Dr Etienne Allart
email: etienne.allart@chru-lille.fr

Romain Viard

Renaud Lopes

Hervé Devanne

Arnaud Delval

Influence of motor deficiency and spatial neglect on the contralesional posterior parietal cortex functional and structural connectivity in stroke patients

Keywords: stroke, connectivity, resting state, DTI, posterior parietal cortex, fronto-parietal networks

The posterior parietal cortex (PPC) is a key structure for visual attention and upper limb function, two features that could be impaired after stroke, and could be implied in their recovery. If it is well established that stroke is responsible for intra-and interhemispheric connectivity troubles, little is known about those existing for the contralesional PPC. In this study, we aimed at mapping the functional (using resting state fMRI) and structural (using diffusion tensor imagery) networks from 3 subparts of the PPC of the contralesional hemisphere (the anterior intraparietal sulcus (aIPS), the posterior intraparietal sulcus (pIPS) and the superior parieto-occipital cortex (SPOC) to bilateral frontal areas and ipsilesional homologous PPC parts in 11 chronic stroke patients compared to 13 healthy controls. We also aimed at assessing the relationship between connectivity and the severity of visuospatial and motor deficiencies. We showed that interhemispheric functional and structural connectivity between PPCs was altered in stroke patients compared to controls, without any specificity among seeds. Alterations of parieto-frontal intra-and interhemispheric connectivity were less observed. Neglect severity was associated with several alterations in intra-and interhemispheric connectivity, whereas we did not find any behavioral/connectivity correlations for motor deficiency. The results of this exploratory study shed a new light on the influence of the contralesional PPC in post-stroke patients, they have to be confirmed and refined in further larger studies.

Introduction

Stroke is a leading cause of acquired disability in the world. Among all stroke-induced deficiencies, upper limb paresis is one of the most frequent, represents a key factor for autonomy [START_REF] Veerbeek | Early prediction of outcome of activities of daily living after stroke: a systematic review[END_REF]) and its rehabilitation remains a challenge. Spatial neglect, defined as a failure to acknowledge or explore stimuli towards the contralesional side [START_REF] Heilman | Neglect and related disorders[END_REF], is another disabling consequence of stroke because it largely impedes stroke recovery and patients' autonomy (Di [START_REF] Monaco | Severity of unilateral spatial neglect is an independent predictor of functional outcome after acute inpatient rehabilitation in individuals with right hemispheric stroke[END_REF]. The posterior parietal cortex (PPC), a region composed of areas located along the intraparietal sulcus (IPS) and of the superior parietooccipital cortex (SPOC), is a key structure for sensori-motor integration, upper limb movement planning and control of spatial attention [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF][START_REF] Buneo | The posterior parietal cortex: sensorimotor interface for the planning and online control of visually guided movements[END_REF][START_REF] Davare | Interactions between areas of the cortical grasping network[END_REF][START_REF] Vesia | Specialization of reach function in human posterior parietal cortex[END_REF]. Beyond specific brain areas, brain connectivity studies have shown that the effect of a brain lesion must be studied at the level of networks it impacts. Indeed, multiple recent connectivity studies have identified altered connectivity patterns that correlate with behavior and cognition using either functional [START_REF] Bournonville | Identification of a specific functional network altered in poststroke cognitive impairment[END_REF], structural [START_REF] Griffis | Structural disconnections explain brain network dysfunction after stroke[END_REF][START_REF] Wiesen | Using machine learning-based lesion behavior mapping to identify anatomical networks of cognitive dysfunction: Spatial neglect and attention[END_REF], or effective connectivity [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[END_REF] methods.

The PPC is part of the dorsal attention network (DAN), which is involved in the voluntary orientation of attention and the generation of attentional sets (top-down attention) [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF]. In neglect patients, the lesion is most often responsible for an intrahemispheric disconnection with the right DAN, leading to an interhemispheric trouble in the balance between activity of both DANs [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF][START_REF] He | Breakdown of functional connectivity in frontoparietal networks underlies behavioral deficits in spatial neglect[END_REF][START_REF] Baldassarre | Large-scale changes in network interactions as a physiological signature of spatial neglect[END_REF][START_REF] Ramsey | Normalization of network connectivity in hemispatial neglect recovery[END_REF]. This induces an hyperexcitability of left parieto-frontal networks that can be directly assessed by transcranial magnetic stimulation (TMS) [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[END_REF]Koch et al. 2008a). This hyperexcitability is a target of non-invasive brain stimulation protocols proposed in neglect patients, most often consisting in inhibitory protocols over the contralesional posterior part of the intraparietal sulcus (pIPS), with encouraging first results (for a review, see [START_REF] Jacquin-Courtois | Hemi-spatial neglect rehabilitation using non-invasive brain stimulation: Or how to modulate the disconnection syndrome?[END_REF]). However, little is known about the specificity of the involvement of each contralesional PPC subpart in the connectivity troubles observed in neglect patients and their relationships with the severity of the disability. In a previous work, we studied the contralesional PPC-M1 connectivity in stroke patients from the 3 subparts of the PPC using a pairedpulse TMS (ppTMS) protocol [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[END_REF]. We showed, as already demonstrated for pIPS (Koch et al. 2008a), that SPOC-M1 connectivity was modified in neglect patients, whereas aIPS-M1 connectivity was not modified. However, we only assessed intrahemispheric connectivity (and not interhemispheric features), ppTMS protocols only address some particular features of brain effective connectivity (assessing an indirect response via M1) [START_REF] Rothwell | Using transcranial magnetic stimulation methods to probe connectivity between motor areas of the brain[END_REF], and to the best of our knowledge no study investigated specifically modifications of structural connectivity of the contralesionnal PPC networks.

In addition to its role in spatial attention, the PPC plays a role in the planning and control of visuallyguided movements of the upper limb. This role is well demonstrated in healthy humans by connectivity studies using transcranial magnetic stimulation [START_REF] Busan | Effect of transcranial magnetic stimulation (TMS) on parietal and premotor cortex during planning of reaching movements[END_REF][START_REF] Karabanov | Timing-dependent modulation of the posterior parietal cortex-primary motor cortex pathway by sensorimotor training[END_REF]G Koch et al. 2008;[START_REF] Koch | Focal stimulation of the posterior parietal cortex increases the excitability of the ipsilateral motor cortex[END_REF][START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goaldirected hand actions[END_REF] or functional imaging [START_REF] Filimon | Multiple parietal reach regions in humans: cortical representations for visual and proprioceptive feedback during on-line reaching[END_REF][START_REF] Cavina-Pratesi | Functional magnetic resonance imaging reveals the neural substrates of arm transport and grip formation in reach-to-grasp actions in humans[END_REF][START_REF] Reichenbach | Contributions of the PPC to online control of visually guided reaching movements assessed with fMRI-guided TMS[END_REF][START_REF] Konen | Functional organization of human posterior parietal cortex: grasping-and reaching-related activations relative to topographically organized cortex[END_REF][START_REF] Monaco | Neural correlates of object size and object location during grasping actions[END_REF]. These works particularly showed that most caudal structures of the PPC (pIPS, SPOC), as well as the dorsal premotor cortex (dPMC) to which they are connected, are mostly involved in the reaching phase of movement. On the other hand, the anterior part of the intra-parietal sulcus (aIPS), connected to the ventral premotor cortex (vPMC), are involved in the grasping phase. In addition, there are some evidence indicating that the PPC exerts a direct influence on M1 and upper limb movements, since an excitatory modulation of the PPC by NIBS techniques is able to enhance M1 excitability [START_REF] Rivera-Urbina | Parietal transcranial direct current stimulation modulates primary motor cortex excitability[END_REF], PPC-M1 connectivity [START_REF] Chao | Induction of motor associative plasticity in the posterior parietal cortex-primary motor network[END_REF] and to modify movement timing in healthy subjects [START_REF] Krause | 1Hz rTMS of the left posterior parietal cortex (PPC) modifies sensorimotor timing[END_REF]. In post-stroke patients, if the integrity of the pyramidal tract and interhemispheric imbalance between primary motor cortices (M1) are the main features associated with motor deficiency and recovery [START_REF] Calautti | The relationship between motor deficit and hemisphere activation balance after stroke: A 3T fMRI study[END_REF][START_REF] Bembenek | The prognostic value of motor-evoked potentials in motor recovery and functional outcome after stroke -a systematic review of the literature[END_REF][START_REF] Stinear | The PREP algorithm predicts potential for upper limb recovery after stroke[END_REF][START_REF] Thiel | Structural and resting-state brain connectivity of motor networks after stroke[END_REF][START_REF] Koch | Structural connectivity analyses in motor recovery research after stroke[END_REF], interactions between lesioned M1 and bilateral non-primary motor areas seem to play a role.

Firstly, it is well known that movement production with the paretic upper limb is associated with activations of ipsilesional M1, but also of the PMC and the PPC [START_REF] Buma | Functional neuroimaging studies of early upper limb recovery after stroke: a systematic review of the literature[END_REF]). In addition, the influence of the PMC and the supplementary motor area (SMA) of both hemisphere on lesioned M1 has been more widely studied [START_REF] James | Changes in resting state effective connectivity in the motor network following rehabilitation of upper extremity poststroke paresis[END_REF][START_REF] Sharma | Motor imagery after stroke: relating outcome to motor network connectivity[END_REF][START_REF] Park | Longitudinal changes of resting-state functional connectivity during motor recovery after stroke[END_REF][START_REF] Rehme | Cerebral network disorders after stroke: evidence from imaging-based connectivity analyses of active and resting brain states in humans[END_REF][START_REF] Wang | Altered functional organization within and between resting-state networks in chronic subcortical infarction[END_REF][START_REF] Zheng | The plasticity of intrinsic functional connectivity patterns associated with rehabilitation intervention in chronic stroke patients[END_REF][START_REF] Zhang | Relationship between functional connectivity and motor function assessment in stroke patients with hemiplegia: a resting-state functional MRI study[END_REF] and recently led to the first applications of non-invasive brain stimulation (NIBS) protocols targeting PMC (and not directly M1) for motor recovery [START_REF] Cunningham | Stimulation targeting higher motor areas in stroke rehabilitation: A proof-of-concept, randomized, double-blinded placebocontrolled study of effectiveness and underlying mechanisms[END_REF][START_REF] Plow | Rethinking stimulation of the brain in stroke rehabilitation: why higher motor areas might be better alternatives for patients with greater impairments[END_REF][START_REF] Andrade | Constraint-Induced Movement Therapy Combined with Transcranial Direct Current Stimulation over Premotor Cortex Improves Motor Function in Severe Stroke: A Pilot Randomized Controlled Trial[END_REF]. Data concerning connectivity of the PPC with M1 are scarcer but of interest. First, recent imaging studies of functional and structural connectivity showed that ipsi-and contralateral connectivity of both PPC to lesioned M1 was altered in the subacute phase post-stroke [START_REF] Wang | Dynamic functional reorganization of the motor execution network after stroke[END_REF][START_REF] Park | Longitudinal changes of resting-state functional connectivity during motor recovery after stroke[END_REF][START_REF] Inman | Altered resting-state effective connectivity of fronto-parietal motor control systems on the primary motor network following stroke[END_REF][START_REF] Schulz | Parietofrontal motor pathways and their association with motor function after stroke[END_REF][START_REF] Schulz | Enhanced Effective Connectivity Between Primary Motor Cortex and Intraparietal Sulcus in Well-Recovered Stroke Patients[END_REF][START_REF] Zhang | Relationship between functional connectivity and motor function assessment in stroke patients with hemiplegia: a resting-state functional MRI study[END_REF], and suggested that ipsilesional parieto-frontal networks could play a role in motor deficiency and recovery after stroke [START_REF] Inman | Altered resting-state effective connectivity of fronto-parietal motor control systems on the primary motor network following stroke[END_REF][START_REF] Schulz | Parietofrontal motor pathways and their association with motor function after stroke[END_REF][START_REF] Schulz | Enhanced Effective Connectivity Between Primary Motor Cortex and Intraparietal Sulcus in Well-Recovered Stroke Patients[END_REF]. This has been confirmed in a recent connectivity study using EEG [START_REF] Bönstrup | Parietofrontal network upregulation after motor stroke[END_REF]. Taken together, these data may underline a potential positive impact of a modulation of the PPC on recovery of the upper-limb disability.

