjects' perceptions of that GF (i.e., the pGF, as reported by each subject during the "AO before MRI" behavioral session), using the correlation coefficient (r) and the significance level (P-value). The statistical analysis was performed using the Statistical Package for the Social Sciences (SPSS) software (version 21.0).

fMRI Data Analysis
Whole Brain Image analysis was performed with SPM12 (www.fil.ion.ucl.ac. uk/spm), implemented in Matlab15b (Mathworks, Sheborn, MA), using conventional preprocessing steps: slice timing, realignment, coregistration, estimation of (nonlinear spatial) normalization parameters between the 3D T1-weighted volume and the standard SPM12 template, application of the normalization parameters to the fMRI EPI volumes, and smoothing with an 8 mm isotropic full-width half maximum (FWHM) Gaussian kernel. The GF trials were modeled as delta functions ) with parametric modulation according to GF. A general linear model (GLM) including polynomial expansions up to the fourth order was applied following the procedures described by Alahmadi et al. . As discussed in previous work, the polynomial expansion allows nonlinear relationships to be characterized in an unbiased way, by modeling a mixture of linear and nonlinear responses in a parsimonious fashion. Interpretation of the nonlinear order lends itself to hierarchical testing (e.g., second-order effects are interesting only after removing first-order effects) (Büchel et al. 1998) and neurophysiological studies have reported different response profiles that have distinct nonlinear forms (Evarts 1968;Smith et al. 1975;Cheney and Fetz 1980;Riehle et al. 1994). Moreover, polynomial expansions are the most common form of expansion (in the absence of boundary conditions) when estimating neurometric functions from imaging data (Ward and Frackowiak 2003;Kuhtz-Buschbeck et al. 2008).
In our setting, the 0th order represents the main effect of hand gripping (executed or observed) compared with the rest condition, irrespective of the level of GF applied. The first order represents any linear dependency on GF level (executed or observed), while nonlinear orders represent more complicated neurometric functions such as U-shaped (second order), sigmoid (third order) and quadratic (fourth order) functions. The parametric modulation of the stick functions-encoding grip trials-with the polynomial expansion of GF produces stimulus functions that can then be convolved with a canonical haemodynamic response function for subsequent standard GLM analyses .
At the first level of analysis (within subject), the realignment parameters were included in the GLM as regressors of no interest (Friston et al. 1996) and t statistics were used to test for the effects of each polynomial coefficient. The associated contrast images of each of the 5 polynomial coefficients were then entered into a second (between-subject) level analysis and tested with one-sample t-tests, following standard procedures. The same analysis pipeline was followed for the AE and AO sessions. In the AO session, the GF levels corresponded to those recorded from the actor's performance. A voxel-wise threshold of P u < 0.001 (minimum extent 5 voxels, P u = P uncorrected for multiple comparisons) was used to define clusters. A threshold of P < 0.05 was applied to the spatial extent of clusters that survived multiple comparisons corrections. The anatomical designations of significant clusters were determined using the SPM Anatomy Toolbox (Version 2.2b). The same criteria were used for AE and AO sessions.

SUIT
The fMRI analysis pipeline, optimized for whole-brain analysis, can give suboptimal results in the cerebellum (Diedrichsen 2006). Therefore, to focus on the cerebellum, we used SUIT (spatially unbiased infratentorial template), a high-resolution atlas template of the human cerebellum and brainstem, which is part of the SPM12 software package (Diedrichsen et al. 2009). The following steps were performed: 1) Extraction of each subject's cerebellum and brainstem from their corresponding whole-brain 3D T1-weighted anatomical images; 2) Normalization of the anatomical images to the SUIT template using nonlinear deformations; 3) Re-slicing of the functional contrast images produced from the first-level analysis using the deformation produced from step 2) and masking out activation outside the region of interest (i.e., the cerebellum). The normalized cerebellum functional contrast images (of each polynomial order) from each subject were then smoothed with an 8 mm FWHM Gaussian kernel and submitted to a (between-subject) standard second-level random effects analysis, testing for increasingly higher-order nonlinear effects within the cerebellum with one-sample t-tests. Significant clusters were defined using a height threshold of P u < 0.001 (and a minimum extent of 5 voxels). The anatomical designations of regionally specific effects were defined using a highresolution probabilistic atlas defined within the SUIT template (Diedrichsen et al. 2009). The resulting statistical parametric maps (SPMs) were projected on to the flat map of the cerebellum provided with the SUIT template (Diedrichsen and Zotow 2015).

