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

Hervé Devanne

Arnaud Delval

Contribution of transcranial magnetic stimulation in assessing parietofrontal connectivity during gesture production in healthy individuals and braininjured patients

Keywords: parietofrontal networks, reaching, grasping, transcranial magnetic stimulation, posterior parietal cortex AG: angular gyrus, aIPS: anterior part of the intraparietal sulcus, CS: conditioning stimulus, dPM: dorsal premotor, IPS: intraparietal sulcus, MEP: motor evoked potential, M1: primary motor cortex, OA: optic ataxia, PF: parietofrontal, pIPS: posterior part of the intraparietal sulcus, PPC: posterior parietal cortex, ppTMS : paired-pulse transcranial magnetic stimulation, rTMS : repeated transcranial magnetic stimulation, SLF: superior longitudinal fasciculus, SPL: superior parietal lobule, SPOC: superior parieto-occipital cortex, TMS: transcranial magnetic stimulation, TS: test stimulus, vPM: ventral premotor

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Contribution of transcranial magnetic stimulation in assessing parietofrontal connectivity during gesture production in healthy individuals and brain-injured patients

Introduction

Prehension and object use allow us to interact with objects and our environment in daily life. These actions do not merely correspond to the execution of a motor program but encompass a number of cognitive-motor steps (from decision to action). Put simply, the movement process begins with the intention of movement and is followed by the integration of sensory information. The movements are planned, and motor programs are encoded and then executed and controlled by different feedback mechanisms. The appropriate execution of these successive steps requires the involvement of several disseminated networks. Here, we review the role of parietofrontal (PF) networks (connecting the posterior parietal cortex (PPC) to frontal regions) in the planning and online control of visually guided movements of the upper limb. These networks' physiological roles in many other behaviors have been frequently demonstrated, notably using electrophysiological methods. This is particularly true for the control of spatial attention, where the posterior part of the intraparietal sulcus (pIPS) and then the dorsal PF network have a role in the control of endogenous attention [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF][START_REF] Koch | Hyperexcitability of parietal-motor functional connections in the intact left-hemisphere of patients with neglect[END_REF][START_REF] Koch | Asymmetry of parietal interhemispheric connections in humans[END_REF], emotions [START_REF] Grosbras | Dance and emotion in posterior parietal cortex: a low-frequency rTMS study[END_REF][START_REF] Mazzoni | State-Dependent TMS Reveals Representation of Affective Body Movements in the Anterior Intraparietal Cortex[END_REF][START_REF] Wyczesany | Hemispheric asymmetries and emotions: evidence from effective connectivity[END_REF], social cognition [START_REF] Bzdok | Left inferior parietal lobe engagement in social cognition and language[END_REF], visual working memory [START_REF] Klingberg | Development of a superior frontal-intraparietal network for visuo-spatial working memory[END_REF], and mathematical cognition [START_REF] Salillas | Single pulse TMS induced disruption to right and left parietal cortex on addition and multiplication[END_REF][START_REF] Montefinese | Causal role of the posterior parietal cortex for two-digit mental subtraction and addition: A repetitive TMS study[END_REF].

In animal models, the PF networks' physiological roles were long studied via invasive electrophysiological recordings of the neural substrates of visually guided upper limb movements.

More recently, the development of non-invasive in vivo recording techniques in humans -particularly transcranial magnetic stimulation (TMS) -have enabled detailed studies of the roles and spatiotemporal involvement of the different PF network components in gesture processing and production in healthy individuals. Lastly, these data have shed new light on changes in PF network connectivity in disease.

In the present mini-review, we first define upper limb gestures and provide an overview of the anatomical structures and networks encompassing PF streams. We then look at how the use of TMS may be of particular value in this field, before discussing the specific involvement of PF networks in reaching and grasping movements in healthy humans. Lastly, we address connectivity changes in patients with brain damage, and look at how these alterations might be related to neuronal plasticity and impairments in gesture production.

Upper limb gestures

Humans are able to use a wide variety of objects to achieve various goals in daily life. This extended repertoire of actions must be regularly updated in response to the constraints that we have to face.

Praxis corresponds to the ability to produce the right gesture for the use of a given object; along with exposure to object-specific constraints, it involves specific learning processes [START_REF] Vingerhoets | Contribution of the posterior parietal cortex in reaching, grasping, and using objects and tools[END_REF]. Many different paradigms have been used to study upper limb gestures; the paradigms can be divided into two categories, depending on whether they solely address movement of the hand to a target/object that is then grasped, or whether they also address object use (i.e. when transitive movements are performed with the goal of using a specific object in a specific task). For example, a tea cup will be handled differently according to whether it contains tea or is being washed. This aspect relates to the theory of mind, and so will not be considered in the present mini-review. We shall focus here on the neural basis of visually guided reach-to-grasp movement in humans, rather than object use.

Firstly, reaching corresponds to movement of the hand (i.e. the manipulating tool) towards the object, with the goal of matching the respective locations of the hand and the target in the working space. In biomechanical terms, reaching mainly involves shoulder flexion and elbow extension when the movement is performed in the anterior peripersonal space. Secondly, grasping puts the hand and fingers in an appropriate conformation for taking hold of the object. It requires the person to analyze the features of the objects, such as its size, orientation, weight and texture, in order to adequately shape the hand and adjust grasping speed and grip force. It mainly involves pronation-supination movements of the forearm, adequate, stable positioning of the wrist, and a hand aperture that depends on the type of grasp. In summary, one can draw a parallel between upper-limb function and a crane moving its bucket (i.e. its manipulating tool) to the target with its arm, and then grabbing the load. Although reaching and grasping are described as two separate components, their interdependence is revealed by changes in finger aperture during the reaching phase of prehension and the influence of disturbance of one phase on execution of the other [START_REF] Castiello | The neuroscience of grasping[END_REF][START_REF] Haggard | Coordinated responses following mechanical perturbation of the arm during prehension[END_REF].

Anatomy of the PPC and parietofrontal networks

The PPC is located within the parietal lobe, behind the post-central sulcus. It is divided into a medial region, the precuneus, and a lateral part. In turn, the lateral part of the PPC is divided into superior and inferior parietal lobules, which are separated by the intraparietal sulcus (IPS) (Figure 1). The inferior lobule encompasses the angular gyrus (AG, Brodmann area 39) and the supramarginal gyrus (Brodmann area 40). Macroscopically, the superior parietal lobule (SPL) is a single structure but it consists of two architectonically regions (Brodmann areas 5 anteriorly and 7 posteriorly).

Here, we shall focus on three areas within the lateral part of the PPC (Figure 1). The anterior part of the intraparietal sulcus (aIPS) is defined as the region located at the intersection between the postcentral sulcus and the IPS [START_REF] Frey | Cortical topography of human anterior intraparietal cortex active during visually guided grasping[END_REF]. The pIPS is located at the intersection between the IPS and the parieto-occipital sulcus [START_REF] Karabanov | Mapping Different Intra-Hemispheric Parietal-Motor Networks Using Twin Coil TMS[END_REF]. The superior parieto-occipital cortex (SPOC) is 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 IPS [START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goal-directed hand actions[END_REF].

The PPC is anatomically connected to ipsi-and contralateral hemispheric structures. Within the hemisphere, the aIPS, the pIPS and the SPOC are mainly connected to premotor and prefrontal regions via the superior longitudinal fasciculus (SLF) [START_REF] Wang | Subcomponents and connectivity of the superior longitudinal fasciculus in the human brain[END_REF]. This voluminous tract is composed of three different branches. The most dorsal branch (SLF-1) links the SPOC and dorsal frontal regions (and particularly the dorsal premotor (dPM) cortex). The SLF-2 is the most voluminous part; it joins the pIPS and the AG to the dPM cortex and the dorsolateral prefrontal cortex. Lastly, the SLF-3 (also referred to as the ventral branch) links the aIPS and the ventral premotor cortex (vPM). Overall, two main PF networks can be identified: the dorsolateral stream connecting the aIPS to the vPM cortex, and the dorsomedial stream connecting the pIPS and the SPOC to the dPM cortex (Fig 1).

Interhemispheric connections are mediated by transcallosal tracts crossing the posterior part of the corpus callosum (regions 4 and 5) [START_REF] Zarei | Functional anatomy of interhemispheric cortical connections in the human brain[END_REF].

Why use TMS in this field?

In non-human primates, in vivo recordings using microelectrode arrays have allowed to build a precise model of the spatial and temporal involvement of the PPC and the premotor areas during the different phases of upper limb gesture production (for review, see [START_REF] Kaas | Cortical networks subserving upper limb movements in primates[END_REF]). In humans, since invasive in vivo recordings cannot be easily performed, non-invasive electrophysiological (EEG, non-invasive brain stimulation) and imaging techniques are required.