Moreover, as applying NIBS over the unaffected hemisphere is easier and more and more widely used, they point the contralesional PPC as a potential adjuvant target in addition to M1 in such protocols. However, as for spatial neglect, little is known about the specificity of the involvement of each contralesional PPC subpart, the modifications of contralesional PPC connectivity and their relationships with the severity of motor deficiency.

In order to answer the points raised for both neglect and upper-limb function, we therefore aimed at mapping the functional and structural networks associated with each of the 3 PPC areas (aIPS,pIPS and SPOC) of the contralesional hemisphere in chronic stroke patients compared to healthy controls using a resting state fMRI (rs-fMRI) and a diffusion tensor imaging (DTI) analyses. We also aimed at assessing the relationship between connectivity and the severity of visuospatial and motor deficiencies. We hypothesized that patients would show intra-and inter-hemispheric modifications in the contralesional PPC functional and structural connectivity, particularly evident for the two caudal parts of the PPC (pIPS and SPOC) regarding neglect status.

Methods

Participants

Patients were recruited among in-and outpatients in the Neurorehabilitation Unit at Lille University Medical Center (Lille, France) between August 2014 and March 2016. A majority of them had already participated in a previous study evaluating PPC-M1 connectivity in the left (contralesional for patients) hemisphere using a ppTMS protocol [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[END_REF]. All patients had suffered a single right ischemic or hemorrhagic hemispheric stroke (diagnosed by MRI) for at least 6 months before inclusion and had displayed left hemiparesis; the presence of spatial neglect was not an inclusion criterion but was assessed in all included patients. We also included healthy age-matched controls. We excluded patients with bilateral lesions and subjects who were unable to consent to or understand the study protocol due to language, cognitive or psychiatric disorders, and those presenting contraindications to MRI. All participants were right-handed (according to the Edinburgh Handedness Inventory [START_REF] Oldfield | The assessment and analysis of handedness: the Edinburgh inventory[END_REF])) and gave their informed written consent to participation. The study was approved by the local investigational review board (Comité de protection des personnes Nord Ouest IV, Lille, France; reference 2013-A01766-39), and was conducted in accordance with the tenets of the Declaration of Helsinki.

Clinical assessment of spatial neglect and motor deficiency

Patients were classified as suffering from spatial neglect ("N+") or not ("N-") with regard to their performance in the three following tests. Peripersonal visual neglect was assessed using the Bells test [START_REF] Gauthier | The Bells Test: A quantitative and qualitative test for visual neglect[END_REF] and patients were considered as neglect if they omitted at least 6 bells [START_REF] Gauthier | The Bells Test: A quantitative and qualitative test for visual neglect[END_REF][START_REF] Rousseaux | Presenting a battery for assessing spatial neglect. Norms and effects of age, educational level, sex, hand and laterality[END_REF]. Personal (body) neglect was assessed with the fluff test (cut-off score: 13) [START_REF] Cocchini | The Fluff Test: A simple task to assess body representation neglect[END_REF]. Lastly, behavioral neglect was assessed via the examiner's part of the Catherine Bergego Scale (cut-off score: > 10) [START_REF] Azouvi | Behavioral assessment of unilateral neglect: study of the psychometric properties of the Catherine Bergego Scale[END_REF]. Motor impairment was evaluated via the upper extremity subsection of the Fugl-Meyer Assessment (FMA-UE), which assesses the motor function of the upper arm, wrist and hand, and overall coordination [START_REF] Fugl-Meyer | The post-stroke hemiplegic patient. 1. a method for evaluation of physical performance[END_REF].

MRI data acquisition

All exams were performed on a 3T Philips Achieva Scanner (Philips Healthcare, Best, The Netherlands) using an 8-channel phased-array head coil and a whole-body coil transmission. The imaging protocol included an anatomical three-dimensional T1-weighted (3DT1), a rs-fMRI, and a diffusion tensor imaging (DTI) sequences:  3D T1 FFE sequence was acquired using the following parameters: voxel size=1×1×1 mm 3 ; matrix=256×256×176; TR=7.2 ms; TE=3.3 ms and FA=9°.

 rs-fMRI was performed with a T2*-weighted EPI sequence lasting 10 min: voxel size=3×3×3 mm 3 ; matrix=64×64×40; TR=2.4 s, TE=30 ms and FA=90°. Patients were required to remain quiet, stay awake and close their eyes.

 DTI was acquired using a single-shot EPI sequence with 32 directions of the diffusion gradient: voxel size=2×2×2 mm 3 ; matrix=128×128×66; TR=12 s; TE=56 ms; b=1000 s/mm 2 . To correct B0 field inhomogeneity-induced distortion, another non-diffusion weighted images (b=0 s/mm 2 ) with opposite phase-encoding direction was also collected [START_REF] Holland | Efficient correction of inhomogeneous static magnetic field-induced distortion in Echo Planar Imaging[END_REF].

T1 processing

Structural T1 images were processed using the Freesurfer software (v.5.6 Massachusetts General Hospital, Boston, MA; http://surfer.nmr.mgh.harvard.edu/). This included the preprocessing steps of non-uniform signal correction, signal and spatial normalizations, skull stripping and brain tissues automatic parcellation [START_REF] Dale | Cortical surface-based analysis. I. Segmentation and surface reconstruction[END_REF]. Then a non-linear registration was applied to match the preprocessed 3DT1 data to the MNI template, using Statistical Parametric Mapping software (SPM12 http://www.fil.ion.ucl.ac.uk/spm/software/spm12 Wellcome Department of Cognitive Neurology, University College London, UK).

Regions of interest and lesion masks

Three regions of interest (ROIs) corresponding to the 3 left PPC regions (aIPS, pIPS and SPOC) were manually segmented on 3DT1 images of all subjects by a single expert (EA), on the basis of coronal and transversal slices.

The aIPS was defined as the region located over the intersection between the postcentral sulcus and intraparietal sulcus [START_REF] Frey | Cortical topography of human anterior intraparietal cortex active during visually guided grasping[END_REF][START_REF] Cavina-Pratesi | Functional magnetic resonance imaging reveals the neural substrates of arm transport and grip formation in reach-to-grasp actions in humans[END_REF]. The pIPS was situated over the caudal part of the intraparietal sulcus [START_REF] Karabanov | Mapping Different Intra-Hemispheric Parietal-Motor Networks Using Twin Coil TMS[END_REF][START_REF] Koch | Focal stimulation of the posterior parietal cortex increases the excitability of the ipsilateral motor cortex[END_REF]. The SPOC was defined as the region along the medial surface of the parietal lobe, anterior to the parieto-occipital sulcus, posterior to the subparietal sulcus and medial to the intraparietal sulcus [START_REF] Cavina-Pratesi | Functional magnetic resonance imaging reveals the neural substrates of arm transport and grip formation in reach-to-grasp actions in humans[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goaldirected hand actions[END_REF]. Volume of each seed was comparable between subjects and controls and the quality of overlap between subjects was good (appendix 1). These ROIs were used as seeds in the rs-fMRI analysis (see below).

In stroke patients, lesion masks were similarly manually segmented by the same expert on 3DT1 images using the same methodology as for ROIs for information about lesion localization and volume.

rs-fMRI analysis

Preprocessing and registration with MNI template

Preprocessing of rs-fMRI data were performed using a combination of SPM and in-house software implemented in MATLAB Version: 8.3.0.532 (R2014a) (Mathworks Inc., Natick, MA, USA). Preprocessing of rs-fMRI data included the removal of the first three image volumes (to avoid T1 equilibration effects), rigid-body head motion correction, slice-timing correction using a mean frame as reference, and registration to 3DT1 images. Nuisance signals were removed using a two-step linear regression. The first regression removed linear/quadratic trends (to account for scanner drift) and six motion parameters (time frames with excessive motion were suppressed). The second regression removed five "nuisance signals" obtained by means of a principal component analysis of white matter and ventricle signals using the component-based noise correction (CompCor) approach [START_REF] Behzadi | A component based noise correction method (CompCor) for BOLD and perfusion based fMRI[END_REF]). Residual data were filtered for high temporal frequencies (low-pass of the frequency filter 0.1 Hz).

Then, preprocessed rs-fMRI data were spatially normalized to match the Montreal Neurological Institute (MNI) template. For that the transformation computed during 3DT1 preprocessing was applied to preprocessed rs-fMRI data and resampled by spline interpolation into a final voxel size of 2 × 2 × 2 mm 3 . Finally, preprocessed rs-fMRI data were spatially smoothed using a 3D 6-mm full width at half maximum Gaussian kernel.

Seed-based connectivity analysis

All seed-based connectivity analyses were performed using the functional data sets that had been previously preprocessed and registered to the MNI standard space. CONN functional connectivity toolbox 16.a (http://www.nitrc.org/projects/conn) (Whitfield-Gabrieli and Nieto-Castanon 2012) was used for analysis, using ROI (aIPS, pIPS and SPOC) as seeds. Additional denoising steps were proceed: Band-pass filter were set to [0.01 0.1] Hz, detrending removes cubic trends, and despiking applies a squashing function to reduce the influence of potential outlier scans. Functional connectivity analyses use a General Linear Model for bivariate correlation measures of the association between the seed BOLD timeseries and each voxel BOLD timeseries. Thus, a functional connectivity map was obtained for each seed per subject. Voxel-wise group comparisons were performed on these maps by a non-parametric approach based on 10000 permutations. Differences were considered significant at p < 0.05 corrected for multiple comparisons by family-wise error approach.

