Marie-Elisa Pinson

Romain Pogorelcnik

Franck Court

Philippe P Arnaud

Catherine Vaurs-Barrière

Catherine Vaurs-Barriere
email: catherine.barriere@uca.fr

CLIFinder: Identification of LINE-1 Chimeric Transcripts in RNA-seq data

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

Introduction

Transposable elements represent 45% of the human genome. Due to the challenge of sequence alignment, their role in the transcriptional landscape is poorly studied. However, it is known that LINE-1 retro-elements (L1s) can drive transcription of adjacent genomic regions. For instance, in the 5' untranslated region (5'UTR) of the most recent L1 subfamilies (from the oldest L1PA10 to the most recent L1PA1), an antisense promoter (ASP) has been identified [START_REF] Speek | Antisense promoter of human L1 retrotransposon drives tran-scription of adjacent cellular genes[END_REF][START_REF] Macia | Epigenetic control of retrotransposon expression in human embryonic stem cells[END_REF]. This ASP can produce L1 Chimeric Transcripts (LCTs) that include the L1 5'UTR sequence in antisense orientation followed by the adjacent genomic region.

LCTs have been characterized mainly using bioinformatics approaches to query dbEST and correspond to spliced ESTs where the L1 5'UTR sequence in antisense orientation is associated with a gene exon [START_REF] Speek | Antisense promoter of human L1 retrotransposon drives tran-scription of adjacent cellular genes[END_REF][START_REF] Nigumann | Many human genes are transcribed from the antisense promoter of L1 retrotransposon[END_REF][START_REF] Mätlik | L1 antisense promoter drives tissue-specific transcription of human genes[END_REF]Wolf et al., 2010;[START_REF] Criscione | Genome-wide characterization of human L1 antisense promoter-driven transcripts[END_REF]. In addition, [START_REF] Cruickshanks | Isolation of cancer-specific chimeric transcripts induced by hypomethylation of the LINE-1 antisense promoter[END_REF] developed a dedicated biomolecular approach (called LCD) that allowed the identification of 18 LCTs. Nevertheless, these studies remain limited by the a priori definition of such sequences (position of the L1 primer in LCD and selection of only spliced exon-containing ESTs). To take advantage of the strong potential of next generation sequencing to unravel the transcriptome composition, we developed Chimeric LINE Finder (CLIFinder), a new bioinformatics tool that identifies chimeras corresponding to potential LCTs in RNA-seq data.

Methods

CLIFinder is a Galaxy tool designed to identify chimeras from one or several samples. This tool was developed mainly to analyze stranded paired-end RNA-seq data. It can also analyze non-stranded paired-end RNA-seq data, but with a higher rate of false-positive chimeras, particularly from events that encompass L1 promoter sequences. Quality and adapter trimming must be done on Fastq files, before their use in CLIFinder.

Finding chimeras

The iterative procedure starts by finding chimeras for each sample (Supplementary Fig. S1).

We consider here that Read 1 (R1, starting at the 5'-end) of the stranded pair must contain an L1 sequence. This parameter is customable according to the stranded or non-stranded sequencing and the repeat element considered. For stranded libraries:

if the first read of the pair (R1) is in the sense of the transcript, R1 is considered to correspond to the transposable element part of the chimera (Fig S1)

if the first read of the pair is in the opposite sense of the transcript, then the second read of the pair (R2) is considered to be the transposable element part of the chimera.

For non-stranded sequencing, both hypotheses are retained.

Step 1 consists in selecting pairs (R1 and R2) that include R1 with a minimum of X consecutive bp that correspond to repeat element sequences given by the user (for instance, 5'-end LINE-1 sub-families sequences) and an unmapped mate (R2). Only paired reads that respect this condition are retained. Mismatches (Y) can be tolerated or not for L1 mapping. In step 2, these paired reads are filtered using the RepeatMasker tool to retain only reads for which at least Z consecutive bp are not detected as a repeated sequence. To identify chimeras (step 3), the retained filtered paired sequences are aligned to the human reference genome with a flexi-ble maximum insert size between paired reads (W).

Therefore, CLIFinder is a fully customizable tool to detect transcripts initiated by different types of repeat elements with X, Y, Z and W values that can be changed by the user to adapt the filter stringency. The parameter settings depend, notably, on the read length and the L1 reference sequence list given by the user in Step 1. In our hands, using one consensus sequence for each L1 element from the 27 sub-families (Khan et al., 2006) as reference for analyzing 100 to 150 bp paired-end reads, the optimal conditions to identify the largest number of chimeras was X = 30 bp, Y = 6 mismatches for Step 1. For Step 2 only the less stringent condition of Z = 30 bp was used to allow at least the design of a primer in the unique sequence for later validation experiments. Finally, W = 50,000 bp was the maximum insert size between paired reads that allowed the identification of the largest number of spliced chimeras.

Merging chimeras from all samples and concatenation

For each sample, the chimera datasets are stored in two bed files that correspond to each part of the paired-end read alignments. For an overview of all data and comparison of different datasets, CLIFinder concatenates the different files in two unique bed files, one that corresponds to the L1 part (R1) and the other to the unique sequence part (R2) (step 4). At this stage, several potential chimeras can overlap in the first or/and second read dataset. Bedtools merge function is used to group the different reads corresponding to the same locus (±100 bp) (step 5) to eliminate repetitive information that might correspond to the same chimera. This task is done for both files. The Getfasta function from Bedtools is then employed to create a unique fasta file (step 6) that contains all the potential chimeras concatenated from all samples to generate the html report.

Visualizing and downloading the resulting chimeras were identified in the MCF-7 RNA-seq datasets than in the Ov1.1 dataset, in agreement with the higher sequencing depth. Nine chimeras were found both in the Ov1.1 and MCF-7 datasets.

Already known LCTs were identified in each dataset.

B. Analysis of the concordance concerning the number of chimeras identified in the two MCF-7 replicates. Among all identified chimeras (detected by at least one read in one replicate), 22%

were common to both replicates. When only chimeras depicted by at least 2, 3 or 4 reads in one replicate were considered, the overlap increased respectively to 52%, 82% and 83%, suggesting that CLIFinder analysis results are reproducible.

Figure 1 :

 1 Figure 1: Analysis of the chimeras identified in stranded paired-end RNA-seq datasets from different tissues by CLIFinder A. Comparison of chimeras identified in the Ov1.1 dataset and the two replicates (Rep1 and Rep2) from the untreated breast cancer cell line MCF-7. (Lit) indicates the number of chimeras corresponding to LCTs already described in the literature. Two to three times more chimeras

Acknowledgements

The authors acknowledge the support of Y Renaud from Byonet (byonet.fr).

Funding

This work was supported by the Plan Cancer-INSERM [CS14085CS, to P.A.], ARC [SFI20121205549, to C.V.B.], the Auvergne Region and the Fonds Européen de Développement Régional (FEDER).