Neuroimaging studies have demonstrated that the PF networks are specialized in the planning of visually guided upper limb movements. In particular, neuroimaging activation studies have evidenced a high degree of specialization of the aIPS [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] Grol | Parieto-frontal connectivity during visually guided grasping[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 | Functional magnetic resonance imaging adaptation reveals the cortical networks for processing grasp-relevant object properties[END_REF] and the vPM cortex [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] in the grasping phase. Other studies have shown that the discrimination of an object's intrinsic properties (but not its location) is governed by the aIPS and the vPM cortex [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] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Monaco | Neural correlates of object size and object location during grasping actions[END_REF]. Concerning the reaching phase, fMRI activation studies have shown that the SPOC and the pIPS are selectively activated during the preparation of movement [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] Culham | Visually guided grasping produces fMRI activation in dorsal but not ventral stream brain areas[END_REF][START_REF] Filimon | Multiple parietal reach regions in humans: cortical representations for visual and proprioceptive feedback during on-line reaching[END_REF][START_REF] Konen | Functional organization of human posterior parietal cortex: grasping-and reaching-related activations relative to topographically organized cortex[END_REF]. Interestingly, much the same parietal activations are noted during motor imagery of upper-limb reaching movements, along with dPM activation [START_REF] Pilgramm | Motor imagery of hand actions: Decoding the content of motor imagery from brain activity in frontal and parietal motor areas[END_REF].

However, fMRI's poor time resolution prevents precise studies of the temporal involvement of the different brain areas in movement processing, and this imaging technique cannot be used to interfere with neural activation. In contrast, TMS meets the latter criterion, and a variety of protocols have been used in this field [START_REF] Sandrini | The use of transcranial magnetic stimulation in cognitive neuroscience: a new synthesis of methodological issues[END_REF]. Firstly, TMS can be used to modulate a region thought to be involved in a given behavior, either by prevent activity by silencing neurons (''virtual lesion'' or temporary inactivation protocol) or by adding supplementary ''noisy'' activity to ongoing processes [START_REF] Siebner | How does transcranial magnetic stimulation modify neuronal activity in the brain? Implications for studies of cognition[END_REF]. Effects can first be achieved online, i.e. by delivering a single pulse or a short train of highfrequency TMS pulses, enabling an assessment of the participation of the targeted region in the ongoing behavior and of the moment in behavior production during which the region is involved, with high temporal resolution (less than a millisecond), and a spatial resolution of 1.5 to 2 cm 2 for a standard 70 mm figure-of-eight coil (better with smaller coils) [START_REF] Thielscher | Electric field properties of two commercial figure-8 coils in TMS: calculation of focality and efficiency[END_REF]. Effects can also be assessed offline for up to one hour after the end of the session [START_REF] Nyffeler | One session of repeated parietal theta burst stimulation trains induces long-lasting improvement of visual neglect[END_REF][START_REF] Wischnewski | Efficacy and Time Course of Theta Burst Stimulation in Healthy Humans[END_REF], i.e. after a period of repeated transcranial brain stimulation (rTMS), either by increasing (with high frequency (>5 Hz) rTMS or an intermittent theta burst mode) or decreasing cortical excitability (with low frequency (<1 Hz) rTMS or a continuous theta burst mode). Paired-pulse TMS (ppTMS, also referred to as twin-coil TMS) can be used to assess effective connectivity (i.e. the directional influence that one neural system exerts over another [START_REF] Friston | Functional and effective connectivity: a review[END_REF]) between a cortical brain region and the primary motor cortex (M1) at rest or during gesture production [START_REF] Lafleur | Assessment of Effective Connectivity and Plasticity With Dual-Coil Transcranial Magnetic Stimulation[END_REF][START_REF] Rothwell | Using transcranial magnetic stimulation methods to probe connectivity between motor areas of the brain[END_REF]. In this paradigm, a test stimulus (TS) applied over M1 gives rise to a motor-evoked potential (MEP) whose amplitude reflects corticospinal excitability. Prior to the TS, a conditioning stimulus (CS) is applied at a fixed interstimulus interval (ISI) with a second stimulator over the region thought to be connected to M1. The CS may result in facilitation (if the MEP amplitude increases) or inhibition (if the MEP amplitude decreases), or may have no influence on M1 (figure 2). Advantageously, ppTMS can be used to test multiple hypotheses by varying the CS's cortical target and intensity, and the ISI. Usually, the intensity of the TS is supraliminal (in order to evoke MEPs) and that of the CS is infraliminal. The influence of the ISI provides information on the nature of connections underlying the observed effect: if an effect is observed for a short ISI, then the connections are likely to be direct, short pathways, whereas an effect of a longer ISI reveals longer and/or indirect pathways (i.e. with several nodes) [START_REF] Rothwell | Using transcranial magnetic stimulation methods to probe connectivity between motor areas of the brain[END_REF]. Whatever the protocol used, since targeted brain areas (in the premotor cortex as in the PPC) are close to each other, small diameter coils should be preferred in order to specifically target one site without modulating the adjacent region [START_REF] Thielscher | Electric field properties of two commercial figure-8 coils in TMS: calculation of focality and efficiency[END_REF].

The role of parietofrontal networks in the planning and control of visually guided reaching and grasping movements.

Although the kinematic interdependence of the reaching and grasping phases is undebated, the phases' respective neural bases have not been fully characterized. In Jeannerod et al.'s initial model [START_REF] Jeannerod | The timing of natural prehension movements[END_REF], each phase is considered to be an independent process: the reaching phase depends on the target's extrinsic properties (mainly its position in working space), whereas the grasping phase depends on the object's intrinsic properties (size, shape, texture, etc.). For many years, this dual processing theory had been supported by evidence of neural segregation between the dorsolateral network involved during the grasping phase and the dorsomedial network involved in the reaching phase. However, recent data have challenged this view, and have shed new light on the dual function of the dorsomedial stream. This mini-review will only address the key aspects of the neural bases of reaching and grasping; for an exhaustive review, we refer the reader to other publications [START_REF] Turella | Neural correlates of grasping[END_REF][START_REF] Vesia | Specialization of reach function in human posterior parietal cortex[END_REF][START_REF] Vingerhoets | Contribution of the posterior parietal cortex in reaching, grasping, and using objects and tools[END_REF].

The dorsolateral network's function in gesture planning

Data from the literature on the dorsolateral network (involved in the grasping phase in non-human primates as in humans) are homogeneous [START_REF] Davare | Interactions between areas of the cortical grasping network[END_REF]. Studies using different TMS protocols have confirmed the effective connectivity between the aIPS, the vPM cortex and M1, and have identified a sequential activation and interaction in the movement planning phase. Temporary inactivation of the aIPS during movement planning is responsible for modifications in hand shaping and force scaling [START_REF] Dafotakis | On the role of the ventral premotor cortex and anterior intraparietal area for predictive and reactive scaling of grip force[END_REF][START_REF] Davare | Temporal Dissociation between Hand Shaping and Grip Force Scaling in the Anterior Intraparietal Area[END_REF]. These two grasping parameters appear to be independently mediated by the aIPS. Indeed, the consequence of inactivation depended on the latter's time of occurrence: when applied 270 to 220 ms before contact of the hand with the manipulandum, the CS specifically altered hand shaping, whereas only grip force scaling was affected when the CS was delivered later (170 to 120 ms before contact) [START_REF] Davare | Temporal Dissociation between Hand Shaping and Grip Force Scaling in the Anterior Intraparietal Area[END_REF]. Furthermore, the two processes appear to differ in their lateralization; although grip force scaling was altered by a unilateral lesion in the left aIPS, a bilateral lesion was required to impair hand shaping. In another study, Davare et al. showed that temporary inactivation of either the left or the right vPM cortex during movement planning also altered the positioning of fingers on the target, whereas the recruitment of intrinsic hand muscles was affected only when both vPM cortices were virtually lesioned [START_REF] Davare | Dissociating the role of ventral and dorsal premotor cortex in precision grasping[END_REF].

Several ppTMS studies have explored the effective connectivity between the aIPS, the vPM cortex and M1 in healthy humans. At rest, a CS applied over either the aIPS [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[END_REF][START_REF] Karabanov | Mapping Different Intra-Hemispheric Parietal-Motor Networks Using Twin Coil TMS[END_REF][START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Koch | Focal stimulation of the posterior parietal cortex increases the excitability of the ipsilateral motor cortex[END_REF][START_REF] Vesia | Human dorsomedial parieto-motor circuit specifies grasp during the planning of goal-directed hand actions[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goal-directed hand actions[END_REF] or the vPM cortex [START_REF] Davare | Selective modulation of interactions between ventral premotor cortex and primary motor cortex during precision grasping in humans[END_REF] exerted an inhibitory influence on M1 for short ISIs (4 ms for the aIPS, and 6 to 8 ms for the vPM). This inhibition might reduce competition between alternative movements planned in parallel during movement preparation [START_REF] Buch | A network centered on ventral premotor cortex exerts both facilitatory and inhibitory control over primary motor cortex during action reprogramming[END_REF][START_REF] Cisek | Neural mechanisms for interacting with a world full of action choices[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goal-directed hand actions[END_REF]. Interestingly, the inhibition changed to facilitation (at the same ISI) when the CS was delivered over the aIPS during the preparation of a grasping movement, regardless of whether or not is was combined with a reaching movement [START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Vesia | Human dorsomedial parieto-motor circuit specifies grasp during the planning of goal-directed hand actions[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goal-directed hand actions[END_REF].