Conjunction
To identify, in terms of a parametric response to GF, the extended AEON, engaged both in AE and AO, we performed a simple conjunction analysis. This entailed testing for action observation effects at a corrected level of significance within a search volume defined by AE.
We first used the SPM, testing for 0th order effects in order to localize the combined effect of AE and AO independently of GF, that is, to identify regions that showed a conjunction of AE/ AO effects, irrespective of parametric force effects. We then identified regions that showed potential nonlinear responses to GF in both action observation and execution. In order to do so, we used a full factorial design and SPMs of the F statistic, testing for one or more significant polynomial coefficients in both execution and observation to obtain maps of the combined AE/ AO force-related effect (FRE). Specifically, we used the SPMs of the F statistic, testing for a parametric effect of GF under AE (threshold P u < 0.0001 for the whole brain analysis and P u < 0.001 for the SUIT analysis) as a localizing contrast to define a search region within which to identify nonlinear effects under action observation (using the equivalent F contrast and a small volume correction to P < 0.05). Finally, we used the F statistic of the first-order effects to investigate the linear FRE and the F statistic of the higher-order effects to investigate the nonlinear FRE.

Results
BOLD fMRI signals were recorded from 12 healthy subjects during one visuomotor and 2 visual tasks for the purpose of comparing brain activation under AE and AO conditions, when different GF levels are applied to an object (in this case a squeeze ball).

AO Behavioral Responses
The behavioral performance, at group level, when watching the AO and AOvc videos, is shown in Fig. 2. The accuracy of the perceived grip force (pGF) significantly differed between AO and AOvc, both before (P = 0.002) and after (P = 0.00008) the MRI session. Within the AOvc condition, pGF accuracy was higher after MRI (P = 0.003), while no significant differences were found in the AO condition (P = 0.955). As expected, GF recognition was higher in AOvc than AO (mean accuracy ± SD, 76 ± 22 and 39 ± 7, respectively), although at the end of the experiment, some subjects reported that the bar indicating levels of force (the visual cue) had not influenced their behavioral responses during AOvc. AO data showed a positive correlation between aGF and pGF (r 2 = 0.98, P = 0.005) (Fig. 3), thus, confirming that the  subjects were able to infer the actor's movement in quantitative terms. Given that subjects correctly perceived the strength of the applied GF also when watching the AO video without the visual cue, subsequent analysis of fMRI data concerned only the AE and AO conditions.

Whole Brain-BOLD Effects
Regionally specific effects for 0th (main effect), linear (+1st, −1st) and nonlinear (+2nd, +3rd, +4th, -3rd) order responses were detected, using whole-brain analysis, on AE and AO. Full data with figures and tables detailing significant effects (including coordinates, T values and cluster extents) are provided as supplementary material. AE activated many more regions than AO (Fig. 4), while both experimental conditions elicited regionally specific effects at 0th, −1st, and −3rd orders. Specifically, AO induced effects not only at the 0th order, but also at +3rd, 1st, and −3rd orders. These results reflect the presence of FRE during action observation.

Whole Brain Conjunction
AE and AO Main Effect (0th Order) Several areas belonged to the extended AEON (in terms of a conjunction of zero order effects), and they included the occipital and temporal lobes, inferior and superior parietal cortices, precentral and postcentral gyri, inferior frontal gyrus, insula, thalamus and cerebellum. The occipitotemporal cluster extended into the cerebellar lobules VI and VII and cerebellar Crus I (Fig. 5 and Table 1).

SUIT-BOLD Effects
The AE condition detected more activated cerebellar regions than the AO one did (Fig. 7). In AE cerebellar specific effects Note, in the AEON, the considerable overlap of effects in both the cerebral cortex and the cerebellum. Different thresholds were used for the 3 maps: P u < 0.0001 (k ≥ 10; P u = P uncorrected for multiple comparisons) was used for the AE condition; P u < 0.05 (k ≥ 10; P u = P uncorrected for multiple comparisons) was used for the AO condition; and P < 0.05 (k ≥ 10), with a small volume correction applied to the AO map, was used to obtain the AEON.  (86) The table reports all the action execution-observation network (AEON) regions that presented a main effect (0th order). The statistical threshold is set using P < 0.05 (k ≥ 10) at the cluster level. Regions (*) survived a P < 0.05 correction for multiple comparisons at the peak level. The first cluster (ext = 1986) contains cerebellar activations (Crus 1 and lobules VI and VII). The last column reports the probability (expressed as a percentage) of these voxels being located in the respective Brodmann area (BA) or specific location (Loc) according to the cytoarchitectonic maps. ext = extension (number of voxels in a cluster); T = T-value at the voxel level. x, y, z are peak coordinates in MNI space (mm).

