David Moss

Photo-thermal tuning of optical waveguides integrated with ultrathin 2D graphene oxide thin films

Keywords: 2D materials, integrated optics, photo-thermal changes, graphene oxide

Photo-thermal tuning of optical waveguides integrated

with ultrathin 2D graphene oxide thin films

Introduction

Graphene oxide (GO) is a two-dimensional (2D) material that has attracted significant interest because of its many attractive properties such as broadband photoluminescence [START_REF] Chien | Tunable Photoluminescence from Graphene Oxide[END_REF][START_REF] Cushing | Origin of strong excitation wavelength dependent fluorescence of graphene oxide[END_REF], high Kerr nonlinearity [START_REF] Zheng | In Situ Third-Order Nonlinear Responses During Laser Reduction of Graphene Oxide Thin Films Towards On-Chip Nonlinear Photonic Devices[END_REF][START_REF] Xu | Observation of Third-order Nonlinearities in Graphene Oxide Film at Telecommunication Wavelengths[END_REF], strong material anisotropy [START_REF] Lim | Graphene oxide-based waveguide polariser: From thin film to quasi-bulk[END_REF][START_REF] Wu | Graphene Oxide Waveguide and Micro-Ring Resonator Polarizers[END_REF], broadband light absorption [START_REF] Lin | A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light[END_REF][START_REF] Lin | Structured graphene metamaterial selective absorbers for high efficiency and omnidirectional solar thermal energy conversion[END_REF], and tunable material properties in wide ranges [START_REF] Loh | Graphene oxide as a chemically tunable platform for optical applications[END_REF][START_REF] Zheng | Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing[END_REF]. In addition, with its facile fabrication processes, GO has a strong capability for large-scale manufacturable on-chip integration [START_REF] Wu | Graphene Oxide Waveguide and Micro-Ring Resonator Polarizers[END_REF][START_REF] Yang | Graphene-Based Multilayered Metamaterials with Phototunable Architecture for on-Chip Photonic Devices[END_REF][START_REF] Yang | Article: Enhanced fourwave mixing in waveguides integrated with graphene oxide[END_REF].

The incorporation of GO into integrated photonic devices has led to the birth of GO integrated photonics, which has become a very active and fast-growing field [START_REF] Wu | Graphene Oxide for Integrated Photonics and Flat Optics[END_REF]. Integrated photonic devices incorporating GO films have been demonstrated for a range of applications, such as light absorbers [START_REF] Lin | A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light[END_REF][START_REF] Lin | Structured graphene metamaterial selective absorbers for high efficiency and omnidirectional solar thermal energy conversion[END_REF][START_REF] Chen | Exceeding the limit of plasmonic light trapping in textured screen-printed solar cells using Al nanoparticles and wrinkle-like graphene sheets[END_REF], optical lenses and imaging devices [START_REF] Zheng | Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing[END_REF][START_REF] Yang | Graphene-Based Multilayered Metamaterials with Phototunable Architecture for on-Chip Photonic Devices[END_REF][START_REF] Cao | Resilient Graphene Ultrathin Flat Lens in Aerospace, Chemical, and Biological Harsh Environments[END_REF], polarization-selective devices [START_REF] Wu | Graphene Oxide Waveguide and Micro-Ring Resonator Polarizers[END_REF][START_REF] Zheng | Jia Free-standing graphene oxide mid-infrared polarizers[END_REF], sensors [START_REF] Tsui | Graphene oxide integrated silicon photonics for detection of vapour phase volatile organic compounds[END_REF][START_REF] He | Fan A Graphene Nanoprobe for Rapid, Sensitive, and Multicolor Fluorescent DNA Analysis[END_REF], and nonlinear optical devices [START_REF] Qu | Enhanced Four-Wave Mixing in Silicon Nitride Waveguides Integrated with 2D Layered Graphene Oxide Films[END_REF][START_REF] Zhang | Enhanced Kerr Nonlinearity and Nonlinear Figure of Merit in Silicon Nanowires Integrated with 2D Graphene Oxide Films[END_REF][START_REF] Zhang | Moss Optimizing the Kerr Nonlinear Optical Performance of Silicon Waveguides Integrated With 2D Graphene Oxide Films[END_REF][START_REF] Zhang | Enhanced Spectral Broadening of Femtosecond Optical Pulses in Silicon Nanowires Integrated with 2D Graphene Oxide Films[END_REF][START_REF] Zhang | Enhanced self-phase modulation in silicon nitride waveguides integrated with 2D graphene oxide films[END_REF].