Lastly, applying a TMS pulse stimulation over the vPM cortex (temporarily inactivating the latter) between the CS over the aIPS and the TS (i.e. a triple-pulse TMS protocol) suppressed the inhibition elicited at rest; this demonstrated the crucial role of parietal connections to the vPM cortex in the modulation of M1 [START_REF] Koch | In vivo definition of parieto-motor connections involved in planning of grasping movements[END_REF][START_REF] Shields | Probing the interaction of the ipsilateral posterior parietal cortex with the premotor cortex using a novel transcranial magnetic stimulation technique[END_REF].

In conclusion, both the vPM and the aIPS (via the vPM) have an influence on the control of the grasping phase of visually-guided upper-limb movements. Hand shaping seems to be planned first, and then force scaling.

The dorsomedial network's functions in gesture planning

The dorsomedial network's influence during planning of the reaching phase

The dorsomedial network's importance in the planning and online control of reaching movements has been clearly demonstrated. Although there are fewer virtual lesion studies of the pIPS and the SPOC than of the aIPS, the research has revealed these areas' influence on the planning of reaching movements in humans [START_REF] Della-Maggiore | Stimulation of the posterior parietal cortex interferes with arm trajectory adjustments during the learning of new dynamics[END_REF][START_REF] Desmurget | Role of the posterior parietal cortex in updating reaching movements to a visual target[END_REF][START_REF] Striemer | Programs for action in superior parietal cortex: A triplepulse TMS investigation[END_REF]. In addition, Busan et al. evidenced, by modulating the pIPS, the SPOC and the dPM cortex during the planning of reaching movements, that visuomotor information is probably processed in parallel in these regions of interest [START_REF] Busan | Effect of transcranial magnetic stimulation (TMS) on parietal and premotor cortex during planning of reaching movements[END_REF][START_REF] Busan | Parieto-occipital cortex and planning of reaching movements: a transcranial magnetic stimulation study[END_REF].

At rest, the connections between the pIPS and the SPOC and between the dPM cortex and M1 (as evidenced by ppTMS protocols) differ from those observed for the dorsolateral network. At rest, M1 excitability was not modified when the CS was applied over the SPOC [START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goal-directed hand actions[END_REF] but increased when the pIPS was stimulated at an ISI of 6 ms [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]. This facilitation appears to be due to the asymmetry of parietal interhemispheric connections, with the right pIPS exerting a strong inhibitory effect on the left pIPS via short-latency connections through the corpus callosum [START_REF] Koch | Asymmetry of parietal interhemispheric connections in humans[END_REF]. Indeed, the facilitation of M1 excitability observed when the CS is applied over the left pIPS is suppressed when the right pIPS is stimulated before the CS, but not vice versa. Interestingly, the degree of this asymmetry was correlated with the severity of pseudoneglect (i.e. a leftward bias in line bisection tests) in healthy subjects. During the planning of a reaching movement, the pIPS and the SPOC behave in the same way in ppTMS studies; MEPs are facilitated when the CS is applied over either the former [START_REF] Koch | Functional interplay between posterior parietal and ipsilateral motor cortex revealed by twin-coil transcranial magnetic stimulation during reach planning toward contralateral space[END_REF] or the later [START_REF] Vesia | Human dorsomedial parieto-motor circuit specifies grasp during the planning of goal-directed hand actions[END_REF][START_REF] Vesia | Human parietal and primary motor cortical interactions are selectively modulated during the transport and grip formation of goal-directed hand actions[END_REF]. Although the pIPS and the SPOC show similar patterns in ppTMS studies, they do not have the same role in reaching planning; the SPOC appears to be involved in the encoding of reach goals, whereas the pIPS and the angular gyrus may be involved in the encoding of reach vectors [START_REF] Vesia | Specialization of reach function in human posterior parietal cortex[END_REF][START_REF] Vesia | Specificity of human parietal saccade and reach regions during transcranial magnetic stimulation[END_REF].

Does the dorsomedial network have a role in the grasping phase?

In line with findings in non-human primates [START_REF] Fattori | The dorsomedial pathway is not just for reaching: grasping neurons in the medial parieto-occipital cortex of the macaque monkey[END_REF][START_REF] Raos | Functional properties of grasping-related neurons in the dorsal premotor area F2 of the macaque monkey[END_REF], there is evidence to suggest that the posterior part of the PPC and the dorsomedial network both have roles in the planning of the grasping phase and in grasping-reaching integration, in addition to their well-known involvement in the reaching phase.

Electromyographic activation patterns during reach-to-grasp movements provided the initial (indirect) evidence of neural coupling between reaching and grasping. In fact, the first dorsal interosseous muscle (a key muscle for precise thumb-index gripping) is activated as expected during the grasping phase but is also activated during the reaching phase [START_REF] Koch | Functional interplay between posterior parietal and ipsilateral motor cortex revealed by twin-coil transcranial magnetic stimulation during reach planning toward contralateral space[END_REF]. Furthermore, the excitability of the hand's intrinsic muscles is modified when the subject's shoulder position is changed passively [START_REF] Dominici | Cortico-motoneuronal output to intrinsic hand muscles is differentially influenced by static changes in shoulder positions[END_REF]. Grol et al. were the first to highlight (using activation fMRI) the dorsomedial network's role in the planning of grasping movements [START_REF] Grol | Parieto-frontal connectivity during visually guided grasping[END_REF]. Whereas grabbing a small object activated only the aIPS and the vPM cortex, grabbing a large object increased activity in the dorsomedial network. Later research confirmed that the dorsomedial network is recruited when grasping movements are complex or when the subject must choose between different types of grasp [START_REF] Gallivan | Decoding action intentions from preparatory brain activity in human parieto-frontal networks[END_REF][START_REF] Rossit | fMRI reveals a lower visual field preference for hand actions in human superior parieto-occipital cortex (SPOC) and precuneus[END_REF][START_REF] Verhagen | Perceptuo-motor interactions during prehension movements[END_REF].

Data from TMS experiments in this field are scarce. Davare et al. first demonstrated that temporary inactivation of the left dPM cortex (but not the right) during the planning of a grasping movement impaired the coupling between gripping and lifting a manipulandum -suggesting that the dPM cortex acts during the grasping phase [START_REF] Davare | Dissociating the role of ventral and dorsal premotor cortex in precision grasping[END_REF]. In a ppTMS study, Vesia et al. studied changes in SPOC-M1 connectivity during the planning of different types of reach-to-grasp movements (pointing, a thumb-index grip, and a palmar grip) [START_REF] Vesia | Human dorsomedial parieto-motor circuit specifies grasp during the planning of goal-directed hand actions[END_REF]. Their results confirmed that the dorsomedial network has a causal role in planning complex, visually guided grasping movements.

Overall, the literature does not support the existence of segregated brain circuits for reaching and grasping. On the contrary, the dorsomedial and dorsolateral networks' respective contributions may depend on the complexity of the movement and the need for precise coordination between reaching and grasping.