Network analysis

As we focused on the role of frontoparietal and inter-PPC connectivity, we only considered these last networks in the functional connectivity network analysis. To take into account for the small sample size, patients' and controls' resting-state connectivity was compared using another approach based on networks. Networks corresponded to regions functionally connected to seeds and were extracted from one-sample T-test control's maps. Regions per hemisphere were identified by selecting 100 voxels around the peak of each significant cluster (p<0.05 False Discovery Rate corrected) respecting a minimal distance of 50 mm. Thus, 3 networks corresponded to each seed were obtained, and for each network mean functional connectivity for identified ROIs were extracted and compare between patients and control groups using a two-sided Mann-Whitney U test, with a significant level at p < 0.05 (FDR corrected).

DTI data analysis

Preprocessing and coregistration with 3DT1

DTI images were corrected for Eddy currents, geometrical and signal distortions [START_REF] Glasser | The minimal preprocessing pipelines for the Human Connectome Project[END_REF]. Eddy current artifacts were corrected using the eddy_correct FSL function (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/). Then, the distortion field, inherent to EPI images in the phase encoding direction and responsible for geometric and signal artefacts, was calculated using a pair of spin echo EPI scans with opposite phase encoding directions [START_REF] Holland | Efficient correction of inhomogeneous static magnetic field-induced distortion in Echo Planar Imaging[END_REF]. The "epiunwarp" function in the Computational Morphometry Toolkit (CMTK 3.2.2 http://www.nitrc.org/projects/cmtk/ ) was used to estimate the distortion field and applied it to DTI images.

3DT1 image was coregistered to corresponding DTI space using the rigid registration provided by SPM12.

White matter fiber tractography

Preprocessed DTI data were analyzed using the MRtrix software (v0.2.9, http://www.brain.org.au/software/mrtrix/) [START_REF] Tournier | MRtrix: Diffusion tractography in crossing fiber regions[END_REF]. For each subject, fractional anisotropy (FA) map was calculated and threshold (FA > 0.7) to determine the response function of highly anisotropic voxels, further used for constrained spherical deconvolution in order to provide sharp fiber orientation distribution (FOD) estimates [START_REF] Tournier | Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution[END_REF]). Whole-brain fiber tracts were generated using a probabilistic tracking algorithm [START_REF] Tournier | MRtrix: Diffusion tractography in crossing fiber regions[END_REF]. Tracking parameters were left to defaults (step size = 0.1 mm, minimum radius curvature = 1 mm, FOD cutoff = 0.1, minimum length = 10 mm), the maximum harmonic order set to 10 and the number of generated tracts set to 1,500,000. The tracking mask was defined by the union of the 1-mm dilated white matter mask and the subcortical labels (provided by FreeSurfer) resampled to the DWI space. The rigid transformation matrix, computed during preprocessing steps, was then applied to seeds (aIPS, pIPS & SPOC) initially defined in 3DT1 space. Clusters extracted from functional connectivity analysis of controls, originally in MNI standard space, were then moved to each subject's diffusion space using registration implemented with FSL software. To estimate integrity of white matter pathways connecting seeds (aIPS, pIPS and SPOC) and functional clusters previously extracted in the rs-fMRI network analysis, the FA was computed for each subject.

It represents a common measurement used in DTI studies and ranges from 0 = isotropic movement of water molecules (e.g., cerebrospinal fluid), to 1 = anisotropic movement of water molecules (e.g., fiber bundles). The FA was sampled along fibers and then averaged (mean FA). Difference between groups was evaluated with a two-sided Mann-Whitney U test with a significant level at p < 0.05 (FDR corrected). As for functional connectivity, only structural connectivity from each seed to ipsi-and contralesional frontal areas and ipsilesional PPC have been studied.

Statistical analysis

The normality of the distribution of demographic and behavioral data was checked with a Shapiro-Wilk test and

Results

Participants

We recruited 11 stroke patients (N+ = 5; N-= 7) and 13 healthy controls. However, DTI acquisition was not performed in 2 patients (due to discomfort in the MRI scanner, the DTI sequence being performed last) and DTI

preprocessing was impossible in one other (due to lesion size), so results of the DTI analysis were available for only 8 patients (3 in the N+ group and 5 in the N-group) (Appendix 2). The characteristics of the study population are summarized in Table 1. There were no significant differences between patients and healthy controls in terms of the mean age (p=0.602) and the gender ratio (p=0.649).

Lesion distribution in stroke patients included in the fMRI and DTI analyses are shown in Fig. 1. The highest overlap was situated subcortically and lesions were highly variable in size. They involved mainly the middle cerebral artery territory. Median lesion volume and interquartile interval were 7.5 [15.3] cm 3 in the fMRI analysis, 6.8 [20] cm 3 in the DTI one.

Functional connectivity

Seed-based analysis

The results of the cluster analysis in stroke patients and healthy controls are shown in Fig. 2 and Table 2. We will only focus on the networks of interest. In healthy controls, the left aIPS was connected to the left inferior frontal region (in two separate clusters, the posterior one encompassing the vPMC) and to the aIPS homologous PPC region within the ipsilesional (right) hemisphere and to the right inferior frontal gyrus. In patients, the aIPS intrahemispheric connections were driven to frontal areas, located slightly more medially compared to controls (middle and superior frontal gyri), whereas links with the ipsilesional hemisphere were only found with the homologous aIPS.

In healthy controls, the left pIPS showed functional connections with the contralesional inferior and middle frontal gyri (borderline between ventral and dorsal premotor cortices) and interhemispheric connections with the homologous pIPS and the posterior part of the middle frontal gyrus. As we showed for the aIPS, the pIPS network was less broad in patients, particularly for the connectivity pattern towards parietal and frontal regions in the ipsilesionnal hemisphere, whereas the connectivity within the contralesional hemisphere was globally the same as in controls.

In healthy controls as in stroke patients, the SPOC was functionally connected to the posterior part of the middle frontal gyrus (dPMC) within the contralesional hemisphere and to its homologous region within the ipsilesional hemisphere.

Between-group comparisons did not reveal any significant difference in functional connectivity between healthy controls and patients for any of the 3 seed ROIs.

Network analysis

Figure 3 shows the significant differences between stroke patients and healthy controls in terms of functional connectivity from contralesional PPC to bilateral frontal areas and ipsilesional PPC using a network-based analysis (cf methods). For the aIPS network, stroke patients showed a significant decrease of connectivity with the left inferior frontal gyrus, the homologous aIPS and inferior frontal regions in the lesioned hemisphere. The connectivity of the pIPS network was decreased to the ipsilesional middle frontal gyrus. Finally, the SPOC network only showed interhemispheric alterations with the ipsilesional SPOC. Levels of functional connectivity were overall more variable in stroke patients than in healthy controls (whatever the hemisphere we considered).

Neglect demonstrated relationship with functional connectivity data (Fig. 4), conversely to motor deficiency. Peripersonnal and behavioral neglect was more severe when alterations of intrahemispheric connectivity from aIPS and pIPS to ipsilateral frontal regions were present. Concerning interhemispheric connectivity, the severity of spatial neglect was only significantly correlated to the level of connectivity between the aIPS and ipsilesional middle frontal gyrus (in the Bells test). However, there was a trend indicating that the decrease of interparietal connectivity between pIPS, SPOC and their homologous areas within the ipsilateral hemisphere may be associated with the severity of spatial neglect (p<0.1 in the 3 tests of neglect for the pIPS, p=0.089 in the Fluff test for the SPOC).

Structural connectivity

For each seed, interhemispheric structural connectivity (mean FA) of the PPC was significantly decreased in patients with the homologous region in the ipsilesional PPC (Fig. 5). Moreover, the SPOC network was the only to show modifications of intrahemispheric connectivity with the dPMC (middle frontal gyrus).

We only found a relationship between mean FA data and spatial neglect and to a much lesser extent compared to what we found for functional connectivity. The number of total omissions in the Bells Test was all the more higher when the connectivity between SPOC areas was decrease (r=-0.679; p=0.044). Thus, this result indicated that interhemispheric anatomical disconnection between SPOC areas was associated with the severity of peripersonal neglect.

Discussion

The present exploratory study is the first proposing a combined functional (rs-fMRI) and structural (DTI) approach to map intra-and interhemispheric connectivity of 3 distinct regions of the contralesional (left) PPC (aIPS, pIPS and SPOC) in chronic post-stroke patients. We also sought to study whether connectivity was associated with the severity of visuospatial and motor deficiencies. We showed that functional and structural connectivity of the PPC was altered in patients, these alterations were particularly obvious to homologous PPC structures in the ipsilateral hemisphere. Interestingly, we demonstrated several links between functional connectivity and the severity of spatial neglect, but not with motor deficiency. Structural connectivity data were less linked to clinical scores. The results of the present study, even if preliminary ones, may confirm the role of the imbalance of interhemispheric connectivity in spatial neglect, particularly between homologous caudal parts of the PPC. The relationship between contralesional PPC connectivity and upper limb function is less obvious and must be further evaluated in future studies that will have to take into account the difficulty to proper assess the multiple determinants of this function.

Functional connectivity in healthy controls

Functional networks identified in the healthy controls were in accordance with previous studies. Concerning intrahemispheric connectivity, and despite their proximity, the 3 PPC sites exhibited functional connectivity to different neural networks in healthy controls. Consistent with previous results, we observed a segregation between the two caudal sites (pIPS and SPOC) on the one hand and the anterior one (aIPS) on the other.

Therefore, aIPS was functionally and anatomically connected to inferior frontal regions, particularly to the vPMC [START_REF] Cavina-Pratesi | Functional magnetic resonance imaging reveals the neural substrates of arm transport and grip formation in reach-to-grasp actions in humans[END_REF][START_REF] Uddin | Dissociable connectivity within human angular gyrus and intraparietal sulcus: evidence from functional and structural connectivity[END_REF], whereas the pIPS [START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Cavina-Pratesi | Functional magnetic resonance imaging reveals the neural substrates of arm transport and grip formation in reach-to-grasp actions in humans[END_REF][START_REF] Konen | Functional organization of human posterior parietal cortex: grasping-and reaching-related activations relative to topographically organized cortex[END_REF]) and the SPOC [START_REF] Cavina-Pratesi | Functional magnetic resonance imaging reveals the neural substrates of arm transport and grip formation in reach-to-grasp actions in humans[END_REF][START_REF] Konen | Functional organization of human posterior parietal cortex: grasping-and reaching-related activations relative to topographically organized cortex[END_REF] were connected to the dPMC. Each ROI was also connected with surrounding parietal areas, especially the supramarginal gyrus for the aIPS (two regions operating in the control of the grasping phase during arm function [START_REF] Koch | Focal stimulation of the posterior parietal cortex increases the excitability of the ipsilateral motor cortex[END_REF][START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF]), the superior part of the angular gyrus for the pIPS and the SPOC (both involved in the control of the reaching phase of upper limb movements) [START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goaldirected hand actions[END_REF].