The code is available at: https://github.com/GReD-Clermont/CLIFinder; and for Galaxy users, it is directly accessible in the tool shed at: https://toolshed.g2.bx.psu.edu/view/clifinder/clifinder/

CLIFinder results can be visualized on a Galaxy interface. An html table is generated where each line corresponds to a chimera defined by its genomic coordinates (hg19), transcription strand, and number of reads detected in each sample. BLASTn searches against EST and RNA databases are performed for chimera annotation, if data are already available. Users can also download: 1) a tabular file with the same content as the html page; 2) a final annotated file with additional information for each chimera: ID, gene name and strand (if it is localized in an intragenic region), and characteristics of the involved L1 element (family name, position, size, transcription strand) (step 7) (Supplementary Table S1) and 3) a CLIFinder execution report with the number of pairs retained after sample filtering.

CLIFinder was first tested on publicly available metastatic high grade serous ovarian cancer mRNA-seq data (Illumina HiSeq2500, 100bp stranded paired-end, 47 million reads) [START_REF] Böhm | Neoadjuvant Chemotherapy Modulates the Immune Micro-environment in Metastases of Tubo-Ovarian High-Grade Serous Carcinoma[END_REF]. The original dataset GSM2122741 (Ov1.1) was used to create: 1) Ov1.2, an implemented dataset similar to Ov1.1, but including also the L1-MET LCT sequence (positive control) and a L1PA2 5'UTR antisense sequence (negative control) and 2) Ov1.3, a depleted dataset in which 30% of reads included in Ov1.1 were randomly eliminated and the L1-MET and L1PA2 5'UTR antisense control sequences were added. Two additional datasets that corresponded to mRNA-seq data for the MCF-7 (untreated breast adenocarcinoma) cell line (E-MTAB-3788, Illumina HiSeq2500, 150 bp stranded paired-end, mean 135 million reads) were also analyzed [START_REF] Philippe | Activation of individual L1 retrotransposon instances is restricted to celltype dependent permissive loci[END_REF]. The parameters used for this analysis are described in Supplementary Figure S1. On average, each analysis required few hours depending on sequencing depth (i.e., less than 3 hours for the three Ov datasets and up to 8 hours for the two MCF-7 replicates) using a Quad-Core workstation with 16Go RAM (Supplementary Table S1).

Results

All results are available in Supplementary Table S2. From Ov1.1, CLIFinder identified 37 chimeras that corresponded to potential LCTs. For Ov1.2, 38 chimeras were obtained: the previous 37 chimeras and L1-MET LCT (ID_27). Ov1.3 analysis high-lighted only three chimeras:

L1-MET and two other chimeras with a reduced number of reads. Some chimeras were associated with multiple L1s (ID_19). In this case, after visualization of the chimera position loaded from the html file on the genome browser UCSC, manual monitoring must be performed to retain the element presumed to initiate the chimera transcription. Attention must also be paid to remove the few chimeras transcribed in the same orientation as the L1 (ID_12_13).

Consistent with the RNA-seq specificities, chimeras defined by only one read, displayed R1 and R2 sequences of 100bp. When a chimera is defined by several over-lapping reads, R1 and R2 size can be increased. Negative (in the case of R1-R2 overlapping) or null distance between R1 and R2 was often observed, suggesting a linear transcription from L1 that continued in the adjacent unique sequence. In some cases, the distance between R1 and R2 was larger than expected (ID_7, ID_30), demonstrating the occurrence of splicing events (Supplementary Fig S2).

To assess whether chimeras detected by CLIFinder in Ov1.1 could correspond to LCTs initiated at L1 ASPs, the L1 elements involved in the 36 chimeras were compared to the list of 14,495

L1s containing a 5'UTR sequence (extracted from RepeatMasker for the 27 sub-families used by CLIFinder). This showed that 33 chimeras involved L1 elements with a 5'UTR. Then, analysis of the L1 sub-families involved in these 33 chimeras revealed that, although CLIFinder used the consensus sequences from the 27 L1 sub-families to identify chimeras, 31 chimeras (94%) involved L1s only from the more recent sub-families (i.e., L1PA1 to L1PA7) that possess ASP. Finally, comparison of the 33 chimeras and of known LCTs demonstrated that five chimeras identified in this metastatic ovarian cancer sample corresponded to EST-LCTs previously found in other tissues. Altogether, these observations suggest that most chimeras identified by CLIFinder from RNA-seq data are true LCTs.

To strengthen these results, two replicates from stranded paired-end untreated breast adenocarcinoma MCF-7 cells were also analyzed. After curation of the chimeras that did not meet the criteria for potential LCTs (i.e., chimeras in the same transcription sense of L1: n= 39;

and chimeras associated with L1 but without 5'UTR ASP region: n=8), in total, 125 chimeras were identified in the two replicates (Supplementary Table S2C). Among these chimeras, 118 (94.5%) involved recent L1s and 20 (16%) corresponded to already described LCTs (Fig 1A ).

Comparison of the genomic position of the chimeras identified in the two MCF-7 replicates indicated that 28 chimeras (22%) were common to both samples (22%) (Fig 1A). This moderate overlap can be explained by the fact that chimeras can be detected only if at least one cDNA fragment encompassing the L1/unique sequence junction is sequenced. When only chimeras defined by at least 2 or 3 reads in one MCF-7 replicate were considered, the overlap between replicates increased to 52% (two reads) and 82% (three reads) (Fig. 1B). This indicates that results are reproducible for highly represented chimeras and that the analysis of different samples together allows assessing precisely LCT expression genome-wide in a specific condition.

Two to three times more chimeras were identified in the MCF-7 RNA-seq datasets than in the Ov1.1 dataset, in agreement with the higher sequencing depth (Supplementary Table S1).

Interestingly, among the identified chimeras, nine were common between the MCF-7 RNA-seq datasets and the Ov1.1 dataset (Fig. 1A). Among these chimeras, some corresponded to already known LCTs (n=4), such as Ov1. S2C).

In summary, CLIFinder is a new bioinformatics tool to identify genome-wide transcribed chimera sequences corresponding to LCTs from stranded paired-end RNA-seq datasets. This tool will be useful for genome-wide analyses of LCT expression in different tissues, in normal or pathological conditions. Moreover, CLIFinder can be adapted to study transcription from other repeat types.

Conflict of Interest: none declared.


Baptiste Busch

Guilherme Maeda
email: maeda@ias.tu-darmstadt.de

Yoan Mollard

Marie Demangeat

Manuel Lopes
email: manuel.lopes@tecnico.ulisboa.pt

Postural Optimization for an Ergonomic Human-Robot Interaction

In human-robot collaboration the robot's behavior impacts the worker's safety, comfort and acceptance of the robotic system. In this paper we address the problem of how to improve the worker's posture during human-robot collaboration. Using postural assessment techniques, and a personalized human kinematic model, we optimize the model body posture to fulfill a task while avoiding uncomfortable or unsafe postures. We then derive a robotic behavior that leads the worker towards that improved posture. We validate our approach in an experiment involving a joint task with 39 human subjects and a Baxter torso-humanoid robot.