Parietofrontal networks and upper limb function after brain injury

Stroke often leads to impairments in upper limb function. Although paresis and muscle hypertonia are the main causes of these impairments, other defects can be involved. In particular, disruption of PF networks (either by an intra-network lesion or a remote lesion that disrupts network function) might be responsible for post-stroke gesture impairments. Firstly, optic ataxia (OA) is a good model of how a lesion limited to the SPL or the IPS disturbs the reaching phase. Optic ataxia is defined as difficulty in reaching targets in the absence of sensory cues other than visual guidance, and which cannot be explained by visual, proprioceptive, motor or coordination disorders [START_REF] Rondot | Optic ataxia: a visuo-motor incoordination[END_REF]. In contrast to apraxia (i.e. the impaired production of learned behaviors), OA is a model visuomotor coordination disorder that affects the reaching phase of visually guided movements. When the person attempts to reach an object, dysmetria results from visual perceptual impairments that have the same kinematic features as in cerebellar ataxia. However, in contrast to cerebellar dysmetria, the dysmetria in OA is markedly reduced or may even disappear when the person uses haptic cues (e.g. movement guidance by external contact) or auditory cues. The symptoms usually worsen when movements are guided by peripheral vision, and OA is sometimes combined with psychic paralysis of gaze and a spatial disorder of visual attention (Balint's syndrome). Lesions associated with OA are located in the SPL and around the IPS, predominantly in the right hemisphere [START_REF] Granek | The role of the caudal superior parietal lobule in updating hand location in peripheral vision: further evidence from optic ataxia[END_REF][START_REF] Karnath | Cortical control of visually guided reaching: evidence from patients with optic ataxia[END_REF]. Three main mechanistic hypothesis for OA have been suggested: (i) a visuomotor impairment, i.e. impaired sensorimotor integration that is specific for visually guided reaching [START_REF] Perenin | Optic ataxia: a specific disruption in visuomotor mechanisms. I. Different aspects of the deficit in reaching for objects[END_REF][START_REF] Rondot | Optic ataxia: a visuo-motor incoordination[END_REF], (ii) a disturbance in visual orientation and thus altered ability to adequately judge the location of an object in space [START_REF] Mcintosh | Correlated deficits of perception and action in optic ataxia[END_REF], and (iii) an impairment in the online control of movement by visual feedback [START_REF] Pisella | An "automatic pilot" for the hand in human posterior parietal cortex: toward reinterpreting optic ataxia[END_REF]. The role of the PPC (particularly that of its most caudal part) in the development of OA has been highlighted by inducing virtual lesions (using TMS) of the pIPS in humans [START_REF] Davare | Role of the medial part of the intraparietal sulcus in implementing movement direction[END_REF] and the parietal reach region (the homologue of the SPOC and the pIPS) in monkeys [START_REF] Hwang | Inactivation of the parietal reach region causes optic ataxia, impairing reaches but not saccades[END_REF]. In contrast, lesions limited to the aIPS in the human impair the precise coordination of finger movements during grasping but do not impair reaching [START_REF] Binkofski | Human anterior intraparietal area subserves prehension: a combined lesion and functional MRI activation study[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]. Spatial neglect is another example of how a connectivity defect in the PF networks might impair gesture. This condition is defined as failure to acknowledge or explore stimuli on the contralesional side [START_REF] Heilman | Neglect and related disorders[END_REF]. Even though the perceptual features of spatial neglect are most frequently apparent, the condition also includes a directional hypokinesia component (i.e. an impairment in initiating or completing movements in the leftward direction) [START_REF] Heilman | Directional hypokinesia: prolonged reaction times for leftward movements in patients with right hemisphere lesions and neglect[END_REF][START_REF] Kim | Directional and spatial motor intentional disorders in patients with right versus left hemisphere strokes[END_REF]. This is evidenced by a longer reaction time when the target is located in the neglected (contralesional) hemispace and slower, less ample movements towards the contralesional space. It has also been shown that spatial neglect is related to a hemispheric imbalance between the activities of the two PPCs and, more broadly, between dorsal attention networks (DANs). Firstly, Koch et al. used ppTMS to reveal hyperexcitability of PF networks (from the pIPS) in the intact left hemisphere in patients with spatial neglect. This hyperexcitability was correlated with the degree of visual neglect [START_REF] Koch | θ-burst stimulation of the left hemisphere accelerates recovery of hemispatial neglect[END_REF][START_REF] Koch | Hyperexcitability of parietal-motor functional connections in the intact left-hemisphere of patients with neglect[END_REF], and downregulation of the hyperexcitability (via an inhibitory rTMS protocol) led to a reduction in the severity of the neglect.

These results are consistent with those obtained in fMRI neuroimaging studies; disconnection between the DANs (involved in the control of endogenous visual attention, and the structures encompassing the dorsolateral network) and the ventral attention network (involved in the control of exogenous attention) within the lesioned hemisphere resulted in increased activity within the contralesional DAN [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF]. An exhaustive presentation of connectivity disorders in neglect is beyond the scope of this mini-review (for a review, see [START_REF] Corbetta | Spatial neglect and attention networks[END_REF]). The data on connectivity in spatial neglect mainly concern the perceptual modality; hence, future connectivity studies should focus on spatial neglect's motor aspects.

Another aspect of PF network connectivity relates to the networks' relationship with neural plasticity and their potential roles in motor recovery after stroke. In fact, recent studies of functional and structural connectivity have evidenced alterations in the ipsi-and contralateral connections between the PPCs and the lesioned M1 (via PM cortex) during the subacute and chronic phases of 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] Park | Longitudinal changes of resting-state functional connectivity during motor recovery 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] Schulz | Parietofrontal motor pathways and their association with motor function after stroke[END_REF][START_REF] Wang | Dynamic functional reorganization of the motor execution network after stroke[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]. In addition, a recent connectivity study using EEG demonstrated that parietofrontal coupling was stronger in hemiparetic stroke patients compared to controls and correlated with the residual motor deficit [START_REF] Bönstrup | Parietofrontal network upregulation after motor stroke[END_REF]. Taken together, these observations suggest that the PF networks may have a role in motor impairment and recovery after stroke. Furthermore, the PPC exerts a direct influence on M1 and upper limb movements; excitatory modulation of the PPC by non-invasive brain stimulation is able to enhance M1 excitability [START_REF] Rivera-Urbina | Parietal transcranial direct current stimulation modulates primary motor cortex excitability[END_REF] and PPC-M1 connectivity [START_REF] Chao | Induction of motor associative plasticity in the posterior parietal cortex-primary motor network[END_REF], and modify movement timing in healthy subjects [START_REF] Krause | 1Hz rTMS of the left posterior parietal cortex (PPC) modifies sensorimotor timing[END_REF]. Nevertheless, the functional significance of these connectivity changes remains to be demonstrated because the latter do not appear to be related to the level of motor impairment [START_REF] Allart | Parietomotor connectivity in the contralesional hemisphere after stroke: A paired-pulse TMS study[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 | Enhanced Effective Connectivity Between Primary Motor Cortex and Intraparietal Sulcus in Well-Recovered Stroke Patients[END_REF][START_REF] Schulz | Parietofrontal motor pathways and their association with motor function after stroke[END_REF].

Lastly, better knowledge of the neural bases of reach-to-grasp planning and control in health and disease may facilitate the development of brain computer interfaces or neural prostheses capable of compensating for motor impairment in disabled people.

Conclusion

Parietofrontal networks are key structures in the planning and online control of visually guided upper limb movements. Although reaching and grasping phases of movement were initially thought to involve segregated neural circuits, TMS studies have demonstrated that the contributions of the dorsomedial and dorsolateral networks may vary according to the complexity of the movement and the need for precise coordination between reaching and grasping. Whereas the dorsolateral network is activated at various times in the grasping phase (for hand shaping and force scaling), the dorsomedial network is activated during the planning of the reaching phase and during more complex visually guided grasping movements. Changes in PF connectivity following brain injury can account for the impairments in visually guided upper limb movements observed in patients, such as OA and the motor component of spatial neglect. These changes may also reflect neuronal plasticity during the recovery of motor function, although this remains to be proven. Lastly, better knowledge of motor planning in patients and healthy individuals may facilitate the development for brain computer interfaces capable of compensating for motor disability. B. In the control modality, only the TS is delivered over M1. In the conditioned modality, the CS is first delivered over the PPC, and then the TS is delivered after a fixed interstimulus interval (ISI). Facilitation corresponds to an increase in the amplitude of the motor-evoked potential, whereas inhibition corresponds to a decrease.

Figure legend Figure 1 .

 legend1 Figure legend

Figure 2 .

 2 Figure 2. A ppTMS protocol for assessing PF networks (PPC-M1 connectivity) A. A schematic representation of how the probes are positioned over M1 (delivery of the test stimulus, TS) and the PPC (delivery of the conditioning stimulus, CS).B. In the control modality, only the TS is delivered over M1. In the conditioned modality, the CS is first delivered over the PPC, and then the TS is delivered after a fixed interstimulus interval (ISI). Facilitation corresponds to an increase in the amplitude of the motor-evoked potential, whereas inhibition corresponds to a decrease.

Acknowledgments:

The authors thank David Fraser PhD for editorial support.

Conflicts of interest: none

Funding: this research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


PhD Hervé Devanne
email: herve.devanne@chru-lille.fr

Etienne Allart

Boosting brain motor plasticity with physical exercise

Keywords: Neuroplasticity, exercise, non-invasive brain stimulation Running title: Boosting brain motor plasticity with physical exercise

Neuroplasticity is a fundamental process that occurs within the central nervous system during learning of a new ability for example, or more generally when internal or environmental conditions are modified. Neuroplasticity involves both functional and structural changes and may help functional recovery when neuronal networks have been damaged (following brain or spinal cord injury or a peripheral nerve lesion) or when afferent or efferent modules of a system are damaged (e.g. sensory loss, limb amputation). One of the challenging and topical issues of neurosciences is to better understand the highly complex mechanisms of neuroplasticity and to become able to augment these when necessary.

Motor cortex plasticity can be influenced by many different factors and interventional procedures such as rehabilitation, physical exercise or non-invasive transcranial brain stimulation (NIBS), and it is likely that combining these various interventions could have a synergistic impact for inducing brain plasticity. For example, NIBS protocols have been used successfully in stroke patients to facilitate the effects of subsequent physiotherapy [START_REF] Dilazzaro | Direct demonstration of the effect of lorazepam on the excitability of the human motor cortex[END_REF]. How the different protocols can be paired for maximizing plasticity and its underlying mechanisms is, so far, not well understood.

Repetitive Transcranial Magnetic Stimulation (rTMS), theta-burst stimulation (TBS),

Paired-Associative Stimulation (PAS) or transcranial Direct or Alternative Current

Stimulation (tDCS or tACS respectively) are different kinds of NIBS methods that are becoming more and more widely employed to increase or decrease cortical excitability (depending on the stimulation pattern used) for minutes or even hours. Low frequency rTMS (<1Hz) and continuous TBS, applied over the primary motor cortex (M1), exert an inhibitory effect on neurons of the corticospinal tract, as assessed by the decrease of motor potential amplitude, recorded in the targeted muscles. In contrast, patterned stimulation, i.e. high frequency bursts separated by periods without stimulation (high frequency rTMS and intermittent TBS), lead to increased corticomotor excitability.