Interhemispheric connections were driven to the contralateral homologous parietal areas in the contralateral (right) hemisphere. This is in line with previous results [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF] and it has been demonstrated that these interactions were supported by transcallosal fibers belonging to the posterior part of the corpus callosum [START_REF] Koch | Asymmetry of parietal interhemispheric connections in humans[END_REF]. The aIPS and pIPS ROIs were also connected to contralateral frontal regions homologous to those to they are connected in the ipsilateral hemisphere (expecially frontal and temporal ares). Together with the interparietal influences, this result highlights the importance of interhemispheric relations between bilateral fronto-parietal networks and more globally between bilateral attentional networks [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF].

Alterations of functional connectivity in stroke patients

As highlighted in previous works about motor deficiency and neglect, interhemispheric functional resting-state connectivity was modified in stroke patients [START_REF] He | Breakdown of functional connectivity in frontoparietal networks underlies behavioral deficits in spatial neglect[END_REF][START_REF] Park | Longitudinal changes of resting-state functional connectivity during motor recovery after stroke[END_REF][START_REF] Rehme | Cerebral network disorders after stroke: evidence from imaging-based connectivity analyses of active and resting brain states in humans[END_REF][START_REF] Baldassarre | Large-scale changes in network interactions as a physiological signature of spatial neglect[END_REF]. Although quite visually evident (Fig 2), particularly between the 3 contralesional PPC areas and their homologous regions in the ipsilesional hemisphere, interhemispheric connectivity was not significantly different between stroke patients and healthy controls based on the whole-brain seed-based analysis (probably due to a lack of statistical power because of the small sample size). We have anticipated this result by à priori planning networks analyses comparing connectivity between patients and healthy controls on the basis of the connexions we identified in healthy controls. These analyses revealed that interhemispheric connectivity was altered to the homologous aIPS and SPOC regions but not to the pIPS one. In neglect patients, such a disconnection has been demonstrated at the subacute stage between bilateral pIPS, SPOC and more broadly between bilateral DANs [START_REF] He | Breakdown of functional connectivity in frontoparietal networks underlies behavioral deficits in spatial neglect[END_REF][START_REF] Baldassarre | Large-scale changes in network interactions as a physiological signature of spatial neglect[END_REF].

Intrahemispheric functional connectivity within the contralesional hemisphere was overall less altered than interhemispheric connectivity. Parieto-frontal connections were less efficient only from the aIPS seed, which could be a consequence of their alterations in the lesioned hemisphere in relation to motor deficit [START_REF] Inman | Altered resting-state effective connectivity of fronto-parietal motor control systems on the primary motor network following stroke[END_REF][START_REF] Schulz | Parietofrontal motor pathways and their association with motor function after stroke[END_REF][START_REF] Schulz | Enhanced Effective Connectivity Between Primary Motor Cortex and Intraparietal Sulcus in Well-Recovered Stroke Patients[END_REF].

When modified compared to patients, functional connectivity was always altered in patients in our study, unlike some previous works that found it could be increased for both its intra-and interhemispheric aspects [START_REF] Wang | Dynamic functional reorganization of the motor execution network after stroke[END_REF][START_REF] Baldassarre | Large-scale changes in network interactions as a physiological signature of spatial neglect[END_REF][START_REF] Ramsey | Normalization of network connectivity in hemispatial neglect recovery[END_REF]. However, such an increase in functional connectivity in these studies was shown using a different methodology (a principal component analysis) and

patients were assessed at the subacute phase. Thus, the observed modifications in functional connectivity could be the reflect of transitory functional adaptations due to post-lesional spontaneous cerebral plasticity [START_REF] Wieloch | Mechanisms of neural plasticity following brain injury[END_REF]. In our study, patients were assessed at the chronic stage when spontaneous post-lesional plasticity is no longer present; so, the alteration in connectivity we noticed seem to be the reflect of a long-term intra-and interhemispheric functional disconnection of the contralesonal PPC.

Contrary to what we expected, motor deficiency was not related to functional connectivity between the PPC (whatever the ROI) and the ipsi-and contralesional frontal frontal areas (especially the PMC). However, motor deficiency is not only determined by paresis, it also encompasses pyramidal hypertonia, muscle contractures, sensory loss and disturbances of motor intention or control [START_REF] Gracies | Pathophysiology of spastic paresis. I: Paresis and soft tissue changes[END_REF]; secondly, motor deficiency is mainly determined by the amount of involvement of the pyramidal tract in the lesion [START_REF] Stinear | The PREP algorithm predicts potential for upper limb recovery after stroke[END_REF][START_REF] Puig | Diffusion tensor imaging as a prognostic biomarker for motor recovery and rehabilitation after stroke[END_REF] and by interhemispheric imbalance between sensori-motor networks [START_REF] Loubinoux | Correlation between cerebral reorganization and motor recovery after subcortical infarcts[END_REF][START_REF] Calautti | The relationship between motor deficit and hemisphere activation balance after stroke: A 3T fMRI study[END_REF]). Future works should address other parameters of upper limb function (such as spatiotemporal parameters of movement, activity limitations) to further study the implication of the contralesional PPC in upper limb function deficiency and recovery.

In contrast to motor deficiency, functional connectivity showed links with neglect severity, dependent on the PPC site considered. Previous studies have already found that contralesional connectivity in frontoparietal networks within the contralesional hemisphere, from pIPS and SPOC, was modified and correlated to peripersonal neglect severity [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[END_REF][START_REF] Baldassarre | Large-scale changes in network interactions as a physiological signature of spatial neglect[END_REF][START_REF] Corbetta | Neural basis and recovery of spatial attention deficits in spatial neglect[END_REF][START_REF] He | Breakdown of functional connectivity in frontoparietal networks underlies behavioral deficits in spatial neglect[END_REF]Koch et al. 2008a;[START_REF] Ramsey | Normalization of network connectivity in hemispatial neglect recovery[END_REF]. The present study extends the relationship to behavioral neglect and outlines for the first time (to the best of our knowledge) such relations for aIPS connectivity network. Finally, previous works demonstrated that neglect severity was strongly associated with a decrease in interhemispheric functional connectivity between caudal parts of the PPC and more broadly between DANs [START_REF] He | Breakdown of functional connectivity in frontoparietal networks underlies behavioral deficits in spatial neglect[END_REF][START_REF] Carter | Resting interhemispheric functional magnetic resonance imaging connectivity predicts performance after stroke[END_REF][START_REF] Baldassarre | Large-scale changes in network interactions as a physiological signature of spatial neglect[END_REF][START_REF] Ramsey | Normalization of network connectivity in hemispatial neglect recovery[END_REF], which was normalized in recovered patients [START_REF] Ramsey | Normalization of network connectivity in hemispatial neglect recovery[END_REF].

Alterations of structural connectivity in stroke patients.

In monkeys, it is well demonstrated that the PPC of one hemisphere has dense structural connections to homologous regions in the contralateral one, but studies have also evidenced a smaller number of direct transcallosal connections to motor and somatosensory areas [START_REF] Neal | The callosal connections of area 7b, PF in the monkey[END_REF][START_REF] Padberg | The Organization and Connections of Anterior and Posterior Parietal Cortex in Titi Monkeys: Do New World Monkeys Have an Area 2?[END_REF]. In humans, interparietal pathways have been identified crossing the splenium of the corpus callosum (part IV) [START_REF] Koch | Asymmetry of parietal interhemispheric connections in humans[END_REF]), but to the best of our knowledge direct interhemispheric connections between the PPC and PMC or M1

have never been demonstrated by imaging studies. In our study, structural connectivity was reduced between each of the left PPC area and their homologous brain region in the lesioned hemisphere (extended to surrounding parietal and middle or inferior temporal regions). Such an interparietal anatomical disconnection has been previously evidenced in chronic neglect patients, and was associated with the severity of neglect and a poorer recovery [START_REF] Bozzali | Microstructural damage of the posterior corpus callosum contributes to the clinical severity of neglect[END_REF][START_REF] Lunven | White matter lesional predictors of chronic visual neglect: a longitudinal study[END_REF]. Consistent with this result, even if only found for SPOC, we demonstrated such an association between the severity of peripersonal neglect and the amount of decrease in interparietal connectivity. Impaired interhemispheric structural connectivity has also been demonstrated after stroke in the medial transcallosal fibers, joining the lesioned M1 to the contralesional M1 and surrounding nonprimary motor regions, and were related to motor deficit (Chen and Schlaug 2013). We did not find any difference in structural connectivity between left PPC and frontal areas of the lesioned hemisphere and no relationship between connectivity within any of the network of the PPC areas and motor function. But as we already stated for functional connectivity, upper limb function is determined by many other factors.

Intrahemispheric structural connectivity was preserved except for the SPOC network where it was decreased to frontal, anterior parietal and temporal areas. Such abnormalities within the contralesional hemisphere have already been shown in chronic stroke patients and could be signs of secondary degeneration of areas (and networks) connected to the lesion [START_REF] Crofts | Network analysis detects changes in the contralesional hemisphere following stroke[END_REF]).

In the present study, we used fMRI to guide DTI analyses in order to reduce the number of fiber tracts to be considered and make the analyses more focused and efficient [START_REF] Zhu | Fusing DTI and fMRI data: a survey of methods and applications[END_REF]. Comparing the results of these two analyses may inform on the underlying mechanisms explaining abnormalities of functional connectivity. Especially, our results showed a convergent decrease in functional and structural connectivity of the PPC networks to homologous parietal areas located in the lesioned hemisphere, suggesting that white matter abnormalities explained functional abnormalities [START_REF] Lunven | White matter lesional predictors of chronic visual neglect: a longitudinal study[END_REF]. But we have to bear in mind that abnormalities in functional but not structural connectivity may be observed when the region is not directly anatomically connected to the contralesional PPC (but functionally connected to it via a relay), or if abnormalities are only due to a functional reorganization without microstructural lesions.

Study Limitations

The present study suffered from several limitations. Above all, the sample size was small (particularly considering the N+ patients) and we had to further exclude patients due to difficulties in the preprocessing phase;

this may have led to a lack of statistical power in comparative (patients vs controls) and correlations analyses. To minimize this limit, we à priori planned to compare functional and structural connectivity data in patients vs controls based on the networks individualized in controls (minimizing the number of comparisons compared to a whole brain voxel analysis or a tracks analysis, as confirmed by results of SLF components and inter-parietal structural connectivity analyses we retrospectively performed (appendix 3)). However, this approach did not allow to make subgroup comparisons (especially N+ vs N-patients) and to study the effect of age, gender and time since stroke as covariables. Instead, we considered the continuous aspect of each clinical score when correlate it with connectivity data to improve statistical power. Moreover, in the network analysis we compared patients and controls connectivity on the basis of functional networks identified in controls; this approach did not take into account the possible alternative connections in patients due to brain plasticity. In order to take the step, from association to causal interaction, a quite interesting perspective could be to use effective connectivity approaches. Indeed, Granger causality [START_REF] Bajaj | Functional organization and restoration of the brain motor-execution network after stroke and rehabilitation[END_REF], dynamic causal modelling (DCM) [START_REF] Bajaj | Dominance of the Unaffected Hemisphere Motor Network and Its Role in the Behavior of Chronic Stroke Survivors[END_REF],

or Bayesian search methods, often enable more precise causal inferences, though they are not without their own limitations [START_REF] Reid | Advancing functional connectivity research from association to causation[END_REF]. Afterwards, as shown in Fig 1, the distribution of the lesions was widespread and not homogenous in terms of cortical or subcortical involvement, and we did not study at this time the involvement of right parietal areas in the lesion; in order to better characterize connectivity modifications, an alternative should have been to include only patients who presented subcortical lesions, and an assessment of lesion localization and of connectivity of fronto-parietal networks within the lesioned hemisphere will have to be performed in future studies. Finally, the population of patients was quite heterogeneous with regard to disease characteristics. To reduce this heterogeneity, we included only chronic stroke patients. However, this choice complicated the inclusion of patients with neglect because this impairment often disappears in the months following stroke. Both for spatial neglect and motor deficit, modifications of functional connectivity are more frequent in the subacute than in the chronic phase since they reflect plasticity occurring after a lesion.