I. INTRODUCTION

Humans and robots are starting to work in shared environments allowing an increasing diversity of tasks they can accomplish together. This also creates new challenges of safety, and acceptability. New robotic assistants should be able to prevent worker's discomfort as well as more aggravated work-related diseases. Some efforts have already been made to improve acceptability by including social behaviors, like proxemics, in the field of human-robot interaction [START_REF] Mitsunaga | Adapting robot behavior for human-robot interaction[END_REF]- [START_REF] Koay | Social roles and baseline proxemic preferences for a domestic service robot[END_REF]. Most advanced robotic planners combine multiple notions, including safety and social acceptance, to create humanaware robotic responses [START_REF] Sisbot | Synthesizing robot motions adapted to human presence: A planning and control framework for safe and socially acceptable robot motions[END_REF]. In contrast to a human-human interaction, where both parties try to maximize their own comfort, sometimes at the expense of the other, an assistive robot should always maximize the comfort of its coworker.

A simple example arises when the robot passes, or presents, an object to the human. When handing over an object, the final object pose influences the way we can grasp it [START_REF] Rosenbaum | From cognition to biomechanics and back: The end-state comfort effect and the middleis-faster effect[END_REF], [START_REF] Kolsch | The postural comfort zone for reaching gestures[END_REF], and thus the comfort of that posture. One way to solve this problem is to analyze how the human receiver grasps a specific object and orient it to improve the receiving posture [START_REF] Aleotti | Comfortable robot to human object hand-over[END_REF]. Another way is to define a cost function that captures all possible hand-over configurations and allows to find the optimal comfortable solution. Common cost functions comprise safety, visibility, and postural comfort [START_REF] Sisbot | Synthesizing robot motions adapted to human presence: A planning and control framework for safe and socially acceptable robot motions[END_REF] or naturalness & appropriateness [START_REF] Cakmak | Human preferences for robot-human hand-over configurations[END_REF]. However, such techniques rely on a generic human model which might not capture the individual characteristics of each user. We believe that having a personalized model to adapt to the specificity of each user would greatly benefit the interaction. Recent research addressed the problem of a personalized human model to reason on human kinematics while planning the Fig. 1: Representation of the setup considered in the user study. The robot presents to the user a spherical toy in which multiple shapes can be inserted. Final pose of the object is calculated from the user posture at his current location. robot's behavior [START_REF] Bestick | Personalized kinematics for human-robot collaborative manipulation[END_REF]. On the other hand, the cost function considered by the authors was chosen for its simplicity and did not include social or postural cost. As they stated, using a more biologically-plausible cost would yield strictly superior results.

"Musculoskeletal disorders" (MSDs) are the single largest category of work-related diseases in many industrial countries [START_REF] Punnett | Work-related musculoskeletal disorders: The epidemiologic evidence and the debate[END_REF]. Over the years, many assessment techniques have been developed to evaluate worker's body posture at their workstation [START_REF] Takala | Systematic evaluation of observational methods assessing biomechanical exposures at work[END_REF]. Methods for postural assessment can be classified according to the accuracy of data collection and the degree of intrusion caused by the required sensors to collect them [START_REF] Beek | Assessment of mechanical exposure in ergonomic epidemiology[END_REF], [START_REF] Wells | Assessment of physical work load in epidemiologic studies: Common measurement metrics for exposure assessment[END_REF]. Observational methods, based on observations of the worker, are straightforward to use and applicable to a large variety of situations [START_REF] Karhu | Correcting working postures in industry: A practical method for analysis[END_REF], [START_REF] Hignett | Rapid entire body assessment (reba)[END_REF]. Their accuracy is however limited as they are mainly developed for paper-based observations without the need of specific tools or sensors. With the development of non-intrusive human tracking system, like depth sensors, automatic postural assessment based on observational methods start to emerge [START_REF] Diego-Mas | Using kinect sensor in observational methods for assessing postures at work[END_REF]. The development of such techniques will have a significant impact in industry by drastically reducing the cost of ergonomic solutions. Moreover, it will also benefit fields like human-robot interaction by allowing a more thorough analysis of the human coworker.

When we, humans, accomplish a task our body posture is (partially) constrained. For example, acting on an object constrains the pose of the hand relatively to the object and the head faces the object we are acting upon [START_REF] Pandey | Towards human-level semantics understanding of human-centered object manipulation tasks for hri: Reasoning about effect, ability, effort and perspective taking[END_REF]. But due to the large number of degrees of freedom (DOF) of the human body, other body parts are unconstrained and several body postures are viable with respect to the task. However, not all of them are viable in terms of ergonomics. Optimizing the model body posture is then the logical next step to find an ergonomically correct posture for the worker to accomplish a specific task.

Most researches on human-robot interaction optimize the robot's placement and behaviors w.r.t specific cost functions that acknowledge human needs [START_REF] Sisbot | Synthesizing robot motions adapted to human presence: A planning and control framework for safe and socially acceptable robot motions[END_REF], [START_REF] Ikuta | Safety evaluation method of design and control for human-care robots[END_REF], [START_REF] Sisbot | A human aware mobile robot motion planner[END_REF]. Similarly, our idea is to find an optimal human body posture to solve a task considering three important aspects of the interaction that are safety, acceptability and task constraints. Those three factors were chosen according to their importance in the existing literature and are very similar to previous researches in the human-robot interaction field [START_REF] Cakmak | Human preferences for robot-human hand-over configurations[END_REF], [START_REF] Sisbot | A human-aware manipulation planner[END_REF]. Our hypotheses, verified in this work, is that the user will intuitively behave similarly to the predictions made by our algorithm. In the case of handing over objects or joint manipulation, the robot can induce the human location and posture by planning the positioning of the object within the shared workspace.

In this paper we introduce a framework for postural optimization of the human body. This framework respects the three aspects of the interaction by introducing notions derived from proxemics [START_REF] Mitsunaga | Adapting robot behavior for human-robot interaction[END_REF], subject laterality, and visibility [START_REF] Pandey | Towards human-level semantics understanding of human-centered object manipulation tasks for hri: Reasoning about effect, ability, effort and perspective taking[END_REF] for the notion of acceptability. Other measures such as legibility could also be considered, as we did in our previous work [START_REF] Stulp | Facilitating intention prediction for humans by optimizing robot motions[END_REF], but here we focus more on physical comfort and not on the impact of perception of intentions in the shared activity. Safety, only considered here as the postural risk of MSDs, is handled by the Rapid Entire Body Assessment (REBA) technique [START_REF] Hignett | Rapid entire body assessment (reba)[END_REF]. The choice of this postural assessment technique was motivated by its range of application and the fact that it provides quantitative measures.