SUIT-Conjunction
AE and AO Effect (0th Order) Lobules VI and VII and Crus I and II were jointly involved in AE and AO (Fig. 8). Note, in AEON, the prevalence of nonlinear associations in both the cerebral cortex and the cerebellum. Different thresholds were used for the 3 maps: P u < 0.0001 (k ≥ 10; P u = P uncorrected for multiple comparisons) was used for the action execution condition; P u < 0.05 (k ≥ 10; P u = P uncorrected for multiple comparisons) was used for the action observation condition; and P < 0.05 (k ≥ 10), with a small volume correction applied to the AO map, was used to obtain the AEON. The table reports all the action execution-observation network (AEON) regions that presented a force-related effect (FRE). The statistical threshold is set using P < 0.05 (k ≥ 10) at the cluster level. Regions (*) survived a P < 0.05 correction for multiple comparisons at the peak level. The last column reports the probability (expressed as a percentage) of these voxels being located in the respective Brodmann area (BA) or specific location (Loc) according to the cytoarchitectonic maps.
ext=number of voxels in a cluster; T = T-value at the voxel level. x, y, z are the peak coordinates in MNI space (mm).

Discussion
In this study, we report for the first time the existence of forcerelated BOLD effects in an extended AEON involving cerebral and cerebellar regions that are both motor and associative in nature. These regions not only respond to observed and executed actions, but also share patterns of linear and nonlinear BOLD responses to parametric variations in GF. Linear BOLD-GF associations occurred in motor regions, while nonlinear BOLD-GF associations were found in regions specific to somatosensory state estimation, motor simulation and cognitive control. The cerebellum was found to be a key structure within the AEON, showing regional-specific correlations with force. These effects support the concept that the AEON extends to the cerebellum and to a set of cortical regions that are critical for imitation learning. The results are discussed and integrated with our current understanding of brain function in terms of the intrinsic functional connectivity of 7 fundamental networks (visual, somatomotor, ventral and dorsal attention, frontoparietal, limbic and default networks) ).

Behavioral Performance and Learning Effects
The subjects were found to be able to evaluate visually the efforts of others. There are 3 considerations indicating that this ability was independent of learning during the test (Weigelt et al. 2008). First, in order to saturate learning, all the subjects underwent AO training before the fMRI experimental sessions; this training is known to facilitate motor learning (Stefan et al. 2005;Salama et al. 2011) and increase force production by optimizing motor neuron recruitment (Porro et al. 2007). Second, the order of presentation of the AE, AO, AOvc sessions was randomized, thus limiting a potential variability in attentional load (e.g., induced by fatigue). Third, the accuracy in force detection was higher in AOvc than in the AO sessions. Therefore, independently of subject performance, the visual cue has a facilitator effect with respect to naturalistic stimulation (i.e., actual movement and changes in body parts during action), but the latter is nonetheless sufficient to perceive the intensity of another's movements.
It should be noted that in the AOvc condition we detected a learning effect, implying a facilitation of force recognition along trials. Moreover, we detected a higher variability of performance between participants in the AOvc compared with the AO condition; this might be due to attention being focused either on the visual cue or on the hand itself. However, the debriefing at the end of the experiment indicated that several participants had ignored the bar. For these reasons, we did not further consider the AOvc condition in our analysis.  lum. Different thresholds were used for the 3 maps: Pu < 0.001 (k ≥ 10; Pu = P uncorrected for multiple comparisons) was used for the action execution condition; Pu < 0.05 (k ≥ 10; P u = P uncorrected for multiple comparisons) was used for the action observation condition; and P < 0.05 (k ≥ 10), with a small volume correction applied to the AON map, was used to obtain the AEON.