Nevertheless, this study is of interest and complementary to those performed at the subacute stage since the modifications we observed at the chronic stage are no longer due to transient plastic phenomena but to long lasting brain rearrangements. Taken as a whole, the results of the present exploratory study shed new lights on parieto-frontal networks plasticity after stroke but have to be considered with caution, and further studies dealing specifically with spatial neglect and motor deficiency, or better integrating holistically these two deficiencies, are still required to better characterize the role of the contralesional PPC areas in post-stroke patients.

Conclusion

Our results revealed that functional and structural connectivity of the contralesional PPC was altered in chronic post-stroke patients. We particularly showed alterations of intrahemispheric functional connexions between the contralesional PPC and posterior frontal regions (especially premotor areas), and interhemispheric functional and structural abnormalities between each part of the contralesional PPC and their homologous area in the ipsilesional hemisphere. Neglect severity but not motor deficiency was associated with alterations in some intraand interhemispheric connectivity patterns. Even if the results of this exploratory study must be confirmed and refined in further larger studies, they shed a new light on the influence of the contralesional PPC in post-stroke patients.

Fig. 1 Lesion overlap map for patients included in the fMRI analysis (at the top) and the DTI analysis (at the bottom). The color scale at the end of each row indicates the proportion of patients with a lesion in that voxel (with higher proportions for colors towards the top of the scale).

Fig. 2

 2 Fig. 2 Functional connectivity of left aIPS (a), pIPS (b) and SPOC (c) in healthy controls (HC) and stroke patients (P), determined in a seed-based approach. L: left hemisphere (lesioned hemisphere in stroke patients) lateral and medial views; SUP: superior view; INF: inferior view; R: right hemisphere medial and lateral view.

Fig. 3

 3 Fig. 3 Functional connectivity of the left aIPS (a), pIPS (b) and SPOC (c) to bilateral frontal areas and the ipsilesional PPC, determined using a network approach. The large red dot represents each seed in the PPC, and green points refer to connected areas identified in healthy controls in a seed-based analysis, considering only bilateral frontal areas and the ipsilesional PPC. Box plots represent the functional connectivity in healthy controls and stroke patients for each network considered; bold lines linking the seed to clusters represent clusters whose connectivity with the seed differed significantly when comparing healthy controls with stroke patients. * p<0.05

Fig. 4

 4 Fig. 4 The relationship between the functional connectivity of each PPC area (a=aIPS, b=pIPS, c=SPOC) and the severity of neglect (as assessed by the bells test, the fluff test and the Catherine Bergego scale (CBS) score). The large red dot represents each seed in the PPC, and green points refer to connected areas identified in healthy controls in a seed-based analysis, considering only bilateral frontal areas and the ipsilesional PPC. The scatter plot of functional connectivity vs. clinical scores highlights the correlations. Bold lines represent networks whose function is correlated with a given clinical score (p<0.05).

Fig. 5

 5 Fig. 5 Structural connectivity of left aIPS (a), pIPS (b) and SPOC (c). The large red dot represents each seed in the PPC, and green points refer to connected areas identified in healthy controls on the basis of the cluster analysis in the rs-fMRI analyses, considering only bilateral frontal areas and the ipsilesional PPC. Box plots represent the FA in healthy controls and stroke patients; bold lines linking the seed to ROIs represent regions whose structural connectivity with the seed differed significantly when comparing healthy controls with stroke patients. * p<0.05

  Q-Q plots. Intergroup comparisons were performed using the Student's t test (or the Mann-Whitney U test, for non-normally distributed data) for quantitative variables and Fisher's exact test for qualitative variables.Correlations between connectivity indices and behavioral assessments were performed using a Spearman correlation test. The threshold for statistical significance was set to p<0.05 and all tests were two-tailed. All statistical analyses were performed with either SPSS software (version 20.0, IBM Corp., Armonk, NY, USA) or MATLAB.

Table 1

 1 Characteristics of stroke patients and healthy controls

		Gender	Age (y)	Stroke type	Median time since stroke (m)	FMA-UE score (out of 66)	Neglect status	Bells test score (total omissions)	Fluff test (left score, out of 15)	CBS score (out of 30)
	Patients (n=11)	M=9 (81.8%)	53.4±14.8	I=8 (72.7%)	11 (158)	36.7±21
	1	F	64	I	7	24	+	7	10	11
	2*	M	58	I	6	60	+	4	12	7
	3*	M	69	I	186	6	+	6	15	4
	4*	M	67	H	6	7	+	9	13	9
	5*	M	40	H	11	33	-	0	15	0
	6*	M	54	I	13	59	-	0	15	0
	7*	M	55	I	99	38	-	3	15	0
	8*	M	67	I	202	33	-	0	14	0
	9	M	20	I	164	23	-	2	15	2
	10	M	41	H	6	62	-	0	15	0
	11*	F	62	I	8	59	-	0	15	0
	Controls (n=13)	M= 10 (75%)	52.8±11.4	-	-	-	-	-	-	-
	Stroke type: I=ischemic; H=hemorrhagic; FMA-UE: upper extremity subsection of the Fugl-Meyer Assessment; CBS:
	Catherine Bergego Scale
	* patients included in the DTI analysis

Table 2 .

 2 Regions showing significant connectivity with each ROI in the PPC (the aIPS, pIPS and SPOC) in healthy controls and stroke patients.

		Healthy controls				Stroke Patients
		Region	Peak MNI Coordinates	Region	Peak MNI Coordinates
			X	Y	Z		X	Y	Z
	aIPS	Left aIPS and sur r oundi ng par i etal ar eas (L. aIPS)	-38	-46	52	Left aIPS and sur r oundi ng par i etal ar eas (L. aIPS)	-40	-52	60
		Left ant inferior frontal gyrus (L. I FG1)	-46	34	-10	Left middle frontal gyrus (L. MFG)	-44	34	34
		Left post inferior frontal gyrus (L. I FG2)	-46	4	36	Left superior frontal gyrus (L. SFG)	-18	2	70
		Right inferior frontal gyrus (R. I FG)	46	42	14	Right aI PS and superior parietal lobule (R.aI PS)	52	-38	48
		Right aI PS and superior parietal lobule (R. aI PS)	32	-68	46	Left inferior temporal gyrus (Left ITG)	-52	-58	0
		Left middle temporal gyrus (L. MTG)	58	-60	-2	Right middle temporal gyrus (Right MTG)	58	-56	-8
		Right postcentral gyrus (R. PG)	58	-22	48
		Right cingulate gyrus (R. CG)	8	20	44
		Right middle temporal gyrus (R. MTG)	-50	-52	-14
	pIPS	Left pIPS and sur r oundi ng par i etal ar eas (L.pIPS)	-28	-70	38	Left pIPS and sur r oundi ng par i etal ar eas (L.pIPS)	-32	-72	46
		Left middle frontal gyrus (L. MFG)	-28	12	62	Left middle frontal gyrus (L. MFG)	-44	30	34
		Left inferior frontal gyrus (L. I FG)	-54	22	16	Left middle temporal gyrus (L. MTG)	-60	-44	-14
		Right pI PS and superior parietal lobule (R. SPL)	26	-68	44	Right inferior parietal lobule (R. IPL)	40	68	38
		Right middle frontal gyrus (R. MFG)	48	12	34	Right cerebelar posterior lobe (R. C)	34	-72	-38
		Left postcentral gyrus (L. PG)	-62	-24	34
		Left inferior temporal gyrus (L. ITG)	-50	-56	-16
		Right inferior temporal gyrus (R. ITG)	56	-54	-16
			-18	-68	58	Left SPOC and sur r oundi ng par i etal ar eas (L. SPOC)	-16	-68	60
		Left middle frontal gyrus (L. MFG)	-20	2	68	Left middle frontal gyrus (L. MFG)	-20	-2	58
		Right SPOC (R. SPOC)	20	-70	50	Right SPOC (R. SPOC)	8	-66	60
		Left postcentral gyrus (L. PG)	-54	-34	50	Left inferior parietal lobule (L. IPL)	-56	-32	32
		Left middle occipital gyrus (L. MOG)	-50	-64	-8	Left lingual gyrus (L. LG)	-16	-86	-18

SPOC

Left SPOC and sur r oundi ng par i etal ar eas (L. SPOC)

Acknowledgment: none

Funding: this work was funded by the 2013 "hospital fund to assist emergence and structuring of activities and research teams" from the Lille University Medical Center, Lille, France; and the Rehabilitation Center of the Lille University Medical Center.

Conflicts of interest: none

Appendix 1

Table . Volume of seeds (mean and standard deviation) in mm 3 for patients and controls in the native T1 space. andL3)) were done using the "DIPY" python package, version 0.14.0 (5). Groups comparisons were performed using Mann-Whitney U test, while correlation analysis between clinical scores (Bells test, Catherine Bergego Scale, Fluff test, FMA) and diffusion parameters were performed using Spearman's correlation test.

Patients (n=11) Controls (n=13

After correction for multiple comparisons (using the False Discovery Rate of Benjamin-), threshold for statistical significance was set to p<0.05.

No significant results were obtained on contralesional and interhemispheric tracks. Only ipsilesional SLF I (p=0.0195) and SLF II (p=0.0223) FA was significantly altered in patients vs controls. In addition, we did not show any behavioral/connectivity correlation.