Indirect evidence suggests that continuous and patterned NIBS train stimulations exert synaptic effects similar to long term-depression (LTD) or long-term potentiation (LTP), respectively, as observed in cortical slices [START_REF] Ziemann | TMS induced plasticity in human cortex[END_REF]. Paired-associative protocols are derived from animal experiments showing that LTP may occur when pre-and post-synaptic elements are stimulated with precise timing, whereas LTD is observed when the same stimuli are not time-locked. In accordance with this spike timing-dependent plasticity rule, changes in corticomotor excitability can be obtained by pairing a peripheral electrical stimulation with one TMS pulse over the contralateral M1 area. The repetition of these doublets every 10-20 seconds for at least 15min induces a directional effect on corticomotor excitability, depending on the inter-stimulus interval : LTP-like effect for ISI around 25 ms and LTD-like effect for ISI of 10ms [START_REF] Stefan | Induction of plasticity in the human motor cortex by paired associative stimulation[END_REF]. In contrast with rTMS, TBS or PAS that produce neuronal firing, tDCS and tACS exert an effect on the membrane potential, tending to shift this toward hyper-or depolarisation, depending on current direction (anodal vs cathodal). An important finding is that the NIBS effect on brain excitability in humans strongly depends on the neural background activity prior to the stimulation, as stated by the Bienenstock-Cooper-Munro (BCM) rule of synaptic plasticity. For example, the net inhibitory influence of low frequency rTMS can be suppressed or even reversed to facilitation when the basal level of neural activity is raised beforehand by an anodal tDCS [START_REF] Siebner | Preconditioning of low-frequency repetitive transcranial magnetic stimulation with transcranial direct current stimulation: evidence for homeostatic plasticity in the human motor cortex[END_REF]. This homeostatic meta-plasticity has been suggested to stabilise the neural networks within an operational range of synaptic changes and to prevent uncontrolled positive feedback processes during skill learning, for example.

Whatever the NIBS protocol employed to induce neuroplasticity, changes of corticomotor excitability lasting beyond the time of stimulation can be observed, but the effects are often modest and not consistent from one subject to another. Though the usefulness of NIBS to induce neuroplasticity in neurological diseases is not questioned ([9] for a review), enhancing effects of NIBS represents an exciting and essential challenge in neuroscience. In this context, priming NIBS with physical activity may be an efficient and convenient manner to boost neuroplasticity.

In animals, the role of physical activity has been evidenced in molecular signalling pathways involved in brain plasticity [START_REF] Aguiar | Short bouts of mild-intensity physical exercise improve spatial learning and memory in aging rats: involvement of hippocampal plasticity via AKT, CREB and BDNF signaling[END_REF] and in the increase of neurotrophic factors such as Brain Derived Neurotrophic Factor (BDNF) accompanying axonal growth, after peripheral nerve crush injury [START_REF] Molteni | Voluntary exercise increases axonal regeneration from sensory neurons[END_REF]. In rats, wheel running is also accompanied by structural changes, such as increased rate of neurogenesis and angiogenesis, as well as greater dendritic spine density (for review, see [START_REF] Hötting | Beneficial effects of physical exercise on neuroplasticity and cognition[END_REF]). Many changes also occur at the cerebral level in the neurotransmitter system which is known to play a crucial role in neuroplasticity. In humans, structural changes were observed in the white and grey matter of older people who underwent regular physical activity [START_REF] Colcombe | Aerobic exercise training increases brain volume in aging humans[END_REF]. As in rodents, physical exercise in humans also induces molecular and cellular changes, such as increased BDNF, or decreased GABA-A transmission [START_REF] Smith | The influence of a single bout of aerobic exercise on short-interval intracortical excitability[END_REF][14] [START_REF] Stavrinos | High-intensity Interval Exercise Promotes Motor Cortex Disinhibition and Early Motor Skill Consolidation[END_REF]. Because the rTMSinduced level of LTP-LTD-like plasticity has been suggested to depend on polymorphisms of the BDNF gene [START_REF] Cheeran | et al common polymorphism in the brain-derived neurotrophic factor gene (BDNF) modulates human cortical plasticity and the response to rTMS[END_REF] and also on GABA transmission, it could thus be considered that physical exercise may prepare the brain for subsequent NIBS protocols.

In line with this hypothesis, a few studies have been conducted in the last decade to look at the effects of exercise and NIBS-induced corticomotor plasticity. Cirillo and colleagues [START_REF] Cirillo | Motor cortex plasticity induced by paired associative stimulation is enhanced in physically active individuals[END_REF] were the first to report that, compared with sedentary subjects, active adults (according to the International Physical Activity Questionnaire) were more receptive to an excitatory PAS protocol. Interestingly, Cirillo and co-workers pointed out that the PAS-induced increase of neuroplasticity was observed in the M1 region controlling the finger muscles, whereas the aerobic activities performed by the active subjects, such as cycling or running, involved the lower limbs. In other words, the influence of physical exercise on the sensorimotor system was broad, i.e. not restricted to the motor region specifically involved in the control of the muscles needed by the physical exercise.

Another recent and promising finding is that a short period of aerobic exercise seems to be sufficient to promote NIBS induced plasticity. For example, a single bout of low-level aerobic pedalling exercise (at 57% of the age predicted maximum heart rate) increased the down-regulatory effect of continuous TBS on corticomotor excitability in circuits controlling the hand muscles [START_REF] Mcdonnell | A single bout of aerobic exercise promotes motor cortical neuroplasticity[END_REF]. The effect of acute exercise on LTP-like plasticity has also been studied, producing contrasting results. Singh et al [START_REF] Singh | Acute exercise enhances the response to paired associative stimulation-induced plasticity in the primary motor cortex[END_REF] reported an increase in the M1 excitability of hand muscles after a PAS protocol preceded by aerobic cycling exercises at moderate intensity, compared to PAS alone. This increase of the LTP-like effect was also reported following high intensity, intermittent exercise, by Mang et al [START_REF] Mang | A single bout ofhigh-intensity aerobic exercise facilitates response to paired associative stimulation and promotes sequence-specific implicit motor learning[END_REF] who measured PAS-induced changes in corticomotor excitability. In contrast, it was recently shown that after a single bout of a continuous pedalling exercise at high intensity, the net influence of intermittent TBS was a decrease in motor cortex excitability, instead of the expected increase [START_REF] Smith | Highintensity Aerobic Exercise Blocks the Facilitation of iTBS-induced Plasticity in the Human Motor Cortex[END_REF].

To date, the mechanisms by which aerobic exercise may promote NIBS protocols remain unclear and are likely to be multifactorial with intermingled effects of cortisol, BDNF (and other neurotrophins), changes in GABAergic transmissions and other neurotransmitters (such as dopamine, norepinephrine or serotonin) at the cortical level.

Increase in BDNF serum concentration with physical exercise has been suspected to be a key element. However, NIBS-induced plasticity increases after low level exercise, even when BDNF serum level does not change [START_REF] Mcdonnell | A single bout of aerobic exercise promotes motor cortical neuroplasticity[END_REF], and there is no evidence for a correlation between individual BDNF serum levels after exercise and PAS-induced LTP-like effect [START_REF] Mang | A single bout ofhigh-intensity aerobic exercise facilitates response to paired associative stimulation and promotes sequence-specific implicit motor learning[END_REF]. Induction of LTP in the motor cortex is strongly dependent on the reduction of GABAergic transmissions, as evidenced by Hess and Donoghue [START_REF] Hess | Long-term potentiation of horizontal connections provides a mechanism to reorganize cortical motor maps[END_REF] who showed in rats that LTP occurred following TBS when bicuculline, an antagonist of GABA-A receptors, was applied prior to stimulation. In humans, physical exercise is also accompanied by the reduction of short latency intracortical inhibition (SICI) [START_REF] Singh | Aerobic exercise modulates intracortical inhibition and facilitation in a non-exercised upper limb muscle[END_REF][19], a mechanism which depends on GABA-A receptors [START_REF] Dilazzaro | Direct demonstration of the effect of lorazepam on the excitability of the human motor cortex[END_REF] and this lowering of GABA inhibition has been suggested to participate, at least in part, in the increase of NIBS-induced plasticity following exercise (for a review see [START_REF] Singh | The effects of acute aerobic exercise on the primary motor cortex[END_REF]).

Taken together, these studies converge toward the idea that physical exercise has the capacity to promote plasticity in the motor cortex. These findings open new opportunities for physiotherapists to increase the efficacy of rehabilitation, since for example, even a single session of exercise (such as 20 minutes of biking at a moderate rate) is likely to increase brain responsiveness to motor rehabilitation techniques.