BOLD Effects Elicited by AE and AO
The BOLD effects elicited by AE occurred mostly in areas directly involved in motor planning, execution, and control ) (for a detailed description see Table 3). The main effect of AE was observed in premotor and sensorimotor cortices as well as in parietal, occipital and cerebellar cortices devoted to global sensorimotor processing (Neely et al. 2013) and included in visual, dorsal attention and somatomotor networks, while a linear activation with force was found in primary motor cortex and anterior cerebellum, that actually do encode force (Keisker et al. 2009) and belong to the somatomotor network. Nonlinear relationships with GF were found in parietal, frontal, cingulate and insular cortices, and in thalamus, basal ganglia and cerebellum, which form large-scale loops involved in the control of fine precision grip forces and motor learning (Graybiel 1998;Ehrsson et al. 2001;Kuhtz-Buschbeck et al. 2001). These loops could be linked with visual, ventral and dorsal attention, frontoparietal, somatomotor and default networks. Minor differences with previous squeeze ball studies  could be related to the higher complexity of the present paradigm (which included behavioral training sessions and 3 different tasks).
The BOLD effects elicited by AO were recorded in an extended and distinctive set of occipital, parietal and frontal regions involved in motor but also sensory and cognitive processing (for a detailed description see Table 3). The main effect of AO was observed in the occipital and parietal regions related to motion perception and attention (Becker-Bense et al. 2012; Thompson and Parasuraman 2012) that are considered to be part of the visual network and the ventral and dorsal attention networks. Linear responses with respect to GF occurred mainly in the postcentral gyrus, involved in processing proprioceptive and tactile representations of the manipulated object (Ebisch et al. 2008) and included in the somatomotor network. Nonlinear responses with respect to GF occurred in occipital and temporal cortices and inferior parietal lobule, involved in object recognition (Reed et al. 2004), inhibition of movement (Menon et al. 2001), spatial focusing of attention (Ptak 2012), and intention understanding (Koul et al. 2018). These functions are supported by the inclusion of activated regions in the visual, dorsal attention and default networks. These components, either main or FREs, probably provide the substrate for the interpretation and simulation of the actions of others (McGregor and Gribble 2015), while actual movement is inhibited.
The detection of specific nonlinear force-related BOLD effects in areas involved in AE or AO could imply complex taskrelated interplay of different neuronal populations (e.g., inhibitory and excitatory) within local networks. Understanding the biophysical basis of such nonlinearities will need realistic models and further investigation of neurovascular coupling under different conditions.

The Common Neural Substrate of AE and AO
The AEON, identified as the voxels shared by AEN and AON, was observed in cerebral cortex, thalamus, basal ganglia, and Different thresholds were used for the 3 maps: P u < 0.001 (k ≥ 10; P u = P uncorrected for multiple comparisons) was used for the action execution condition; P u < 0.05 (k ≥ 10; Pu = P uncorrected for multiple comparisons) was used for the action observation condition; and P < 0.05 (k ≥ 10), with a small volume correction applied to the AON map, was used to obtain the AEON.  (Buccino et al. 2001;Grèzes and Decety 2001;Jovicich et al. 2001;Tanaka et al. 2001;Knauff et al. 2002;Gazzola and Keysers 2009;Shomstein 2012) Precentral G°# §° §°# § Mirror neurons/response inhibition/ attention/inhibition of motor execution/motor goal/hand-object integration/motor planning/working memory (Cheng et al. 1995;Fagg and Arbib 1998;Shima and Tanji 1998;Brass et al. 2001;Grèzes and Decety 2001;Menon et al. 2001;Leung et al. 2002;Kasess et al. 2008;Morin and Grèzes 2008;Nakata et al. 2008;Caligiore et al. 2013) Deep GM Thalamus°# §° § Modulation of movement, motivation and reward/modulation of motor preparation/force amplitude generation and prediction (Spraker et al. 2007;Wasson et al. 2010;Braadbaart et al. 2013;Caligiore et al. 2013) Basal Forebrain # § Maintenance of spatial attention during goal-directed actions/action style processing/sensorimotor integration/ preparatory suppression of imitative responses (Luks and Simpson 2004;Cauda et al. 2012;Leech et al. 2012;Di Cesare et al. 2016;Campbell et al. 2018) cerebellum (Christensen et al. 2014) (for a detailed description see Table 3). The main effect of AEON was observed in occipital cortex, middle temporal gyrus, precentral and postcentral gyri, inferior and superior parietal lobules, insula, thalamus, and posterior cerebellum. These areas are involved in visual imagery of hand gestures, including visuospatial and motion processing (Hermsdörfer et al. 2001;Knauff et al. 2002), forward/ inverse control for movement planning and execution, action style processing (Cauda et al. 2012), inhibition of motor execution to prevent imitative responses (Kilner 2011). These are, indeed, the fundamental ingredients of motor planning based on observation of actions (Caligiore et al. 2013). The activation of inferior and superior parietal lobules (which are part of the core mirror network) (Molenberghs et al. 2012) with occipital cortex, precentral and postcentral gyri and insula, suggest that AEON includes components from the visual, mirroring/somatomotor, ventral and dorsal attention networks. The AEON areas showing FREs were also extensively distributed in occipital cortex, superior temporal gyri, inferior and superior parietal lobules, precentral and postcentral gyri, inferior frontal gyrus, medial frontal gyrus, precuneus, cingulate gyrus, caudate, thalamus, and cerebellum. These areas are involved in the experience and observation of touch (Blakemore et al. 2005), maintenance of spatial attention during goal-directed actions (Wasson et al. 2010;Cauda et al. 2012;Leech et al. 2012), sensorimotor integration, and force amplitude generation and prediction (Grèzes and Decety 2001;Blakemore et al. 2005). Moreover, the medial frontal gyrus is considered, with the temporoparietal junction, the "core network" of attribution of mental states (Schurz et al. 2014;Molenberghs et al. 2016) while the precuneus has been proposed to have a role in mental imagery to represent others' perspective (Cavanna and Trimble 2006). Therefore, FREs are particularly important in conferring the ability to detect the effort of others not just requiring the intervention of the mirroring/somatomotor, ventral and dorsal attention and frontoparietal networks but also of the mentalizing/default network.
Interestingly, activation in the AEON areas was mostly nonlinear, while linear relationships with GF were found only in a restricted part of the precentral and postcentral cortices (Gazzola and Keysers 2009) that are included in the mirroring/ somatomotor network. Therefore, the AEON is engaged mainly in a nonlinear fashion during force processing.