V Almeida

A Cameirão

J-M Herri

P Glenat

Experimental investigation of gas hydrate plugging mechanisms in pipelines and the influence of the flow pattern

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Experimental investigation of gas hydrate plugging mechanisms in pipelines and the influence of the flow pattern

Vinicius Almeida, Ana Cameirao, Jean-Michel Herri, Philippe Glenat

To cite this version:

Vinicius

Expected results

Experimental methodology

Operational conditions:  100-500 l/h  Up to 80 bar  0-30 °C  ~50m  Water, oil, gas, AA, salt

  Almeida, Ana Cameirao, Jean-Michel Herri, Philippe Glenat. Experimental investigation of gas hydrate plugging mechanisms in pipelines and the influence of the flow pattern. Journée Scientifique 2018 du Codegepra, Nov 2018, Saint-Etienne, France. , Journée scientifique du CODEGEPRA -Le Génie des Procédés en Rhône-Alpes Auvergne, pp.32/P22. hal-03185913 Introduction Objectives:  Influence of GLL flow pattern on hydrate formation and plugging  Agglomeration and deposition over time and space  Understanding the mechanisms of Anti Agglomerant additives

Conclusions

  Few understanding on literature about high water cut systems  Acoustic emission to follow the crystallization, the flow and the deposition in the pipeline over time and space is a relatively new approach  Anti-agglomeration behavior mechanisms are still not well understood  Need to understand the effects of salt on reducing the risk of plugging showing hydrate crystals 100% WC, 200 l/h Pressure drop, chord length distribution and absolute energy for an experiment with 40% water cut and 400 L/h (gas injection at 56 min, hydrates formation onset at 85 min). (Cameirao et al., 2018)Context  Flow assurance with gas hydrates in oil and gas pipelines Plugging tendencies according to the oil-water flow pattern  Influence of a commercial anti-agglomerant and salt Oil-water flow patterns commonly reported in the literature (Adapted fromBrauner, 2004)


Glide -high vowel alternation at the syntax-phonology interface

Mohamed

Introduction

Anyone who has once thumbed through a textbook on Amazigh (Berber) phonology has probably come across one of the most productive processes in the language, namely the alternation of glides and high vowels, some aspects of which still challenge standard phonological theories. In Tashlhiyt, like in many other Amazigh varieties, glides typically appear in the immediate vicinity of a vowel, in complementary distribution with the corresponding high vowels, as the following examples illustrate (the alternating segments are in bold):

(1) gru 'pick up' agraw 'assembly' bri 'crush' abraj 'crushed seeds' nu 'be cooked' tinwi 'cooking'

Standard analyses generally address this issue from a syllabic point of view, claiming that glides and high vowels are phonetic reflexes of two underlying high vocoids I and U. These vocoids surface as high vowels when attached to a nucleus position, and as glides when associated to margin positions (cf. [START_REF] Bensoukas | Stem forms in non-templatic morphology of Berber[END_REF]: 35, Boukhris et al. 2008: 23, Dell & Elmedlaoui 2002: 190-198, Iazzi 2018: 429, Lahrouchi 2001, 2010[START_REF] Lahrouchi | A propos de I et de U en berbère : de la phonologie, de la morphologie et des phases[END_REF][START_REF] Lahrouchi | Peripheral vowels in Tashlhiyt Berber are phonologically long: Evidence from Tagnawt[END_REF][START_REF] Lahrouchi | From babbling to first words in Tashlhiyt language acquisition: a longitudinal two-case study[END_REF]: 504, Ridouane 2014: 214, among others).

The problem with the above generalization arises when considering contexts where the underlying vocoids surface as high vowels when they should normally be realized as glides. Let us consider the dative forms of the verbs gru and bri, compared to those of skr 'do' and fk 'give':

(2) Verb Dative a. gru gru-j-as bri bri-j-as b. skr skr-as fk fk-as

From the examples in (2b), one concludes that the phonological form of the dative morpheme is /as/, immediately following the final consonant of the verb base. When attached to verbs like in (2a), the initial vowel of the dative marker should normally allow the verb's final vocoid to surface as a glide, leading to the forms *grwas and brjas. Instead, the high vocoids are realized as vowels, resulting in a hiatus context which is then resolved by means of j-epenthesis.

The question then arises as to whether this type of phonological opacity [START_REF] Kiparsky | Abstractness, Opacity, and Global Rules[END_REF]) can be addressed without having recourse to any specific boundaries, junctures [START_REF] Trager | Some thoughts on juncture[END_REF][START_REF] Lehiste | Juncture[END_REF], phonological cycles [START_REF] Kiparsky | From cyclic to lexical phonology[END_REF](Kiparsky , 1985) ) or any other morpheme-specific phonology [START_REF] Pater | Morpheme-Specific Phonology: Constraint Indexation and Inconsistency Resolution[END_REF].

The key to understanding this phenomenon lies, we argue, in the morpho-syntactic structure of the forms at stake. In line with recent works at the syntax -phonology interface (cf. [START_REF] Marvin | Topics in the stress and syntax of words[END_REF][START_REF] Marantz | Phases and words[END_REF], Newell & Pigott 2014, Samuels 2010, among others), we claim that the behavior of the high vocoids in the forms of the type in (1) and ( 2) is the result of the application of spell-out and phase impenetrability condition [START_REF] Chomsky | Derivation by phase[END_REF] at different levels in the syntactic structure. In particular, we show that vP corresponds to a phase where I and U are spelled-out as high vowels before the dative enclitic /-as/ is added. The hiatus is then resolved by means of j-epenthesis, leading to grujas and brijas. In agraw and abraj, U and I surface as glides since they belong to the same phase (nP) as the neighboring vowel /a/.

External evidence in favor of this analysis will be drawn from the phenomenon of emphasis spread. It will be shown that the emphatic coronals spread their feature to the neighboring segments within the vP and nP domains. That is, verbal and nominal bases containing an emphatic consonant will be entirely emphaticized, to the exclusion of their suffixes which will remain unaffected.

The paper is structured as follows. Section 2 presents the data more fully, and illustrates the set of alternations just outlined. It also explains how the standard syllabic approach to theses alternations remains valid, provided that extra-phonological information is taken into account. The examples in this paper are all from the Tashlhiyt variety, but the facts are similar in other Amazigh varieties (cf. [START_REF] Destaing | Etude sur le dialecte berbère des Ait Seghrouchen[END_REF], Basset 1952[START_REF] Appelgate | The Berber Languages[END_REF][START_REF] Guerssel | Glides in Berber and syllabicity[END_REF][START_REF] Maarten | Berber Phonology[END_REF]: 467, Iazzi 2018: 429, among others). Section 3 provides the theoretical background necessary to understanding the proposed analysis. Our phase-based analysis is presented in section 4. Section 5 provides another piece of evidence in favor of our analysis: It will be shown that emphasis spreads within the domains of nP and vP, exactly where glides alternate with high vowels. Section 6 concludes the paper.

Glide vs. high vowels: features, representations and alternations

Amazigh phonemic system: an outline

Tashlhiyt, like almost all other Amazigh varieties, has a simple vocalic system with three phonemic vowels /i, a, u/, and a central short vowel, generally referred as to schwa [ə], whose phonological status is highly controversial. According to many scholars (Dell & Elmedlaoui 2002, Ridouane 2008, among others), this short vowel found in certain consonant clusters is a mere transitional vocoid that has no syllabic status (contra. [START_REF] Coleman | Declarative syllabification in Tashlhiyt Berber[END_REF][START_REF] Puech | Syllabification in Berber: The case of Tashlhiyt[END_REF], 2001[START_REF] Puech | Syllabification in Berber: The case of Tashlhiyt[END_REF].

As to consonants, Tashlhiyt has 35 phonemic units (including the glides /j, w/), each of which has a geminate counterpart. Although the phonemic status of the two glides is clearly established, as they contrast underlyingly with high vowels (e.g. rwl 'escape' / ruħ 'go away', rˤmi 'be tired' / rwi 'soil') and like any other consonant they undergo imperfective gemination (e.g. lkkm 'arrive.imperf' / rwwi 'soil.imperf'), they very often appear in complementary distribution with the corresponding high vowels (further discussion and data in section 2.3). This fact has led many linguists to claim that both glides and high vowels are merely phonetic reflexes of the same underlying segments, whose syllabic representations can easily account for their surface realization.

Glides vs. high vowels: features and representations

Glides, also termed semi-consonants or semi-vowels, have been largely documented in the literature, from both empirical and theoretical points of view. Their behavior has constantly posed a problem to phonological theory. On the one hand, they closely interact with vowels, alternating with them in various well-defined contexts, not only in the language under scrutiny, but also in many other typologically unrelated languages (see [START_REF] Rosenthal | Vowel-glide alternation in a theory of constraint interaction[END_REF][START_REF] Padgett | Glides, vowels and features[END_REF][START_REF] Levi | Glides[END_REF]. On the other hand, they behave as consonants, underlyingly contrasting with vowels.

With the advent of syllable theory, many phonologists have proposed that the difference between vowels and glides can be derived directly from syllable structure (cf. [START_REF] Clements | CV Phonology: A generative theory of the syllable[END_REF][START_REF] Kaye | [END_REF][START_REF] Levin | A Metrical Theory of Syllabicity[END_REF][START_REF] Selkirk | Syllables[END_REF][START_REF] Selkirk | On the major class features and syllable theory[END_REF], thus making redundant the standard SPE featural distinctions: [±vocalic], [±consonantal], [±syllabic] (Chomsky & Halle 1968: 303, 354), and [±approximant] (Clements 1990: 293). That is, vowels appear in the syllable nucleus, whereas glides attach to coda and onset positions. In this respect, Kaye & Lowenstamm (1984: 130-138) claimed that in French, the high vocoids /U/ and /I/ are realized as vowels in verbs like loue 'rent.IMPERATIVE.SG' and lie 'tie.IMPERATIVE.SG', and as glides in the corresponding infinitive forms louer and lier. This is illustrated in the representations in (3).

(3) a. [lu], [li] b

. [lwe], [lje]

The underlying segments /U, I/ behave as syllabic in (3a), while they form part of a complex onset in (3b). Their position in the syllable structure allows assigning them a phonetic interpretation, without the mediation of any specific feature. The same reasoning underlies the representation of alternating glides and high vowels in Amazigh, as it will be shown in the next section.

Glide -high vowel alternations in Amazigh

This section provides the empirical basis for the generalizations briefly introduced in the previous sections, through a closer, fuller examination of the glide-high vowel alternations in Tashlhiyt.