Since GO can be converted to a reduced form with graphene-like properties under strong light irradiation or high temperature [START_REF] Zhang | Sun Photoreduction of Graphene Oxides: Methods, Properties, and Applications[END_REF][START_REF] Compton | Graphene oxide, highly reduced graphene oxide, and graphene: versatile building blocks for carbon-based materials[END_REF], it has long been used as a precursor for the preparation of graphene [START_REF] Wu | Graphene Oxide for Integrated Photonics and Flat Optics[END_REF][START_REF] Zhu | Graphene and Graphene Oxide: Synthesis, Properties, and Applications[END_REF][START_REF] Brisebois | Siaj Harvesting graphene oxide -years 1859 to 2019: a review of its structure, synthesis, properties and exfoliation[END_REF]. Given the difference between the material properties of GO and reduced GO (rGO) [START_REF] Zheng | In Situ Third-Order Nonlinear Responses During Laser Reduction of Graphene Oxide Thin Films Towards On-Chip Nonlinear Photonic Devices[END_REF][START_REF] Yang | Graphene-Based Multilayered Metamaterials with Phototunable Architecture for on-Chip Photonic Devices[END_REF][START_REF] Pei | The reduction of graphene oxide[END_REF], investigating the mechanisms and conditions for GO reduction in hybrid integrated photonic devices is of fundamental importance for applying this functional 2D material to integrated photonic devices [START_REF] Wu | Graphene Oxide for Integrated Photonics and Flat Optics[END_REF][START_REF] Chong | Photo-induced reduction of graphene oxide coating on optical waveguide and consequent optical intermodulation[END_REF].

Previously, we observed power-sensitive photo-thermal changes in GO films coated on integrated photonic waveguides [START_REF] Qu | Enhanced Four-Wave Mixing in Silicon Nitride Waveguides Integrated with 2D Layered Graphene Oxide Films[END_REF] and ring resonators [START_REF] Wu | 2D Layered Graphene Oxide Films Integrated with Micro-Ring Resonators for Enhanced Nonlinear Optics[END_REF] in nonlinear four-wave mixing experiments. In this paper, we provide a more detailed characterization for such changes arising from a range of effects such as photothermal reduction, thermal dissipation, and self-heating in GO layers. We experimentally investigate photo-thermal tuning (PTT) of 2D GO films coated on integrated optical waveguides. We measure the light power thresholds for reversible and permanent GO reduction in silicon nitride (SiN) waveguides integrated with 1 and 2 layers of GO. We identify three reduction stages according to the existence of reversible versus permanent reduction. Raman spectra at different positions of a hybrid waveguide with permanently reduced GO film are also characterized, showing the inhomogeneous nature of GO reduction the direction of light propagation through the waveguide. Finally, we compare the PTT induced by a continuous-wave (CW) laser and a pulsed laser with the same average power, and observe negligible difference between them. This confirms that the PTT mainly depend on the average power rather than the peak power of input light. These results reveal interesting features for the reduction of GO induced by the photo-thermal changes, which are useful for controlling and engineering GO's material properties in hybrid integrated photonic devices.