This work aims at being a study on the effects of incorporating postural assessment techniques derived from ergonomic researches in the human-robot interaction. The main contribution of our work is the integration of the REBA method in a planning framework to provide a realistic estimate of a motion's ergonomic cost. Second, we introduce a solution to automatically assess the worker's body posture using the same REBA method and couple it to a graphical interface to feedback the user on the risk of his or her posture. This graphical interface is presented in Section IV. Finally we have realized an extensive user study with 39 participants that validate the benefits of our approach on the interaction. We have collected both the subject's perception of the system and quantitative measures provided by the automatic assessment of the subject's posture and analyzed them in Section VI.

Closer to our work is the research of Sisbot et al. [START_REF] Sisbot | Synthesizing robot motions adapted to human presence: A planning and control framework for safe and socially acceptable robot motions[END_REF], [START_REF] Sisbot | A human aware mobile robot motion planner[END_REF], [START_REF] Sisbot | A human-aware manipulation planner[END_REF] and the recent works from Bestick et al. [START_REF] Bestick | Personalized kinematics for human-robot collaborative manipulation[END_REF] and Suay et al. [START_REF] Suay | A position generation algorithm utilizing a biomechanical model for robot-human object handover[END_REF]. With the exception of [START_REF] Suay | A position generation algorithm utilizing a biomechanical model for robot-human object handover[END_REF], the cost function we have chosen to respresent the human factor is more biologically grounded and taken directly from the ergonomic field. Moreover, our implementation of the visibility cost, firstly introduced by Sisbot et al., also optimizes the object orientation and not only its position. This is particularly important for the object used in our user study, illustrated in Fig. 1.

Details of the implementation are given in Section V. The framework has been tested on a user study, introduced in Section VI, by comparing different methods for handing over the spherical object illustrated in Fig. 1.

II. AUTOMATIC POSTURAL ASSESSMENT

Automatic postural assessment, based on observational methods, has started growing in interest with the development of cheap and easy to use human tracking systems [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. Although the REBA technique has been initially developed for pen-paper observations [START_REF] Hignett | Rapid entire body assessment (reba)[END_REF], the fact that it handles static as well as dynamic postures and that it relies on quantitative values makes it suitable for an automatic assessment. The technique is based on the observation of joints of the human body. Each joint value is associated with a score which corresponds to a risk of MSDs. The higher the score, the higher the risk. As a high score on the upper arm is not equivalent to the same score on the trunk, the method also provides comparative tables to calculate the final score that ranges from 1 (no risk of MSDs) to 12 (very high risk, recommendation to change posture immediately).

To be fully automatized, the technique requires a human kinematic model that returns the joint values from the specific part of the human body (e.g. elbows, hands...). In Section V we detail the process of creating a personalized human model based on Kinect skeleton model. Joint values and REBA score of the observed posture are calculated from the tracked frames.

This assessment technique is the main component of our framework for postural optimization detailed in Section III. While other techniques for MSD assessment are available, here we opt to use the REBA metric due to its generality and the provision of a quantitative assessment.

III. POSTURAL OPTIMIZATION

To respect the three main aspects of interaction, that are safety, acceptability, and task constraints, we define several cost functions and constraints to find an optimal body posture during the interaction. In the following paragraphs we detail, for each aspect, the associated cost function or constraint.

A. Safety and Comfort

Human safety is a central piece of the interaction. In term of body posture, safety corresponds to minimizing the risk of MSDs. To achieve this we find the body posture that minimizes the score returned by the postural assessment technique REBA [START_REF] Hignett | Rapid entire body assessment (reba)[END_REF].

In its original formulation, the REBA method does not show suited for numerical optimization due to the discrete grading and the presence of plateaus. Thus, we approximate the discontinuous nature of the scores by a sum of weighted polynomials, and optimize the weights to closely reproduce the score in the continuous domain,

C posture (q) = n i=1 w i Q i (q) ( 1
)
Where n is the number of joints considered in the REBA techniques and Q i (q) is a 2nd order polynomial of joint i. Coefficients of the polynomials are calculated from the original REBA score of each joint. The weights w i are learned from the total REBA score calculated on several body configurations. For learning the weights, we define a set of random poses, ensuring each class of the original REBA cost (from 1 to 12) are evenly represented. We then find the weights that minimize the difference between the original REBA cost and its polynomial approximation for all the posture of the set.

The posture of the body, represented by its vector of joints q is considered as being static and independent from the initial body configuration. We only consider static postures. This choice was motivated by the fact that any initial body configuration might be ergonomically incorrect and therefore should not interfere with the final posture.

Although the cost function ( 1) is an approximation of the REBA score, postures that minimize it also minimizes the original score as the minima of the two functions are identical. In the rest of this paper we use the score function (1) to optimize the body posture but assess the obtained posture with the original REBA method.

In its implementation the REBA method also takes the weight of the load into consideration. For the moment, we have discarded it in our experiments as it was considered as negligible. However, this is an important notion to add in the future.

B. Task constraints

For some tasks, the pose of a specific body part, like the hand, is constrained to a specific location. For example when we use a tool our hand is tied to it, which itself is linked to the object we are acting upon. This part of the framework is the only specific part that needs to be specified for each task. Most common task constraints would be to set parts of the worker's body to a certain pose.

Considering the forward kinematic of our human model F K, the pose in Cartesian space of body part i is represented as F K i . Constraining a body part to a certain location in space is equivalent to minimizing the distance between the forward kinematic and the desired pose F K des i . This distance is expressed as two subcomponents, one for the position as Euclidean distance and one for the orientation as distance between two quaternions. The distance between two quaternions is defined as

(Q 1 , Q 2 ) = 1 -Q 1 , Q 2 2 .
Constraining multiple body parts is performed by summation of the distances,

C task (F K, F K des ) = i ( F K i,pos -F K des i,pos + k(1 -F K i,rot , F K des i,rot 2 )). (2)
Because position and orientation distances do not share the same unit, it requires the addition of a scaling factor k ∈ R. In practice, we have set k ≈ π. As the quaternion distance varies between 0 and 1, this then corresponds to the distance between the two angles traveled on the unit circle. We also note that F K des might be expressed w.r.t the object frame. This is particularly interesting when the object is free to move in space and its pose is part of the optimization.

C. Acceptability

The concept of acceptability is not easy to define. It is usually divided into social acceptability: How does the society perceive robotic systems?, and practical acceptability: How do people perceive the robot when interacting with it? [START_REF] Nielsen | Usability engineering[END_REF]. In this paper we focus on the latter. We incorporate visibility, proxemics and user's laterality (right or left-handed) in our framework in order for the worker to feel at ease during the interaction.

Visibility: Visibility is an important notion to consider. When the robot moves an object, it should always do so in the worker's field of view. Otherwise, it might surprise the user. We have put the visibility notion under acceptability although it does not uniquely belong to this category. For example, a non trained worker would most probably look at the object he is acting upon in order to fulfill his task (task constraints). Such as novices in computers look at their keyboard when typing. Another one might get hurt if he uses some tools and cannot visually verify the results of his actions (safety).