In their review of the literature about the synergistic action of aerobic exercise and NIBS protocols, Hendrikse et al [START_REF] Hendrikse | Combining aerobic exercise and repetitive transcranial magnetic stimulation to improve brain function in health and disease[END_REF] pointed out that, because aerobic exercise has a broad impact on brain circuits with widespread neurogenic and neurotrophic effects, it can also be used to enhance NIBS effects in non-motor regions, to improve cognitive function for example, or more generally to increase brain responsiveness to NIBS protocols in neurological diseases. In pharmacoresistant depression for example, aerobic exercise could be performed before NIBS over the dorsolateral prefrontal cortex to increase its effects. However, to date, the literature is rather scarce and shows great variability in terms of outcome measures, the kind of physical exercise and NIBS protocols. Future studies are therefore essential to consider the clinical usefulness of physical exercise. An important challenge is to better understand the mechanisms involved in the potential effect of exercise (in particular the role of BDNF, neurotransmitters, cortisol and lactates), and to determine the protocol able to maximise NIBS, or motor rehabilitation, with exercise.

Conflicts of interest: none


Thi-To-Quyen Tran
email: thi-to-quyen.tran@irisa.fr

Thuong-Cang Phan

Anne Laurent
email: anne.laurent@lirmm.fr

Laurent D'orazio
email: laurent.dorazio@univ-rennes1.fr

Optimization for Large-Scale Fuzzy Joins Using Fuzzy Filters in MapReduce

Keywords: Fuzzy join, Similarity join, MapReduce, Fuzzy Filter

A fuzzy or similarity join is one of the most useful data processing and analysis operations for Big Data in a general context. It combines pairs of tuples for which the distance is lower than or equal to a given threshold ε. The fuzzy join is used in many practical applications, but it is extremely costly in time and space, and may even not be executed on large-scale datasets. Although there have been some studies to improve its performance by applying filters, a solution of an effective fuzzy filter for the join has never been conducted. In this paper, we thus extend our previous work by proposing a novel fuzzy filter to optimize fuzzy joins. This filter is a compact, probabilistic data structure that supports very fast similarity queries by maintaining a bit matrix, with small false positive rate and zero false negative rate. We show that our proposal is more efficient than others because of eliminating redundant data, reducing computation cost and avoiding duplicate output.

I. INTRODUCTION

Join is a critical operation within a data management system, making it possible to enrich data from a source with external information. That is why literature on join optimization is rich, especially in parallel and distributed systems [START_REF] Bamha | An efficient equi-semi-join algorithm for distributed architectures[END_REF]- [START_REF] Bruno | Advanced join strategies for large-scale distributed computation[END_REF]. In recent years, researches have focused on the problem of efficient joins in large-scale parallel environments. First results on equi-join [START_REF] Phan | A Theoretical and Experimental Comparison of Filter-Based Equijoins in MapReduce[END_REF], impose strong constraints on data (one of the sets having to be small enough to be distributed to all the machines used for the treatment) or their organization (sorting according to the join attribute, placement of data on specific nodes), leading to many data transfers (some unnecessary) and heavy workload on machines or requiring multiple (expensive) execution phases. The problem is even more difficult when the equality constraint is released while this type of query is often necessary. It is motivated by applications requiring similar matching. As a query example [START_REF] Vernica | Efficient Parallel Set-similarity Joins Using MapReduce[END_REF] in mining social networking sites where user's preferences are stored as bit vectors (where a "1" bit means an interest in a certain domain), applications want to discover the similar interests of users. A user with preference bit vector "[1,0,0,1,1,0,1,0,0,1]" possibility has similar interests to a user with preferences "[1,0,0,0,1,0,1,0,0,1]". Another example, widely used in image content-based search engines as Google, Baidu, Bing, discover images whose features maps into binary code by their similarities are greater than a predefined threshold. This query is defined as a fuzzy or similarity join and plays an important role in various applications, including data cleaning [START_REF] Chaudhuri | A primitive operator for similarity joins in data cleaning[END_REF], data integration [START_REF] Doan | Principles of Data Integration[END_REF], detecting attacks from colluding attackers [START_REF] Metwally | Detectives: Detecting Coalition Hit Inflation Attacks in Advertising Networks Streams[END_REF], mining in social networking sites [START_REF] Spertus | Evaluating similarity measures: A large-scale study in the Orkut social network[END_REF], detecting nearduplicate web-pages in web crawling [START_REF] Henzinger | Finding Near-duplicate Web Pages: A Large-scale Evaluation of Algorithms[END_REF], plagiarism detection [START_REF] Hoad | Methods for identifying versioned and plagiarized documents[END_REF], document clustering [START_REF] Broder | Syntactic Clustering of the Web[END_REF], master data management [START_REF] Sahami | A Web-based Kernel Function for Measuring the Similarity of Short Text Snippets[END_REF], bioinformatics [START_REF] Wandelt | Rcsi: Scalable similarity search in thousand(s) of genomes[END_REF].

Stage-of-the-art. Fuzzy join execution consists of a Cartesian product and processing pair distances. Therefore, this operation is expensive in traditional databases [START_REF] Jiang | String similarity joins: An experimental evaluation[END_REF], [START_REF] Gravano | Approximate string joins in a database (almost) for free[END_REF]. Moreover, when dealing with large amounts of data, fuzzy join becomes a challenging problem in a distributed and parallel environment with expensive costs due to data shuffling, in addition to space and efficiency constraints. As a result, data redundancy and duplication are very difficult to accept. MapReduce [START_REF] Dean | MapReduce: Simplified Data Processing on Large Clusters[END_REF] is a famous framework proposed by Google to process large-scale data in parallel. It is widely applied to modeling, processing and calculating costs in large-scale fuzzy join studies [START_REF] Fier | Set similarity joins on mapreduce: An experimental survey[END_REF], [START_REF] Silva | An Experimental Survey of MapReduce-Based Similarity Joins[END_REF]. Most of the existing solutions follow a filtering-verification framework in multiple stages to generate candidates, apply principles (prefix filter, length filter, segment techniques) to prune out hopeless pairs, based on similarity functions to determine all pairs within a radius. Vernica et al. [START_REF] Vernica | Efficient Parallel Set-similarity Joins Using MapReduce[END_REF] proposed a similarity join method using a 3stage MapReduce approach which utilized the prefix filtering method by inverted index on tokens to support set-based similarity functions. Metwally et al. [START_REF] Metwally | V-SMART-Join: A Scalable MapReduce Framework for All-Pair Similarity Joins of Multisets and Vectors[END_REF] proposed a 2-stage algorithm VSMART join for similarity join on set, multisets and vector. Deng et al. [START_REF] Deng | Massjoin: A mapreducebased method for scalable string similarity joins[END_REF] use signatures to calculate inverted index and process in 3-stage for set similarity join. [START_REF] Wang | Qjoin: A q-sample-based method for largescale string similarity joins[END_REF] improved [START_REF] Deng | Massjoin: A mapreducebased method for scalable string similarity joins[END_REF] by replacing signatures with q-gram technique in 3-stage. Afrati et al. [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF] proposed multiple algorithms to perform a fuzzy join with Hamming, Edit and Jaccard distance in a single MapReduce stage without filters. Other algorithms [START_REF] Silva | Exploiting MapReduce-based Similarity Joins[END_REF]- [START_REF] Chen | Pivotbased metric indexing[END_REF] use pivots to split data into disjoint partitions by recursive jobs.

Motivation. One challenge in distributed computing is to avoid expensive data transmission and large disk I/Os. While recent studies on the fuzzy join have common limitations such as input re-reading by multiple phases, wasteful redundancy and duplication of data, we have introduced filter-based approaches [START_REF] Phan | Toward Intersection Filterbased Optimization for Joins in MapReduce[END_REF], [START_REF] Phan | A Theoretical and Experimental Comparison of Filter-Based Equijoins in MapReduce[END_REF], [START_REF] Tran | Improving hamming distance-based fuzzy join in mapreduce using bloom filters[END_REF]. Our team was interested in using Bloom Filters [START_REF] Bloom | Space/Time Trade-offs in Hash Coding with Allowable Errors[END_REF], Intersection Filter [START_REF] Phan | Toward Intersection Filterbased Optimization for Joins in MapReduce[END_REF]. The idea is to filter irrelevant data as soon as possible to reduce data transfers and workload on different machines. Besides, the computation of the Hamming distance is shown faster than the computation of the distance in the input space. Therefore, we take advantage of its theory to propose a new filter for fuzzy joins.

Contributions. This study focuses on the improvement for large-scale fuzzy join. The main contributions of our works are

• a novel fuzzy filter (FF) structure for detecting if an element is close to any members in a set. Moreover, FF can determine which records in the set are real similarities of this element. • large-scale FF based fuzzy join algorithm to avoid useless re-computation. • a theoretical analysis of various similarity join algorithms in MapReduce and their cost comparison in a mapreduce-shuffle computation. The remaining part of this paper is organized as follows. Section 2 summarizes the research background of the MapReduce framework, the fuzzy join definition, the previous filter studies, and position of our paper with respect to related work. In section 3, our approaches for modeling the Fuzzy filter (FF) and optimizations for large-scale FF based fuzzy join are presented. Finally, section 4 concludes and discusses future work.