Cerebellar Involvement in AEON
The cerebellum is known to operate as a generalized forward controller (D'Angelo and Casali 2012) that aids motor planning by predicting the sensory consequences of a motor act, such that a motor plan is coded in terms of an anticipatory sensory state (Blakemore, Goodbody et al. 1998;Callan et al. 2013). In the present context, the sensory state would be provided by AO, and motor predictions would be based on internal cerebellar representations of the system (body and muscle) state (Diedrichsen et al. 2010;Shadmehr and Mussa-Ivaldi 2012). Thus, the cerebellum is well geared for simulating movements after receiving information about the movement of others, in terms of the appropriate sequence (timing) and force (gain) (Yamazaki and Nagao 2012;Callan et al. 2013).
The cerebellum is strongly interconnected with the cerebral cortex through 7 fundamental resting-state networks ). In particular, Buckner et al. (2011) clearly identified in the cerebellum distinct mirroring and mentalizing networks (as part of the larger somatomotor and default networks respectively) that were directly connected to homolog networks in the cerebral cortex. Confirming this network structure, Van Overwalle and colleagues reinterpreted their initial metaanalysis (Van Overwalle et al. 2014) in terms of this network structure and found strong evidence for it (Van Overwalle, Baetens et al. 2015). In addition, a meta-analytical connectivity analysis revealed a strong distinction between anterior mirroring and posterior mentalizing areas in the cerebellum linked to classic mirror and mentalizing areas in the cerebral cortex (Van Overwalle, D'aes et al. 2015). This was confirmed by functional connectivity studies relating mentalizing and executive control functioning to the cerebellum (Van Overwalle and Mariën 2016). Therefore, the cerebellum could also be involved in predicting the consequences and scope of other's actions by reconstructing hypothetical events (Buckner et al. 2011;Van Overwalle and Mariën 2016).
It should be noted that, in our study, cerebellar responses were embedded in a larger cluster that included occipitotemporal areas. The combined activation in the AEON in lobules VI and VII and Crus I and II could be considered part of the ventral and dorsal attention, frontoparietal, and mentalizing/default networks compounded by the mirroring/somatomotor network from specific FREs (Buckner et al. 2011). Indeed, the linear FRE in lobules V, part of the mirroring/somatomotor network, reveals the involvement of cerebellum in motor functions (Glickstein et al. 1994;Schmahmann 1996;Stoodley et al. 2012). The nonlinear effect in lobules VI and IX, part of both mirroring/somatomotor and mentalizing/default networks, would suggest the cerebellar involvement in the integration of motor processing and cognitive/emotional control (Stoodley and Schmahmann 2010).
Altogether, these effects confirm the cerebellar involvement in both mirroring and mentalizing networks. Moreover, these patterns of linear and nonlinear responses in the cerebellar components of the AEON are consistent with results showing that motor-generating areas respond linearly with GF, while associative and cognitive areas have a more complex relationship with GF. These response profiles may reflect distributed responses, mediated by connections that have been characterized structurally and physiologically in rodents, primates, and humans (Schmahmann and Pandya 1995;Kelly and Strick 2003;Ramnani 2006;Strick et al. 2009;Watson et al. 2014;Palesi et al. 2015Palesi et al. , 2017.