To optimize for visibility, the model's head pose is directly linked to the pose of the object X obj acted upon. Pose of the object can be considered as fixed, attached to the model's hand by a predefined transformation or set as a variable of the optimization. We denote the sight vector coming from the head as H x , H corresponding to the forward kinematic of the head F K head . We consider that this vector originates from the center of the head and is parallel to the ground when the head is straight. The visibility cost corresponds to the angle between the vector from the center of the head to the object X obj H and H x . It is calculated using the dot product between them as arccos( H x • X obj H). This way we ensure that the object is approximately at the center of the vision cone when this cost is close to 0.

For some objects, the orientation also matters. For example, the handle of a tool should be directed toward the user to ease the grasping. To represent this we consider a feature vector v obj that need to be aligned with the directional vector of the head H x . At the moment, this vector is predefined for each object used in the experiments. The corresponding cost is also defined by the dot product arccos( H x • v obj ). The final cost for visibility corresponds to the sum of the two dot products,

C visibility (F K Head , X obj ) = arccos( H x • X obj H) + arccos( H x • v obj ). (3)
Proxemics: People have special concerns about their personal space either in terms of intimacy and safety. We consider proxemics -physical and psychological distancing from others [START_REF] Hall | The Hidden Dimension[END_REF] -to address such concerns. Close interaction like handing-over an object would be socially unacceptable and create uncomfortable situations if it happens too close to the worker, especially for non-trained ones.

In our framework we have added the proxemics notion as a constraint to ensure that the optimized posture will not violate the worker's intimate space. The proxemics constraint corresponds to the minimal distance from the human waist to the object. Only planar distance (x and y coordinates) are here constrained. This limit correspond to the boundary of the subject's intimate space, i.e 0.45m [START_REF] Hall | A system for the notation of proxemic behavior[END_REF],

X Obj ∈ proxemics constraints. ( 4
)
Laterality: Every worker is unique. Some are righthanded, other left-handed. Therefore, the model should also take into account this specificity. We leave the possibility to select the worker's laterality. This impacts which hand is constrained to act upon an object.

D. Framework definition

Finally, we group all the previous cost functions and constraints (1-3) to define a parameterized framework, whose pseudocode is detailed in algorithm 1, for optimizing the human body posture while solving a task. Our formalism is very generic and considers many tasks beyond the ones presented in this paper. The task constraint function and its parameters are the parts that have to be redefined depending on the specific task to solve.

Algorithm 1 Postural Optimization Framework 1: procedure OPTIMAL BODY POSTURE(laterality, w, F K des , obj dof , H X obj ) 2:
model laterality ← laterality if obj dof is "fixed" then 6:

p ← H X obj

7:

else if obj dof is "position" then 8:

p ← random position 9:

else if obj dof is "orientation" then 10:

p ← random orientation 11:

else if obj dof is "full" then 12:

p ← random pose 13:

f (q, p) = w 1 C posture (q) + w 2 C task (F K(q), F K des ) + w 3 C visibility (F K Head (q), p) 14:
q opt , H p opt ← min f (q, p) subject to p ∈ proxemics constraints 15:

return q opt , H p opt

The final cost function is a weighted sum of the different elements, some of them with different units for which we need different weights w i ∈ R. This weights will most probably be task dependent. For example, in some industrial tasks, visibility might be a critical aspect. In this case increasing the weight that account for visibility will lead to the desired behavior. The outputs of the algorithm q opt and H p opt correspond to the optimal human posture in joint space and the optimal object pose w.r.t the human reference frame respectively.

IV. FEEDBACK INTERFACE

Most of the time, workers are unaware of the risk induced by a wrong posture. Dangerous postures might not have a direct effect on the body but it is the repetition that increases the risk of MSDs. Therefore, a direct feedback is an interesting feature that could help workers maintaining a good posture at their workstation. To that extent, we have developed a graphical interface to animate a model with the user's observed body posture. The projection on the model is almost real-time. We also evaluate the risk of his or her posture, using the REBA assessment technique, and displays it with spheres located at the evaluated body joints. The color of each sphere represents the risk at its corresponding location. It ranges from "green" (no risk) to "red" (high risk) according to the REBA method. In Fig. 2 we show two screenshots of the graphical interface. Using the buttons on the right side, the user can choose to display a male or a female version of the model. He or she can also switch between a front or a back view. After some trials with test subjects, it has been decided that the front view should mirror the user's body configuration, i.e rising the right arm translates to a rising of the model left arm. In back view, however, the body configuration is normally displayed.

V. IMPLEMENTATION DETAILS

In this section we define the implementation choices we have made to track the human body for the automatic assessment of Section II and to optimize the body posture using the framework defined in Section III.

A. Model generation and human tracking

The automatic postural assessment requires a human model that returns joint values from pose of body segments. To this end, we calibrate a personalized human model as a URDF with 32 degrees of freedom (DOF) by calculating the length of each body segments on the observed subjects skeleton using Kinect cameras. This personalized model is then used during the optimization described in Section III. While during the calibration of the model the environment can be setup such that the human can stand directly in front the camera, during the execution, we found that the presence of the robot, constant occlusions, and space constraints make it difficult to reliably assess the REBA score using the same camera.

Thus, currently, at runtime we opted to track the human using optical markers. 1 Each subject has been equipped with a suit covered by OptiTrack markers to track the main body segments (head, hands, elbows, torso and waist). The models frames are recorded during the whole interaction. To obtain the model joint values we compute its inverse kinematic on the recorded data. As the legs are not tracked, we set them in rest position, i.e. with joint values leading to the minimal REBA score.

The waist frame is the most important frame of the OptiTrack suit. It corresponds to the model base frame. We also use it to express the position and orientation of the subject in the robot workspace.

B. Optimization of the cost functions

To minimize the costs defined in Algorithm 1 we use a simple gradient descent algorithm from scipy library. This is sufficient as we consider only static postures and not trajectories.

C. From human to robot space

The solution provided by Algorithm 1 corresponds to the optimal body posture in joint space, q opt and the optimal object pose H p opt in the human space. We must now generate a robot trajectory that positions and orients the object in its optimal location H p opt such that the human is in the optimal posture q opt . The relation between q opt and H p opt is defined as the forward kinematic F K. The robot trajectory can be designed by expressing the pose of the object w.r.t the robot's reference frame, R p opt . To this end, at runtime we locate the current position of the human w.r.t the robot's frame using, for example, optical markers or depth cameras to compute a transformation R T H . This process is illustrated in the left part of Fig. 3.

Transformed into the robot's space, the optimized solution represents the optimal posture for the human to interact with the robot. For simplicity, take the case where R p opt needs to be satisfied only at the end of the interaction (e.g. in handover) and the robot starts from a pre-defined home position R p init . Depending on the location of the human w.r.t. the robot, and the degree of redundancy of the robot, two situations are possible. If the final object position is within the workspace of the robot, many possible robot trajectories that lead to the satisfaction of R p opt can be designed. Conversely, if the final object position is outside the workspace of the robot, no trajectory can be generated.