II. RELATED WORK A. MapReduce

MapReduce [START_REF] Dean | MapReduce: Simplified Data Processing on Large Clusters[END_REF] is a parallel and distributed programming model to process large amounts of data on data centers consisting of commodity hardware. This model allows users to focus on designing their applications regardless of the distributed aspects of the execution. Figure 1 illustrates the MapReduce execution.

A MapReduce program consists of two distinct phases, namely, the Map phase and the Reduce phase. Each phase performs a user function on a key/value pair. The function Map (M) takes a pair of entries (k1, v1) and emits a list of intermediate pairs (k2, v2).

(k1, v1) map ---→ (k2, v2)
The intermediate values associated with the same key k2 are grouped together and then transmitted to the Reduce function which aggregates the values.

(k2, v2) reduce ----→ (k3, v3)
A MapReduce program is executed on multiple nodes. During the Map phase, each Map task reads a subset (called split) of an input dataset and applies the Map function for each key/value pair. The system supports grouping of intermediate data and sends them to the relevant nodes to apply the Reduce phase. This communication process is called Shuffle. Each Reduce task collects the key/value pairs of all the Map tasks, sorts/merges the data with the same key and calls the Reduce function to generate the final results.

B. Fuzzy join

A fuzzy join aims to combine data based on their similarity. It relies on a distance measure to find all pairs (x, y) in the input dataset(s) with a distance (d) bellow some pre-defined threshold ε. Different solutions have been proposed for big data systems [START_REF] Vernica | Efficient Parallel Set-similarity Joins Using MapReduce[END_REF], [START_REF] Metwally | V-SMART-Join: A Scalable MapReduce Framework for All-Pair Similarity Joins of Multisets and Vectors[END_REF], [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF], [START_REF] Silva | Exploiting MapReduce-based Similarity Joins[END_REF], [START_REF] Tran | Improving hamming distance-based fuzzy join in mapreduce using bloom filters[END_REF], [START_REF] Silva | MapReduce-based Similarity Join for Metric Spaces[END_REF]- [START_REF] Xiao | Efficient Similarity Joins for Near-duplicate Detection[END_REF]. The surveys [START_REF] Fier | Set similarity joins on mapreduce: An experimental survey[END_REF], [START_REF] Silva | An Experimental Survey of MapReduce-Based Similarity Joins[END_REF] have been written on MapReduce-based fuzzy join studying supported data types (fixed-length string, variablelength string, numeric, vector, set) and distance functions (Hamming distance, Edit distance, Jaccard similarity, Tanimoto Coefficient, Cosine Coefficient, Ruzicka similarity, Dice Similarity, Set Cosine Sim, Vector Cosine Sim). Continuing to develop our previous studies, thus, throughout this paper, we focus on fuzzy join algorithms, using Hamming distance [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF], [START_REF] Tran | Improving hamming distance-based fuzzy join in mapreduce using bloom filters[END_REF] with fixed-length data inputs (b-bit strings), and show it as the examples. Our proposal can be easily extended to a general Σ q finite set of the alphabet which has q elements (q ≥ 2).

Hamming distance (HD) between two strings s, t is the number of positions in which they differ. Given a set, S, of b-bit strings, a fuzzy join is stated using a Hamming distance used to define similarity and a threshold ε is

{(s, t)|s, t ∈ S, HD(s, t) ≤ ε}
The Ball of radius r (B r ) signifies all close elements of any given element within a distance r. The Hamming ball of radius r (B r ) can be obtained by flipping the value of at most r bits of any given b-bit string. Thus, it is computed by the following formula [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF]:

|B r | = r k=0 b k ≈ b r /r! B r (s)
consists of all similar elements in the ball of radius r around of s. In other words, [START_REF] Bloom | Space/Time Trade-offs in Hash Coding with Allowable Errors[END_REF] is a space-efficient randomized data structure used for testing membership in a set with a small rate of false positives. Figure 2 presents a Bloom Filter structure consisting of m = 12 bits, k = 3 independent hash functions, and a set S of n elements represented by BF (S). BF never returns false negatives. However, it can return false positives. A false positive element of BF is an element that does not belong to a set S while testing it on BF leads to the opposite result. Indeed, in some cases, a hash function can return the same value for multiple elements. As a consequence, an element that does not belong to S can also have a hash value at its position of 1. BF is a space-efficient structure to accelerate queries. The size of a filter is fixed, independently of the number n of elements. However, there is a relation between the size of the structure m and the false positive probability [START_REF] Guo | Theory and Network Applications of Dynamic Bloom Filters[END_REF] The BF and its variations have proven increasingly importance for many applications [START_REF] Broder | Network applications of bloom filters: A survey[END_REF]. Intersection Bloom Filter (IBF) [START_REF] Phan | Toward Intersection Filterbased Optimization for Joins in MapReduce[END_REF] is an extension of BF, represents the intersection of the datasets to be joined. IBF is used to test an element if it is a disjoint element.

∀t ∈ B r (s), d(s, t) ≤ r C. Filters A Bloom Filter (BF)
f BF (S) = (1 -(1 - 1 m ) nk ) k
SuRF [START_REF] Zhang | Surf: Practical range query filtering with fast succinct tries[END_REF] is a fast and compact filter that provides exactmatch filtering, range filtering, and approximate range counts. It is a tree-based filter structure. So it does not fit with the fuzzy join problem because it has to browse through all the branches to find its real close elements, lead to inefficient and high costs.

In our study, fuzzy filters have not been proposed yet.

D. Fuzzy Join Algorithms in MapReduce

This paper aims to improve fuzzy joins in a MapReduce environment, relying on Filters. In order to compare the costs of different algorithms, it adapts a previous model (M, C, R) [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF], where M , R, C are used to measure the effectiveness of an algorithm. The notations and parameters are described in Table I. Naive Algorithm [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF] can be used for any data type and distance function. It relies on a single MapReduce job. The main idea is to distribute each input record to a small set of reducers so that any two records be mapped to at least one common reducer for computing distance. Each input record must be compared with all others, leading to data redundancy and inefficiency.

Ball Hashing Algorithms [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF] (BH) rely on the "ball of radius r" to reduce unnecessary comparisons. This means that each record is compared to the others within its similarity radius. To do this, there is one reducer for each of the n possible strings of length b. The number of reducers is thus n = 2 b . The mappers generate all elements t in the ball of radius r of each input record s (B s (r)) as (key, value) pairs of the form (s, -1) and (t, s) such that t = s and send them to the corresponding reducers. t is a string obtained from s by changing i ∈ [1, r) bits. An issue with BH is data duplication due to ts and st similarity. A proposed solution is to proceed lexicographically [START_REF] Kimmett | Fuzzy Joins in MapReduce: An Experimental Study[END_REF]. A mapper only emits (t, s) if t < s. However, redundant data still exist because similar records in B s (r) are sent to reducers although they are not elements in S. BH 2 is an extension of BH. The difference is that during the map phase, BH 2 generates balls of radius r/2. Because of this, every reducer is active and checks for the similarity between all the possible combinations of two strings it receives and eliminates the duplicate outputs.

Splitting Algorithm [START_REF] Afrati | Fuzzy Joins Using MapReduce[END_REF] is based on a principle of which have any of two similarity b-bit strings with a distance less than r, there exists at least one same substring of length b/(r + 1). Mappers decompose each input string s into r + 1 equal-length substrings s 1 , s 2 , ..., s r+1 and emits (s i , s). Reducers test each string to see if it is within distance r of all other received strings, similar to the Naive algorithm. To avoid duplicate results, when a reducer in the ith family finds that s and t are at distance r or less, it checks that there is no j < i for in which jth substrings are also equal and outputs s, t if there is no such j. However, the Splitting algorithm has also the same issue of redundant data as the Ball hashing algorithm.

Bloom filter based fuzzy joins [START_REF] Tran | Improving hamming distance-based fuzzy join in mapreduce using bloom filters[END_REF] During the map phase, BH generates all elements within a distance r from s and sends them to the reducers for combining with similar input records. It is easy to see that not all elements in the B r (s) belong to S. The Splitting algorithm also generates redundant data by sending each record to r + 1 reducers. In fact, each record just needs to be sent to some identified reducers if all its actual similar elements present in S and its substrings are known. Our approach integrates BF (S) to remove elements in B s (r) that do not belong to S before sending it to the reducers in the BF-BH algorithm. With the BF-Splitting, we propose to combine Ball Hashing, Splitting and BF. By the membership test in BF (S), it determines which elements t = s in B r (s) may actually be similar to s. Then each of them is divided in to r + 1 equal-length substrings s i and t i , i = 1..(r + 1). For each s i , if there exists a substring t i of t in the intersection of S and B r (s) that matches with s i , the pair (s i , s) will be output, and then t will never be considered again. This solution consists of two stages: (1) in pre-processing stage, the filter is built on a join key-value set of the input dataset S; (2) in join processing stage, the filter is distributed to all the computing nodes and used to eliminate non-similar elements of the input dataset in each ball of radius d during the map phase. After filtering none relevant data, the join algorithm then proceeds on real similar elements with a small false positive probability. An example of the join stage of BF-BH for the fuzzy join with 3-bit string and threshold r = 1 is shown in Figure 3.