Contexts of alternation

The paradigm in (4) elaborates on ( 1 Each pair in these examples clearly shows how the verb's final vowel turns into a glide when for morphological reasons a vowel appears in its immediate vicinity: this is especially the case for the infix -a-, which is inserted after the stem's second consonant (and which is similarly found in derivations like sʁr 'to dry' > asʁar 'wood, tree', frs 'be sharp' > afras 'sharpening'). This ( 5)

SG PL iflu iflwan 'plank' ikru ikrwan 'kid' amdlu imdlawn 'cloud'
The plural suffix -an (also found in forms like ifrg-an 'enclosure' (< SG ifrg) and ifr-an 'caves' (< SG ifri)) is responsible for the semi-vocalization of final [u] of the singular form. Many other formations exhibit similar patterns in Amazigh, including the construct state forms whose vowel marker [u-] alternates with [w-] (e.g. u-frux 'boy.CS' vs. w-adgal 'widower.CS'; cf. Dell & Elmedlaoui 2002[START_REF] Lahrouchi | On the internal structure of Tashlhiyt Berber triconsonantal roots[END_REF], 2013, among others) and the perfective forms where the 3MS marker [i-] alternates with [j-] (e.g. i-skr 'he did' vs. j-ukr 'he stole'). The focus on the forms of the type in (4) and (5) will become more evident when analyzing their datives and demonstratives, whose final high vowels resist alternation. The basic rule underlying all of the examples examined so far is the avoidance of any hiatus context: semi-vocalization is one of these strategies that Amazigh utilizes in this respect.1 Many Amazigh phonologists have analyzed these alternating segments as variants of the same underlying segments, whose realizations are fully derivable from their position in the syllable structure, (cf. [START_REF] Dell | Syllabic Consonants and Syllabification in Imdlawn Tashlhiyt Berber[END_REF][START_REF] Marvin | Topics in the stress and syntax of words[END_REF], Bensouskas 1994, 2001[START_REF] Lahrouchi | Aspects morpho-phonologiques de la dérivation verbale en berbère tachelhit[END_REF][START_REF] Lahrouchi | A propos de I et de U en berbère : de la phonologie, de la morphologie et des phases[END_REF][START_REF] Lahrouchi | Peripheral vowels in Tashlhiyt Berber are phonologically long: Evidence from Tagnawt[END_REF][START_REF] Soutsane | Syllabification and phonological rule application in Tashlhiyt Berber[END_REF], Ridouane 2014, among others). In line with standard approaches to syllable structure (cf. [START_REF] Pike | Immediate constituents of Mazateco syllables[END_REF][START_REF] Levin | A Metrical Theory of Syllabicity[END_REF][START_REF] Blevins | The syllable in phonological theory[END_REF]; see also [START_REF] Bosch | Syllable-internal structure[END_REF][START_REF] Goldsmith | Syllables[END_REF], and Scheer 2015 for detailed reviews of the relevant literature), the representation of the verb gru 'pick up' and its nominal form agraw 'assembly' is shown in ( 6).

(6) a. [gru] b

. [agraw]

A thorough discussion of the above syllabic representations and the ability for any segment to be syllabic in Tashlhiyt would take us beyond the scope of this paper (cf. [START_REF] Dell | Syllabic Consonants and Syllabification in Imdlawn Tashlhiyt Berber[END_REF][START_REF] Marvin | Topics in the stress and syntax of words[END_REF][START_REF] Boukous | Phonotactique et domaines prosodiques en berbère[END_REF], and Lahrouchi 2018). We simply draw the reader's attention to the syllabic positions where the vocoid /U/ appears: When attached to a nucleus position, the vocoid is realized as a high vowel (6a), while it surfaces as a glide when associated to a margin position (6b). Similar representations hold for the vocoid /I/ in words like bri 'crush' and abraj 'crushed seeds'. The reader is also referred to Dell & Elmedlaoui (2002: 198) for similar syllabic representations of the high vocoids /I/ and /U/ in words like t-suj 'she let pass' and t-zwi 'she beat down'.

The syllabic approach entirely accounts for the high vowel-glide alternations that occur within a specific domain, which the present study aims to define in a principled way. The following section turns to cases where the so far called 'alternating high vowels' cease to undergo alternation.

Lack of alternation

One striking context in which the high vowels of the forms in (4) resist alternation arises with the dative and 3 rd person object suffix /-as/. This is shown in the following examples.

( Unlike in (4), the verbs final vowels resist gliding even though they are immediately followed by a vowel initial suffix. In such a context, the high vowels should normally surface as glides, leading to the dative forms *grwas and *brjas, to take but two examples. Instead, a glide [j] is inserted in order to avoid hiatus.

The same phenomenon takes place in the nominal forms of the type in (5). The high vowels of their singular forms resist alternation when immediately preceding the demonstrative enclitic /-ad/, as shown in ( 8).

(8) Noun Noun+Demonstrative iflu 'plank' iflu-j-ad 'this plank' ikru 'kid' ikru-j-ad 'this kid' amdlu 'cloud' amdlu-j-ad 'this cloud'

Based on similar facts in Tamazight, Guerssel (1986: 03) claimed that the difference observed between non-alternating high vowels as in t-uri 'she wrote' vs. t-uri-j-ax 'she wrote us' (not *turjax), and t-essu 'she made a bed' vs. t-essu-j-ax 'she made us a bed' (not *tesswax) and alternating ones like in i-ru 'he cried' vs. aha j-ru 'then he cried' receives "a natural explanation if a phonemic distinction between glides and high vowels is established."

This has been proposed in the case of Tamazight. The data under scrutiny hardly fit into such an analysis for the very simple reason that the final high vowels in ( 7) and ( 8) actually undergo alternation within the stem domain, as shown previously in the examples in ( 4) and (5). They resist alternation only when followed by certain vowel initial suffixes, such as the dative -as and the demonstrative -ad. While keeping a syllabic approach to these alternations, we will call on those formal mechanisms which integrate extra-phonological information capable of explaining why alternating segments cease to do so beyond a certain domain. Cyclic derivation at the interface between syntax and phonology, nowadays referred as to "phases", is one such device which better accounts for these paradoxical cases where the same underlying segments may or may not undergo alternation. Before expanding on this issue, we provide some theoretical background necessary to understanding our analysis.

Boundaries, phases and spell-out: The basics

Grammatical carriers in phonology

One undeniable property which characterizes the contexts in which alternating high vowels cease to do so is that they contain a boundary between the stem and the enclitic (dative -as and demonstrative -ad). The question is what the exact nature of these boundaries is and how they affect the phonological interpretation of sound strings. Do they carry any morphosyntactic information which impacts phonology? Many studies have long been investigating various phenomena whereby automatic phonological processes fail to occur when they come up against a certain type of boundaries. Back in the 1960's, structuralist phonologists (cf. Kager 1962, and[START_REF] Lehiste | Juncture[END_REF]) drew a distinction between phonemes as basic units of phonological analysis and juncture phonemes as carriers of grammatical information in phonology. Generative phonologists resorted to similar objects, including classical SPE types of diacritics (# and the like) and prosodic constituents (ω, φ and the like), as means by which phonologically relevant domains are delimited. These so-called representational ways of implementing morphosyntactic information in phonology are distinguished from derivational solutions, successively known as transformational cycles (Chomsky 1966), phonological cycles, levels or strata [START_REF] Mascaró | Catalan phonology and the phonological cycle[END_REF][START_REF] Kiparsky | From cyclic to lexical phonology[END_REF], 1985[START_REF] Mohanan | Lexical phonology[END_REF][START_REF] Bermúdez-Otero | Cyclicity[END_REF], and phases [START_REF] Chomsky | Derivation by phase[END_REF][START_REF] Chomsky | On phases[END_REF]. The reader is referred to [START_REF] Scheer | A Guide to morphosyntax-phonology interface theory[END_REF] for a thorough review of the relevant literature.

Derivation by phase

Derivation by phase allows for a model of grammar in which pre-specified chunks of syntactic structure are sent to the phonological and semantic components. According to [START_REF] Chomsky | Derivation by phase[END_REF][START_REF] Chomsky | On phases[END_REF], vP and CP correspond to phases, within which lexical material is inserted and constituents may move up to higher syntactic positions. Generalizing from vP, [START_REF] Marantz | Words. Ms[END_REF][START_REF] Marantz | Phases and words[END_REF] claims that any category-forming projection uniformly defines a phase within which the phonological and semantic properties of words are interpreted.

Relying on these proposals, many studies have addressed various non-automatic phonological processes that standard analyses fail to capture in a satisfactory manner. In her fundamental work, [START_REF] Marvin | Topics in the stress and syntax of words[END_REF] addressed among other phenomena the opacity characterizing schwa-insertion in words like meter [mi:tər], metering [mi:təriŋ], and metric [mεtrik]. She argued that the adjectival suffix -ic which prevents schwa from appearing in metric is spelled out in the same phase as /metr/, as opposed to the gerund suffix -ing which is added later in the syntactic structure, once /metr/ is spelled out along with its schwa (see also Marvin 2013 for a phase-based account of stress assignment in English). The Phase Impenetrability Condition [START_REF] Chomsky | Derivation by phase[END_REF]) allows explaining why a previously spelled-out schwa resists deletion. Various phenomena in languages like German [START_REF] Kratzer | Phase theory and prosodic spellout: The case of verbs[END_REF], Basque [START_REF] Samuels | Phonological derivation by phase: evidence from Basque[END_REF], Ojbwe [START_REF] Newell | Interactions at the syntax-phonology interface: Evidence from Ojibwe[END_REF], Abruzzese [START_REF] D'alessandro | Modular PIC[END_REF], and Kiowa [START_REF] Miller | Polysynthesis at the Phonology-Syntax Interface: A Case Study of Kiowa and Saulteaux Ojibwe[END_REF], have since been analyzed in a comparable manner, despite differences in the versions of phase theory and the direct vs. indirect reference to morphosyntactic categories (cf. [START_REF] Scheer | Why the prosodic hierarchy is a diacritic and why the interface must be direct[END_REF][START_REF] Scheer | A Guide to morphosyntax-phonology interface theory[END_REF]. The common denominator of these studies is that morpho-syntactic chunks which correspond to phases locally determine the domain of application of certain phonological processes.

Unlike phonological cycles which may appear as ad hoc stipulations and which lack any external evidence, phases have independent morpho-syntactic motivation, outside the realm of phonology. Moreover, derivation by phase allows specific chunks to be spelled-out, thus leading to a grammar whose computation is much simpler in terms of memory load and processing.

In the following section, we return to glide-high vowel alternations. We argue that phasal spell-out better explains why high vowels fail to alternate with glides when followed by certain vowel-initial suffixes.

Phasal spell-out of the high vocoids I, U

The crux of the matter lies, as we have seen in section 1.3, in the non-alternation of final high vowels with glides in verbs like bri 'crush' and gru 'pick up'. When adjacent to the vowelinitial dative enclitic /-as/, [i] and [u] should normally surface as glides, especially since they do so in the corresponding nominal forms abraj 'crushed seeds ' and agraw 'assembly'. Instead, a glide [j] is inserted between the verb's final vowel and the enclitic in order to resolve hiatus, leading to brijas 'crush him/her' and grujas 'pick for him/her'. Similarly, the final high vowels of singular nouns like iflu 'plank' and ikru 'kid', which surface as glides in the corresponding plural forms iflw-an and ikrw-an, paradoxically remain unchanged when followed by the demonstrative suffix /-ad/.

The key to understanding these opaque cases lies in the syntactic structure of the dative and demonstrative forms. The failure of the high vowels to change into glides in the dative forms receives a natural explanation once we assume that the verbal projection (vP) constitutes a phase, within which the phonological and semantic features of the verb base are fully interpreted. More specifically, the high vocoids of verbs like gru and bri are spelled out inside the vP phase as vowels before the dative enclitic /-as/ is added. The phase domain within which these verbs are interpreted is rendered opaque to further operations, including the suffixation of the dative enclitic, whose initial vowel cannot recover the phonological identity of the verb's final segment, hence j-epenthesis. This is illustrated in the structures in (9a) and (9b), as opposed to the ones in (9c) and (9d) where the same vocoids undergo semi-vocalization in the corresponding nominal forms.