To account for both cases and quickly generate a trajectory, we solve a motion planning problem where the initial and final end-effector positions of the robot are connected by a straight line (in Cartesian space), as an initial guess. The orientation of the end-effector is interpolated by slerp between the initial and final poses. If an IK solution on this straight Fig. 3: Left: finding the desired object pose in Cartesian space w.r.t. the robot's reference frame R p opt given the solution of the ergonomic optimization q opt and H p opt . Right: a straight trajectory is used as an initial guess to bring the object from the robot's home position to the handover position. If a solution is not possible, stochastic optimization is used to optimize the trajectory. trajectory is not found, we use stochastic optimization to slightly perturb the final desired position of the end-effector and also to reshape the straight line to search for a valid robot's IK trajectory 2 . Perturbing the final desired position of the end-effector will make the exact reproduction of R p opt and force the human model to deviate from its optimal posture q opt . Thus, we penalize deviations from the original desired location to find a compromise between the optimal posture of the human and a kinematically feasible robot trajectory. This process is illustrated in the right part of Fig. 3.

D. Graphical interface

The feedback graphical introduced in Section IV has been developed using Unity software. The male and female model were imported from Mixamo website without license nor restriction of use. The code for the graphical interface is available on a GitHub repository 3 .

VI. USER-STUDY EXPERIMENT

We apply the postural optimization framework on an experiment with real users interacting with our Baxter torsohumanoid robot. Two points are tested: Are the postures generated with our framework perceived better than other types of postures? and Does the optimal robot's behavior leads the real user to a safer posture? During those experiments, the feedback interface was not presented to the subjects to avoid perceptual biases toward the postures generated by our algorithm.

With the object illustrated in Fig. 1 we mimic an industrial scenario where the robot helps the worker by positioning and orienting an object in which the worker has to insert specific shapes. In total five shapes were considered, located on the blue side of the ball. Name of the shape to insert was written on the robot's screen. Between each insertion the robot was sent back to a neutral pose to let the user prepare the next shape.

We have conducted an extensive user study with 39 participants (18 females and 21 males, 2 left-handed, aged 35 ± 11.26). Before the experiment, subjects were asked to rate their experience with robotic systems on a scale from 1 (no experience) to 5 (daily usage). Result is 2.18 ± 1.27.

Relative pose

Optimized pose Fig. 4: Difference between the pose obtained with the relative (left picture) and the optimized conditions (right picture). Three robot's behaviors have been compared. We refer to them as fixed, relative and optimized conditions. Each participant has been presented a sequence of two behaviors from the set of all permutations. Each run of a behavior is composed by the five shapes to insert in a random sequence. Behaviors are detailed in the following paragraphs:

Fixed: In this behavior the robot does not take into account the worker position and deliver the object to a fixed pose. We have used this behavior as a baseline.

Relative: Research from ergonomics tells us that handing-over an object should happen at torso height at twothird of the receiver's arm maximum elongation [START_REF] Kolsch | The postural comfort zone for reaching gestures[END_REF], [START_REF] Granjean | Fitting the Task to the Man: an Ergonomic Approach[END_REF]. For orientation, we constrained the insertion hole to face the user. At execution, the user's torso frame is tracked and the pose of the object on the reference frame of the robot is computed using the required homogeneous transformations.

Optimized: Using our framework from Sec. III we optimize the user's body posture to receive the object and calculate where to deliver it with reference frame transformations. Computing the optimization of the receiving pose is achieved within ∼ 5s on a i7-3720QM 2.60GHz computer.

After observing the two behaviors, the subjects were asked to order them according to their preferences and to complete a survey composed of a 12 Likert scale items for each observed behavior. Affirmations were ranked from 1 (I strongly disagree) to 5 (I totally agree). They are based on the System Usability Scale methodology [START_REF] Brooke | Sus-a quick and dirty usability scale[END_REF] with one affirmation over two written with the negative form. The survey was divided in three subcategories representing the considered aspect of the interaction, i.e safety, acceptability and task constraints. This separation was not made visible to the subjects for whom the 12 affirmations were shown in a random order. After answering the 12 items, subjects had the possibility to leave comments on the observed behaviors. Complete results and survey questions are detailed in Fig. 5. For clarity, the affirmations in the negative form are drawn with negative values from -5 to -1. Subjects' body poses were recorded, using the OptiTrack suit, to evaluate their posture during accomplishment of the task.

The data of the experiment are available on a Zenodo repository 4 alongside a GitHub repository that contains all the necessary materials to read them 5 . A video of the experiment is available on our Vimeo channel 6 .

Qualitative Results

From the survey results Fig. 5 and the recorded data we want to validate the three following hypotheses:

-The Fixed condition should have the lower rank for all the considered aspects as it does not respect the task constraints and do not account for user's safety (H 0 ). -In terms of task constraints and acceptability the relative and optimized conditions should produce similar results. Main differences between them should arise from safety related affirmations (H 1 ). -On the recorded data the optimized condition should have the lowest REBA value (H 2 ). Almost all subjects who have observed the optimized condition have put it first in their preference ordering. Only one person, who got the relative and the optimized conditions, has chosen the relative one first. Second preferred method is the relative condition. The Fixed condition has never been ranked first. For all the affirmations in Fig. 5 there is a tendency for the optimized condition to be preferred over the two other ones. Results have been compared using Mann-Whitney U test and show a significant preference for the optimized condition when summing up all the affirmations (p-values < 0.05 for the three combinations). The order of the conditions does not influence the results (p -values ≈ 0.5 for the three method). Due to the small number of left-handed people we cannot check for any significant differences between laterality.

Considering the results for the three subcategories, there is no significant differences between the optimized and the relative conditions for the questions on task constraints and acceptability (p -values = 0.19 and 0.33 respectively). All the other combinations are significantly different.

Fig. 4 shows the difference between the pose obtained with the relative and the optimized conditions. In the relative condition, we observe that the interaction happens at a higher level and forces the subject to bend his wrist.

Quantitative Results

During all the process the subjects' body motions have been recorded and their posture evaluated using the REBA method. We only consider the moment of insertion and average over the few time-steps it has taken the subject to do this action. The moment of insertion was automatically detected from the Cartesian distance between the subject's dominant hand (the one that have been used to insert the shape) and the center of the ball. We arbitrarily set that distance to be less than 20cm for the time-step to be accepted as an insertion. Fig. 6 shows the averaged REBA score over all the subjects for the three behaviors for some parts of the body. Differences between the conditions have been tested using a paired t-test on paired data from subjects, merging conditions in opposite order. For example, statistical differences between the fixed and the optimized conditions have been obtained from people that have observed the fixed then the optimized conditions and people that have observed the optimized then the fixed conditions.