Discussion: by the theoretical analysis and cost model in [START_REF] Tran | Improving hamming distance-based fuzzy join in mapreduce using bloom filters[END_REF], applying filters will improve processing costs. However, Ball of radius r computation is sensitive to distance. With the greater the distance d, the number of elements in B r increases dramatically. [START_REF] Kimmett | Fuzzy Joins in MapReduce: An Experimental Study[END_REF] has shown the slowness of the BH algorithm without filters. On the other hand, for a finite set of alphabets, the elements in every ball are determined. The ball recalculation for each record is redundant and unnecessary while the processing cost of this calculation is worth considering. From these limitations of the existing solutions, we propose a new filter type called Fuzzy filter to avoid excess calculations.

III. MODELING FUZZY FILTER

This section shows the approach to build the Fuzzy filter with the criteria: small size, in-memory, quick response, with-out false negative probability. As illustrated in Figure 4, with a query y, a fuzzy filter has to give a quick test: ∃x ∈ S, d(x, y) ≤ r? Which x? or ∃x ∈ S ∩ B r (y)? Which x? For convenience during this paper, we assume that all the balls of radius r in the finite alphabet set are known, regardless of the distance function. This calculation will be discussed later.

A. Fuzzy filter structure

The idea begins with finding the intersection between dataset and balls. The Fuzzy filter F F (S) combines a Bloom filter BF (S) to identify elements, and a table to store real similar elements in the ball of each element. We illustrate this approach by Figure 5 The m bit Bloom filter BF (S) uses one hash function h to calculate positions for an element of S and sets the bit at the resulting positions. The ball list is an array of size m of m bit Bloom Filters (a matrix of m × m bits), each one stores its ball BF (B(s i )).

The build operation of the fuzzy filter F F (S) is described as follows.

C (2) = |2 b | • The build cost for F F (S) is C F F (S)-build ≈ b r r! 2 b + |S| + 2 b = ( b r r! + 1)2 b + |S|
For clarity, we consider an example of the FF build with b = 4, r = 1, S = (0000, 1010, 1110, 1000) illustrated in Figure 6 Fig. 6. Example of FF build with b=4, r=1, S=(0000,1010,1110,1000)

Consider the query examples:

• Y 1 = 0000 h(0000)=0 -----→ S(0) = 1, B 1 (0000) = {S 0 , S 8 } = {0000, 1000} • Y 2 = 0111 h(0111)=7 -----→ S(7) = 0, B 1 (0111) = {∅} • Y 3 = 1011 h(1011)=11 ------→ S(11) = 0, B 1 (1011) = {S 10 } = {1010}
By this way, each query has a quick response in O(1)

B. Optimizing large-scale fuzzy joins

With the integration of FF, our proposal ignores the costly and redundant ball calculation. Specifically, the FF-FJ algorithm consists of two phases: ((h(s), h(t i )), s), ∀t i ∈ B r (s) ∩ S, h(s) < h(t i ) ((h(t i ), h(s)), s), ∀t i ∈ B r (s) ∩ S, h(t i ) < h(s) The map cost for each record in this phase is only 1, instead of k|B r | in BF-BH algorithm. The number of intermediate elements for each record is optimized, instead of |B r | in BH algorithm, and may be approximate with BF-BH algorithm because of the same filtering technique. In the ideal case, regardless of the false positive, our approach has no redundant intermediate data and no duplicated results without verification in reducers. An example of join stage of FF-FJ for the fuzzy join with 4-bit string and threshold r = 1 is shown in Figure 8.

C. FF analysis and optimization

With an overview structure as above, FF can be applied to some data types (string, vector, set), some distance functions (Hamming, edit distance) as long as the balls can be calculated. In the binary space, FF uses m = 2 b , the exact probabilities of filtering are guaranteed 100%, without false probabilities. However, in practice, for a large finite alphabet set, a large string length, to optimize memory, the filter size is designed to be smaller than the actual set size. Hence, it may lead to a false probability. In the case of multiple balls that have the same hash index position, the ball in this position is the union of these collision balls. The response will include the real similar elements and also the mistaken records in another collision ball. These records are mistakenly assumed to be a similar element and must be calculated the distance in the join step.

The small false positive probability is caused by one of two cases follows

• (1) for the filter: an element in another collision ball is returned as an answer. • (2) for the join step: an irrelevant record of S has the same hash index with an exact answer. Conversely, it does not exist a false negative probability. In other words, no real similar element is not answered in the response. The false positive probability is shown in Figure 9 The precision of the fuzzy filter depends on the similarity function complexity, the size of FF (m), the quality of the hash function. For example, with Hamming distance threshold r, a dataset S of b bit-strings, for n real elements (|S| = n < 2 b ), the false positive of a hash bucket list of size m bits is

f S = 1 -(1 -1/m) n
r (1 -1/m) b r /r! mr! (1 - b r (1 -1/m) b r /r! mr! )
However, this false bit becomes a false positive answer only if its index in hash bucket S is also set.

The building of the matrix that includes all the balls with a reasonable alphabet, an acceptable length of a string is feasible. For large-scale datasets, avoiding repeated calculations for the pre-known balls will reduce a large workload.

In cases where the set of balls cannot be pre-calculated, the input dataset S can be read one time as a distinct key set to compute its balls. This cost can be amortized, especially using streaming or caching techniques (e.g Spark [START_REF] Zaharia | Spark: Cluster computing with working sets[END_REF]).

Another advantage of FF is the flexibility with distance, capable of equi-join and fuzzy join. The ball list can be easily updated quickly as soon as a new record appears. This can be applied in stream join applications. The solution given is that the AND operation in step (3) during the building phase is not performed. The ball list stores all the balls. The answer to each new query t is the intersection of S and the ball B(t).

IV. CONCLUSION

In this paper, we study theoretical details on large-scale fuzzy join algorithms in MapReduce. We propose approaches for building a Fuzzy Filter, a scalable solution with respect to the distance and the volume of the input datasets. This filter is a compact, probabilistic data structure that supports very fast similarity queries by maintaining a bit matrix, with small false positive rate and zero false negative rate. We show the relevance of this structure in fuzzy self join. In addition, our solution for the FF-FJ algorithm is more efficient than previous solutions without filters or with a Bloom Filter since it significantly reduces redundant data, costly and wasteful computations, and thus produces fewer intermediate data, eliminates duplicated results, and avoids unnecessary comparisons. Although FF-FJ algorithm has false positives and an extra cost for the pre-processing step, its efficiency in spacesaving and filtering often outweighs these drawbacks. We use the MapReduce cost model to prove it.

Future work includes extending Intersection Fuzzy Filter for fuzzy two-way join, fuzzy multiway join and fuzzy recursive join. Our optimizations may be extended in the cache or streaming supported framework to reuse the pre-processing cost. Perspectives also include validating our solutions, comparing them with other approaches and extending the research for other fuzzy join algorithms. Besides, experimental evaluation and a solution for skewness problems will also be considered.

Fig. 1 .

 1 Fig. 1. MapReduce Execution

Fig. 3 .

 3 Fig. 3. Join processing stage of BF-BH Algorithm

Fig. 4 .

 4 Fig. 4. Fuzzy filter modeling

Fig. 5 .

 5 Fig. 5. FF(S) structure

• ( 0 )

 0 Hash each ball to a bit array of length m. With bbit string, it exists 2 b balls, each ball has about b r /r! elements. Let us recall the assumption that hash operation performs in unit time. This step has the cost C (0) ≈ 2 b b r /r! • (1) Hash S to bit array of length m. C (1) = |S| • (2) Ball list compute by the intersection of BF (S) and BF (B(s i )).

•

  Stage 1 (Pre-processing): A filter F F (S) is built on a join key set of the input dataset S. Each worker hashes tuples of input splits to find h(s i ), emits a list of [h(s i )] to one reducer for the FF building. Thus, the Map cost is M = |S|, the communication cost isD = #mappers, the computation cost is the FF building cost C F F (S)-build ≈ b d d! 2 b + 2 b = ( b d d! + 1)2 b .If the ball list is pre-known, the processing cost is only 2 b of AND operations. Figure7describes an example of the pre-processing stage of FF-FJ for the fuzzy join. • Stage 2 (Join processing): F F (S) is distributed to all the computing nodes and is used to quickly emit real similar elements of the input dataset during the map phase. Each record s is hashed by h(s). BF [h(s)] returns a list of similar elements. Finally, mappers emit the intermediate tuple with the key is in form (h(s), h(t i )) if h(s) < h(t i ) and vice versa. The number of reducers is (2 b )(2 b -1)/2 s map ----→ F F (S)

Fig. 7 .Fig. 8 .

 78 Fig. 7. FF-FJ Pre-processing stage

Fig. 9 .

 9 Fig. 9. FF-FJ filtering process