High-Order Force-BOLD Relationships in the Cerebellum and Cerebral Cortex
While a monotonic relationship between BOLD response and GF levels was found in primary motor areas (M1 and anterior cerebellum)-and could be related to the increased neuronal recruitment with increasing GF (Cramer et al. 2002;Keisker et al. 2009)-nonlinearities were typically detected in areas implicated in multimodal integration and higher aspects of motor control (premotor, associative and sensory areas both in the cerebral cortex and the cerebellum), where a complex blend of signals converges to regulate motor output. It has been previously argued ) that secondorder responses at intermediate force levels could be "metabolically optimal" and reflect more efficient processing in a motor regime requiring fewer corrective actions and less attention to sensory inputs. For example, nonlinearity may be due to fluctuation of attention levels modulating neural activity (Binkofski et al. 2002). However, it should be appreciated that it is difficult to make detailed neurophysiological inferences based exclusively on fMRI signals. For example, nonlinearities (including nonlinear neuronal responses, nonlinear engagement of local inhibitory circuits, nonlinear mapping from neuronal activity to haemodynamic responses and finally, nonlinearities associated with the haemodynamic response function generating T2* signals) could arise at a number of different levels (Friston et al. 2000;Mechelli et al. 2001). The engagement of the underlying neuronal circuits, both in the cerebral cortex and the cerebellum, may benefit from further investigation using repetitionsuppression fMRI paradigms (Kilner 2011;Barron et al. 2016) or multivoxel pattern analysis (Turella et al. 2009) in conjunction with animal recordings and large-scale model simulations (D'Angelo and Gandini Wheeler-Kingshott 2017).

Potential Limitations
Despite the coherent functional framework emerging from this investigation, the relatively small number of subjects may affect its statistical power in detecting active areas. Although previous studies used similar numbers of subjects, a larger sample may be beneficial to confirm our findings. However, it is important to note that significant results obtained using a small sample usually mean that the effect size is large (Flandin and Friston 2017). From a statistical point of view, the use of parametric models is an efficient way of accommodating nonlinear (neurometric) response functions within the established GLM framework (Friston 2012). However, given the concern that detection of active areas may have been reduced because of habituation due to multiple engagement in AO (Krekelberg et al. 2006), it would be useful to devise alternative paradigms in order to refine our AEON parametric characterization.

Conclusions
The extended AEON identified in this fMRI study engages largescale brain networks capable of remapping the visual detection of the actions, and also effort, of others onto the observer's own motor system. These circuits, furnish not only understanding of other people's goals, that is, the "mirror" effect (Rizzolatti and Craighero 2004), but also the building blocks of executive control, impacting on various aspects of motor planning and programming, working memory, selective attention, and behavioral inhibition (Rizzolatti and Craighero 2004;Calvo-Merino et al. 2006;Filimon et al. 2007;Thompson et al. 2007;Hamilton and Grafton 2008;Caspers et al. 2010;Cavallo et al. 2015). The cerebrocerebellar loops, using the motor system as a forward model (Miall 2003;Kilner et al. 2007;Ito 2008;D'Angelo and Casali 2012;Callan et al. 2013), could play a crucial role in sensorimotor prediction and internal simulation of movement. It has been suggested that the insular and cingulate cortices, activated in parallel to the sensorimotor loops, allow exteroception to be integrated with interoception (Bodegård et al. 2001;Craig 2003;Pineda et al. 2009) and external observational cues to be transformed into internal sensorimotor plans. The identification of this extended AEON as a plausible substrate for imitation learning could facilitate and improve the clinical application of action observation in neurorehabilitation (Porro et al. 2007;Garrison et al. 2013;Buccino 2014).

Supplementary Material
Supplementary material is available at Cerebral Cortex online.