The data in Fig. 6 show a significantly lower score on shoulder, wrist and total values for the optimized condition. The Relative condition presents the highest wrist score. In their comments some subjects have written that their wrist was not in a correct pose when they had to insert the shapes. Especially one subject that had a wrist tendinitis said he felt some discomfort.

Analysis

From the results of the user study we validate the three hypotheses enunciated previously. The fixed condition is the worst possible behavior both in terms of subject's perception and REBA score (H 0 ). Although relative condition seems to be an acceptable solution it produces a significantly higher body posture score, especially on the wrist. In terms of acceptability and task constraints it is perceived similarly to the optimized solution returned by the framework. Yet in terms of user's safety it performs significantly worst (H 1 ). Fig. 6: Average score and standard error of the mean of the recorded body posture using the REBA method. Only dominant arm have been included in the figure for clarity, but data for the opposite arm are also available. Significance have been tested using Wilcoxon test on paired data. The recorded postures for the optimized condition present a lower REBA score. The relative condition leads to an higher wrist score that can create some discomfort.

From the analysis of the recorded data, we observe that the optimized condition significantly reduces the body posture cost. There is 1.1 point of reduction (3.35 to 2.21 in average) compared to the fixed condition and 0.4 point (2.63 to 2.21) compared to the relative condition. Although this is not a huge improvement, we have to note that only the dominant arm is used to solve this task. We can expect better results for some task that put a strain on all the body parts. Nevertheless, the repetition of a suboptimal posture can increase the risk of MSDs. Interestingly, the higher wrist score for the relative condition can be linked to the comments made by the subjects. During the insertion their wrist was put in extension due to the orientation of the insertion hole. This have been correctly detected by the assessment technique and it is the main weakness of the relative condition.

Obviously the relative condition results could be improved by changing the orientation that causes the wrist discomfort. But then this would require to empirically find a "correct" solution for each task considered. For some of them this might be not trivial. Therefore, the genericity of our framework allows to automatically find better postures in any task.

VII. CONCLUSION

For a safe and comfortable human-robot interaction it is important to respect three aspects of the interaction: task constraints, safety and acceptability. The growing number of MSDs shows that people might be unaware of the risk of their working posture. By optimizing the human posture to minimize that risk, we can deduce robotic behaviors that are safer in the long-term.

In our work, we introduce a postural optimization framework that account for task constraints and acceptability while minimizing the risk of MSDs. For the latest we rely on a personalized human model and postural assessment techniques developed for ergonomic, mainly the REBA assessment method [START_REF] Hignett | Rapid entire body assessment (reba)[END_REF]. Coupled to a motion tracking system we also assess the worker's posture during the interaction. We have validated our approach in a user study with 39 volunteers interacting with a Baxter torso-humanoid robot.

Results of the user study prove the efficiency of our framework. It successfully generates body postures to solve the considered task. Moreover, not only are the obtained posture perceived as better solution compared to naive approaches, the real subject's posture are also rated better with the REBA method. The main strength of the framework is to not provide an a priori knowledge on the object pose in order to solve the task. By only defining the task constraints, the framework provides the optimal object location for interaction. However, some limitations are worth noting. One of the actual limitation arises when the robot cannot reach the desired position. For a mobile robot this problem can probably be solved by moving the robot to another location. For a fixed robot the solution would be to reorganized the working cell. If the worker can move in the workspace, then we should find his optimal placement. Second limitation is that our method only consider static posture, although motions with a high dynamic present a high risk of MSDs. Finally, a current limitation of the method is the use of marker tracking, which may hinder the application in real industrial scenarios. Thus, we are currently investigating alternative non-intrusive methods that work in close range.

The graphical feedback interface presented in the paper also requires an extensive study to validate its usage. To avoid potential biases it was turned off during the conducted user study. Therefore, an extension of the work is to analyze how it impacts the worker's posture during the execution of a task.

Fig. 2 :

 2 Fig. 2: Screenshots of the graphical interface in two possible configurations. The same body posture is used in both pictures. In front view, by contrast with the back view, the body configuration mirrors the real posture.

Fig. 5 :

 5 Fig. 5: Average results and standard error of the mean for the responses to the survey. Each subject have observed two of the three behaviors in a random order. Affirmations are Likert scale items, based on the SUS methodology, ranked from 1 to 5 [29]. The negative values for the affirmations in negative form only appear in the figure for clarity matters. Significance have been tested using Mann-Whitney U test and noted according to the standard defined by the APA(American Psychological Association).

We are working on replacing the optical markers by Kinect cameras also during the execution, creating a less invasive measurement system that can be seamlessly integrated in real industrial scenarios, for example.

details of this method can be found in[START_REF] Maeda | Acquiring and generalizing the embodiment mapping from human observations to robot skills[END_REF]

https://github.com/3rdHand-project/PosturalFeedbackInterface

https://doi.org/10.5281/zenodo.321599

https://github.com/3rdHand-project/PosturalOptimizationDataReader

https://vimeo.com/163699896

ACKNOWLEDGMENTS

This work was supported by national funds through Fundac ¸ão para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013 and by the EU FP7-ICT project 3rdHand under grant agreement no 610878.


Miloud Bessafi
email: miloud.bessafi@univ-reunion.fr

M R Lollchund
email: r.lollchund@uom.ac.mu

Jean-Pierre P Chabriat
email: jean-pierre.chabriat@univ-reunion.fr

Jean-Daniel Lan
email: jean-daniel.lan-sun-luk@univ-reunion.fr

Sun Luk

Patrick Jeanty
email: patrick.jeanty@univ-reunion.fr

J D Lansunluk

Climatology in Mauritius 1983-2005: potential solar radiation modulation by Quasi-Biennial oscillation and El Niño-Southern oscillation

Keywords: solar radiation, QBO, Quasi-Biennal oscillation, ENSO, El Niño-Southern oscillation, interannual, climate change

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

Introduction

Mauritius is a small-island developing state (SIDS) located in the Southwest Indian Ocean (between 19°50'S and 20°32'S latitudes and 57°18'E and 57°46'E longitudes: 890 km off the east coast of Madagascar). The island covers a surface of roughly 1875 km 2 and eroded topography with hills, plateau, river valley and plains [START_REF] Nigel | Mapping of monthly soil erosion risk of mainland Mauritius and its aggregation with delineated basins[END_REF]. The highest altitude of the island is 828 m at Piton de la Petite Rivière Noire. Typically, weather prevailing over Mauritius is a tropical maritime climate with two distinct seasons. During austral winter from May to November, the Hadley-Walker cell circulation strengthens and produces steady low-level easterly tradewinds and upper-level westerly winds. This is the dry and windy season. In austral summer, the trade-winds weaken and wet conditions are dominant, especially from January to April with strong convective activity and cloudy sky in relation with Inter Tropical Convergence Zone (ITCZ). Additionally to this, the weather is often driven by tropical perturbations (Monsoon, Madden Julian Oscillation, Tropical cyclones) throughout the year and by the El Niño-Southern Oscillation (ENSO) over the interannual time scale [START_REF] Senapathi | Evidence for long-term regional changes in precipitation on the East Coast Mountains in Mauritius[END_REF].