(9) a. gru-j-as 'pick up for him!' b. bri-j-as 'crush for him!' c. agraw 'assembly' d. abraj 'crushed seeds'

These structures are simplified for expository reasons. The reader is referred to [START_REF] Ouhalla | The syntax of head movement: A study of Berber[END_REF], [START_REF] Ouali | Agreement, pronominal clitics and negation in Tamazight Berber[END_REF], [START_REF] Achab | Internal structure of verb meaning: A study of verbs in Tamazight (Berber)[END_REF], among others, for a thorough treatment of verb and clause structure in Amazigh. Of immediate concern is that the dative clitic is base-generated outside the vP domain, as the structures in (9a, b) illustrate (cf. Boukhris 1998[START_REF] Ouali | Verb Movement and Object Pronominal Clitic Distribution in Berber[END_REF], 2011, and Omari 2012 on this issue). Under the assumption that Phase Impenetrability condition holds in phonology, the phonological string spelled-out within the vP domain becomes inaccessible to subsequent operations, leading to a situation where the high vocoids I and U are realized as vowels before the dative clitic is added. The resulting hiatus is then resolved by means of jepenthesis. In other words, the rule regulating glide-high vowel alternations holds only within the same domain/phase: The high vocoids I and U surface as glides when adjacent to a vowel, as in the forms represented in (9c, d), and as vowels elsewhere.

The same reasoning holds for nouns like iflu 'plank' and ikru 'kid', previously introduced in ( 5) and ( 8): Their high vowel turns into a glide when followed by the plural suffix -an, while it remains unchanged when followed by the demonstrative clitic -ad. The reason, we argue, is that the high vocoid U is spelled-out along with the plural suffix within the same phase (nP). Conversely, the demonstrative marker is generated higher in the structure, once the high vocoid is spelled-out as a vowel. The representations in (10) illustrate both situations.

(10) a. iflw-an 'plank.pl' b. iflu-j-ad 'this plank'

Two observations are in order. First, number and plurality are assumed to be realized as a feature under the head of noun phrase, as shown in (10a) (see [START_REF] Lowenstamm | On little n, √, and types of nouns[END_REF][START_REF] Acquaviva | Lexical plurals: A morphosemantic approach[END_REF][START_REF] Kramer | A split analysis of plurality: Evidence from Amharic[END_REF]. Second, the demonstrative marker -ad heads its own projection below DP, as shown in (10b). The linear order (postposed to the noun) is derived through movement of N to the D position. The reader is referred to Belkadi (2017: 117) for further details and references, and to El Moujahid (1997: 223) for an alternative analysis according to which the demonstrative acts as a complement of N.

The crucial point about the above structures is that the high vocoid U surfaces as a glide in (10a) since it is spelled out along with the plural marker within the same phase nP. Conversely, it surfaces as a vowel in (10b) because it is spelled out before the vowel-initial suffix /-ad/ is added. The resulting hiatus is then resolved by means of j-epenthesis, exactly like in (9a) and (9b).

External evidence in favor of this analysis is drawn from emphasis spread. In the next section, we show that phasal spell-out better explains how the verbal and nominal bases containing an emphatic consonant are entirely pharyngealized, to the exclusion of any segmental material generated outside the domains of vP and nP.

Emphasis spread in verbs and nouns: acoustic data

Emphasis, also called dorsopharyngealization, refers to a secondary articulation whereby a specific set of Tashlhiyt consonants is produced with a backward movement of the tongue towards the posterior pharyngeal wall, while the anterior part of the tongue is lowered [START_REF] Ridouane | Pharyngealization and pharyngeal Tashlhiyt in Berber: A descriptive and comparative study[END_REF]. At the phonemic level, emphasis is a property of individual segments. Tashlhiyt includes the following set of emphatic consonants, all of which are coronal : /tˁ, tːˁ, dˁ, dːˁ, sˁ, sːˁ, zˁ, zːˁ, ʒˁ, ʒːˁ, rˁ, rːˁ, lˁ, lːˁ/ (Elmoujahid 1979[START_REF] Elmedlaoui | Le parler berbère chleuh d'Imdlawn Maroc: Segments et syllabation[END_REF], 1995[START_REF] Boukous | Phonotactique et domaines prosodiques en berbère[END_REF][START_REF] Boukous | Pharyngalisation et domaines prosodiques en berbère[END_REF][START_REF] Lasri | Aspects de la phonologie non-linéaire du parler berbère chleuh de Tidli[END_REF], Dell and Elmedlaoui 2002).

At the surface level, dorsopharyngealization is a property that can be displayed by any segment; an instance of emphasis spread by which underlying pharyngealized coronals spread their secondary articulation on neighboring sounds. For instance, the form /matˁiʃa/ 'tomato' contains one underlying emphatic coronal /tˁ/, but all the segments contained in the word can be phonetically dorsopharyngealized [mˁaˁtˁiˁʃˁaˁ]. Pharyngealized words may be composed of emphatic coronals only (e.g. [sˁrˁdˁ] 'to file a complaint'). In such items there is no principled way of determining whether only one or more coronals are underlyingly dorsopharyngealized.

The exact delimitation of the propagation of dorsopharyngealization is not clearly established. The segments in a CV sequence must be both plain or both emphatic. This requirement must be satisfied regardless of the morpho-syntactic relationship between C and V (Dell & Elmedlaoui 2002). But it is generally considered that the domain of this propagation may be larger than the word [START_REF] Elmedlaoui | Le parler berbère chleuh d'Imdlawn Maroc: Segments et syllabation[END_REF], 1995[START_REF] Boukous | Pharyngalisation et domaines prosodiques en berbère[END_REF][START_REF] Lasri | Aspects de la phonologie non-linéaire du parler berbère chleuh de Tidli[END_REF]. There are important acoustic differences between pharyngealized coronals and their plain counterparts, which induce highly salient auditory differences between items containing emphatic consonants and items containing plain ones. The most important and consistent difference is manifested by a lowering of F2 of the vowels contained in the emphatic items. This pattern has been extensively shown in different Arabic varieties, including Moroccan Arabic [START_REF] Yeou | Locus equations and the degree of coarticulation of Arabic consonants[END_REF][START_REF] Zeroual | Propos controversés sur la phonétique et la phonologie de l'arabe marocain[END_REF][START_REF] Lahrouchi | On diminutives and plurals in Moroccan Arabic[END_REF]). The same pattern has been observed in Tashlhiyt. [START_REF] Ridouane | Suites de consonnes en berbère: phonétique et phonologie[END_REF], based on vowel productions in the context of /tˁ/ and its plain counterpart /t/ (e.g. [atˁa] vs. [ata]) by 5 Tashlhiyt speakers, showed that emphasis lowers F2 of the adjacent vowels in a systematic way. In this context the realization of the vowel /a/ is close to back [ɑ].

We conducted a pilot acoustic study in order to determine whether the vowel /a/ in the dative enclitic /-as/ and the demonstrative /-ad/ is affected by the presence of emphatic consonants within the same words. The acoustic data were recorded by two subjects producing 6 pairs of words contrasting emphatic to plain consonants in verbal and nominal forms. Each pair was repeated 3 times by each speaker. The data set is presented in (11) below. We measured F2 values at the midpoint of the vowel /a/ (bolded in the data below).

(11) List of items used in the acoustic experiment Verbs bdu-j-as 'begin' bdˤu-j-as 'divide' ndu-j-as 'demolish' ndˤu-j-as 'jump' mdi-j-as 'trap, intercept' mdˤi-j-as 'taste' Nouns ssif-ad 'sword' ssˤif-ad 'summer' adan-ad 'bowls' adˤan-ad 'nights' izri-j-ad 'mugwort' izˤrˤi-j-ad 'sight'

From our perspective, segmental material generated outside the domains of vP and nP will not be affected by emphasis spread. According to this view, the vowel /a/ in /-as/ and /-ad/ will have similar F2 values whether the base contains an emphatic consonant or not. That is, the vowel /a/ in the words /bdu-j-as/ and /bdˤu-j-as/, for example, will display similar F2 values although the latter word has an emphatic consonant. This is exactly what the results of our study show. The vowel /a/ displays virtually identical F2 values in both the emphatic and non-emphatic contexts. This pattern is illustrated in Figure 1. The reason why the vowel of the dative and demonstrative suffixes resist emphasis is the same which, from our point of view, prevents the stem final vowel from surfacing as a glide, as previously discussed in section 4. In other words, vP and nP demarcate a phase, wherein emphasis spreads and glides alternate with the corresponding high vowels.

Conclusion

In this study, we have accounted for glide-high vowel alternations in Amazigh at the interface between syntax and phonology. This phenomenon which has long resisted exclusively phonological analyses, has been argued to occur within specific syntactic domains, corresponding to phases (vP and nP) wherein I and U in words like bri 'scratch' and iflu 'plank' are spelled out as high vowels. Interestingly, these vowels remain unchanged when followed by vowel-initial suffixes generated outside the phasal domain, including the dative /-as/ and the demonstrative /-ad/. Emphasis spread was used as evidence in support of our analysis of glide-high vowel alternation. Based on acoustic data from two subjects, we showed that the dative and demonstrative suffixes, which are generated outside vP and nP domains, remain unaffected by emphasis spread, whether their base contains an emphatic consonant or not.

  Lahrouchi 1 & Rachid Ridouane 2 1 CNRS & Université Paris 8 2 CNRS & Université Paris 3

  infix allows [u] to change into [w] (4a) and [i] into [j] (4b). The affixal vowel can also appear after the target segment, like in the nominal form tinwi where [i] turns the stem's final [u] into [w]. Similar alternations are found in plural nouns, as shown in the examples in (5).

Figure 1 .

 1 Figure 1. F2 values (Hz) of the vowel /a/ in emphatic and non-emphatic contexts for the two subjects S1 and S2.

  ) above. It shows the structural environments where high vowels alternate with glides.

	(4) Verb		Noun
	a.	gru	'pick up'	agraw	'assembly'
		xlu	'destroy'	amxlaw	'madman'
		aru	'give birth to' arraw	'child'
		nu	'be cooked'	tinwi	'cooking'
	b. bri	'crush'	abraj	'crushed seeds'
		sti	'sort'	astaj	'sorting'
		fsi	'untie'	afssaj	'untying'
		ngi	'overflow'	angaj	'overflowing'
		mlilli	'feel dizzy'	timlillaj	'dizziness'

In Amazigh, hiatus may also be resolved by means of j-epenthesis, a fact we will be highlighting in subsequent sections (e.g. fk-as 'give him' vs. ini-j-as 'tell him') or by deletion of one of the vowels in contact (e.g. afus-inu 'my hand' vs. tasa-nu 'my liver, my dear', azˤrˤu (SG) vs. izˤrˤ-an (PL) 'stone', itri (SG) vs. itr-an (PL) 'star'). The reader is referred to[START_REF] Boukous | La formation du glide en Tamazight (dialecte tachelhit)[END_REF]

2009) andIazzi (2018: 459) for further details and analysis.