The use of renewable energy resource remains a challenge for the island due to its vulnerability to climate-change impacts. As pointed out by [START_REF] Jeetah | Feasibility of using solar energy as a source of renewable energy in Mauritius under collaboration of DIREKT[END_REF], Mauritius has a significant potential of solar energy resource and the expertise to use this renewable energy through the photovoltaic technology. More recently, [START_REF] Ramgolam | Unveiling the solar resource potential for photovoltaic applications in Mauritius[END_REF] have used four sets of solar radiation parameters (Sunshine hour, Global Horizontal Irradiance, monthly average insolation, sky clearness index, climatological yearly solar radiation) and revealed relevant information on the variability of solar radiation under the daily, monthly and yearly scale over Mauritius. As mentioned previously, the weather prevailing over the island is highly variable through different time scale. Moreover, solar radiation being an intermittent energy resource due to cloud cover adds up to such variability in the weather. In his study, [START_REF] Lean | Late twentieth-century warming and variations in cloud cover[END_REF] highlighted a correlation between interannual oscillation (ENSO) and total cloud cover for the six 30° -latitude bands over the globe. He pointed out a decrease of total cloud cover from 1984 to 1997. Moreover, low-level (resp., middle and upper) cloud cover decreased (resp., increased) during 1984-2009 period. This paper focuses on the observed solar radiation variability over Mauritius under interannual time scale.

Data and analysis

The data used for this study is surface global solar radiation derived from satellite observations. They are obtained from the EUMETSAT's Satellite Application Facility on Climate Monitoring (CM SAF). This is a gridded product on high-resolution (15 × 15 km²) which is public and free-of-charge via CM SAF webpage (http://www.cmsaf.eu). For more details, see the paper of [START_REF] Schulz | Operational climate monitoring from space: the EUMETSAT satellite application facility on climate monitoring (CM-SAF)[END_REF]. Climate indices used in this paper are monthly time series from NOAA's website (http://www.esrl.noaa.gov/psd/data/climateindices/list/). OLR is used as a proxy for convective activity (http://www.esrl.noaa.gov/psd/data/gridded/data.interp_OLR.html). As shown in Figure 1(a), solar radiation over Mauritius exhibits seasonal cycle through the 1983-2005 period record. In addition, there is no significant observed trend. Moreover, we can notice interannual component in the spectrum of solar radiation as well (Figure 1(b)). The El Niño-Southern Oscillation (ENSO) and the Quasi-Biennal Oscillation (QBO) are the most dominant interannual mode in the troposphere and the stratosphere, respectively. The former is associated with a coupled ocean-atmosphere interaction and covers large quasi-periodic time scale (3-7 years timescale) and has a planetary teleconnection [START_REF] Diaz | ENSO variability, teleconnections and climate change[END_REF]. The QBO is a zonal stratospheric wind oscillation and have shorter period of alternation within 24-30 month range [START_REF] Baldwin | The Quasi-Biennal oscillation[END_REF]. Some authors have pointed non-linear interaction between these two oscillations and trigger the precipitation and cloud cover [START_REF] Lau | Annual cycle, Quasi-Biennal oscillation, and southern oscillation in global precipitation[END_REF][START_REF] Terray | Revisiting the possible links between the Quasi-Biennial oscillation and the Indian summer monsoon using NCEP R-2 and CMAP fields[END_REF].

Correlation analysis

In order to assess the relationship between solar radiation variability and interannual oscillations, their correlation coefficient is computed. The correlation coefficient r between two sets of sampling data x i and y i (i = 1, …, n) is obtained using the formula

( )( ) ( ) ( ) 1/ 2 2 2 1 1 1 , n n n i i i i i i i r x x y y x x y y - = = =     = - - - -         ∑ ∑ ∑ (1)
where x and y are the mean values of x and y, respectively. The values of r are within

[ 1, 1]. - If 0.3, r <
then the correlation of the two samples is considered to be low (or no correlation). If 0.3 0.7, r ≤ < then the samples correlate moderately with each other. For 0.7, r ≥ the two datasets are said to highly correlate with each other [START_REF] Aron | Statistics for the Behavioral and Social Sciences: A Brief Course[END_REF].

Figure 3(a) displays positive correlation between yearly solar radiation range (maximum minus minimum) and yearly QBO range. This result reveals that QBO could have an impact on the solar radiation variability over Mauritius. Conversely, there is no significant correlation between solar radiation and SOI. It means that the impact of ENSO events on the solar radiation is more complex. Nevertheless, the link with convective activity (cloud cover) and solar radiation is clear as shown in Figure 3(b).

Conclusion

This study shows that solar radiation range has a seasonal as well as an interannual variability. During the period January 1983-December 2005, moderate and strong El Niño events have been identified to trigger solar radiation disturbances to highest levels. Nevertheless, the correlation remains difficult to assess. Conversely, QBO seems to significantly modulate the yearly seasonal cycle solar radiation over Mauritius. OLR analysis confirms the modulation of convective activity and cloud cover over interannual timescale. Quasi-periodicity and possible interactions with intra-seasonal atmospheric perturbations (Madden Julian Oscillation, Indian Ocean Dipole and Southern Antarctic Mode) lead to intermittent solar radiation basically. Mixing modes through several decades yield to non-linear and multivariate analysis which could be further studied.

Figure 1

 1 Figure 1 (a) Monthly global solar radiation observed during 1983-2005 period and (b) power spectrum of monthly solar radiation

  Figure 2(a) depicts the yearly anomalies of minimum (resp., maximum) solar radiation observed over Mauritius during the period January 1983-December 2005 and the departure from the normal condition in terms of standard deviation. Only years which exceed two or three standard deviations are labelled. Figure 2(b) highlights the state of ENSO and QBO state of the atmosphere throughout the period. Eleven years within 1983-2005 reveal an abnormal solar radiation level over Mauritius and could be affected by ENSO and QBO separately or combined (coupled). Lower maximum and minimum solar radiation was observed during El Niño's 1983, which was one of the strongest El Niño events of the twentieth century. Other El Niño's year (Moderate and Strong) was retrieved. During 1997, the QBO was in its eastward phase and the solar radiation exhibits a lower maximum and higher minimum.

Figure 2

 2 Figure 2 (a) Yearly solar radiation standardised anomalies over Mauritius during 1950-2013 period and (b) Monthly SOI and QBO indices for the same period

Figure 3

 3 Figure 3 (a) Yearly solar radiation range vs. yearly QBO index observed over Mauritius during 1983-2005 period and (b) yearly deseasonalised solar radiation range vs. OLR range observed for the same period