Device design and fabrication

Figure 1a show a schematic illustration of a GO-coated SiN waveguide with a monolayer GO film. The bare SiN waveguide has a cross-section of 1.70 μm × 0.72 μm. A complementary metal-oxide-semiconductor (CMOS) compatible crack-free method [START_REF] El Dirani | Sciancalepore Annealing-free Si3N4 frequency combs for monolithic integration with Si photonics[END_REF][START_REF] Demongodin | Ultrafast saturable absorption dynamics in hybrid graphene/Si3N4 waveguides[END_REF][START_REF] El Dirani | Sciancalepore Ultralow-loss tightly confining Si 3 N 4 waveguides and high-Q microresonators[END_REF] was utilized to fabricate the uncoated SiN waveguides. First, a twostep deposition of SiN films was achieved via low-pressure chemical vapor deposition (LPCVD) for strain management and crack prevention. Next, 248-nm deep ultraviolet lithography and CF4/CH2F2/O2 fluorine-based dry etching were employed for patterning the SiN waveguides. After that, a silica upper cladding was deposited using high-density plasma-enhanced chemical vapor deposition (HDP-PECVD), followed by opening a window on it down to the top surface of the SiN waveguides via lithography and dry etching processes. The window was located near the waveguide input to enable a relatively high optical power injected into the GO coated segment [START_REF] Qu | Moss Analysis of Four-Wave Mixing in Silicon Nitride Waveguides Integrated With 2D Layered Graphene Oxide Films[END_REF]. The length of the opened window was Lw = 1.4 mm. Finally, 2D layered GO films were coated onto the SiN waveguide by using a solution-based method that enabled transfer-free and layer-by-layer film coating, as reported previously [START_REF] Wu | Graphene Oxide Waveguide and Micro-Ring Resonator Polarizers[END_REF][START_REF] Yang | Graphene-Based Multilayered Metamaterials with Phototunable Architecture for on-Chip Photonic Devices[END_REF][START_REF] Yang | Article: Enhanced fourwave mixing in waveguides integrated with graphene oxide[END_REF][START_REF] Jia | Moss Fabrication Technologies for the On-Chip Integration of 2D Materials[END_REF]. Compared to the cumbersome film transfer processes employed for the on-chip integration of other 2D materials such as graphene and TMDCs [START_REF] Feng | Enhanced optical Kerr nonlinearity of graphene/Si hybrid waveguide[END_REF][START_REF] Liu | Enhanced optical Kerr nonlinearity of MoS2 on silicon waveguides[END_REF][START_REF] Yang | Song Bottom-up fabrication of graphene on silicon/silica substrate via a facile soft-hard template approach[END_REF], our GO coating method is highly scalable, enabling the precise control of the GO layer number (i.e., film thickness), the ability to coat large-area films, and good film attachment onto integrated chips [START_REF] Yang | Graphene-Based Multilayered Metamaterials with Phototunable Architecture for on-Chip Photonic Devices[END_REF][START_REF] Wu | Graphene Oxide for Integrated Photonics and Flat Optics[END_REF]. The total length of the SiN waveguide was L = 2 cm. A micrograph of the fabricated device corresponding to Figure 1a is shown in Figure 1b. The GO film coated on the chip surface exhibited good morphology, high transmittance, and high uniformity. Figure 1c shows the schematic cross section of the hybrid waveguide in Figure 1a, the corresponding TE mode profile is shown in Figure 1d. The light-matter interaction between the waveguide evanescent field and the GO film can induce power-sensitive photothermal changes in the GO film, which has been observed previously [START_REF] Qu | Enhanced Four-Wave Mixing in Silicon Nitride Waveguides Integrated with 2D Layered Graphene Oxide Films[END_REF][START_REF] Chong | Photo-induced reduction of graphene oxide coating on optical waveguide and consequent optical intermodulation[END_REF][START_REF] Wu | 2D Layered Graphene Oxide Films Integrated with Micro-Ring Resonators for Enhanced Nonlinear Optics[END_REF]. In this paper, we only investigate PTT induced by the TE polarized light. This is because the TE polarization supports the in-plane interaction between the waveguide evanescent field and the 2D GO film, which is much stronger compared to the outof-plane interaction given the significant anisotropy of 2D GO films [START_REF] Wu | Graphene Oxide Waveguide and Micro-Ring Resonator Polarizers[END_REF], thus allowing for the excitation of higher levels of photo thermal changes.

Experimental results

Figure 2 shows the experimental setup for characterizing PTT of GO films coated on integrated optical waveguides. Two CW light sources having different powers were employed. The low power one was used to measure the loss at low powers without obvious photo thermal changes in the GO films, whereas the highpower one was achieved by amplification with an erbium-doped fiber amplifier (EDFA) to excite the PTT. A pulsed laser source (repetition rate: 60 MHz, pulse width: 3.7 ps) was also employed to compare the level of photo thermal changes with that induced by the CW light. The wavelengths of both the CW sources and the center wavelength of the picosecond optical pulses were around 1550 nm. Polarization controllers (PCs) were employed to ensure the TE polarization of the input light. An optical isolator was inserted in the high-power light path to prevent the reflected light from damaging the light source. The input laser was split into two beams via a 50:50 beam splitter, with one injecting into the device under test (DUT) and the other being sent to an optical power meter (OPM) for monitoring the input power. Lensed fibers were used to butt couple light into and out of the DUT with a coupling loss of ~2 dB / facet. A charged-coupled device (CCD) camera was placed above the waveguide to monitor the adjusting of the coupling. Another OPM was employed to measure the output power after passing through the DUT. Figure 3a depicts the measured insertion loss of the integrated waveguide coated with 1 layer of GO versus input CW power. Unless otherwise specified, the input power of CW light or optical pulses in this paper represents the power coupled into the waveguide after subtracting the fiber-to-chip coupling loss. In order to characterize both the reversible and permanent changes of the material properties, after each measurement at a specific input power, we turned off the high-power CW light and remeasured the insertion loss using a low-power CW light with a power of 0 dBm. The results measured using the high-power and the low-power CW light sources are shown by the red and blue dots, respectively. As can be seen, the evolution of the PTT of the GO film can be divided into three reduction stages. At Stage I, when the input power was below 20 dBm, the insertion loss of the waveguide remained constant despite the increase in input power, reflecting that there was negligible change in the absorption of the GO film and the light power was not high enough to induce obvious photo-thermal changes. At Stage II starting from 20 dBm, the insertion loss showed a slight but observable increase with the input power, indicating the occurrence of the photo-thermal changes in the GO film. The results measured using low-power CW light after tuning off the high-power CW light remained constant. This reflects the fact that there were no permanent changes in the GO films, and the photo-thermal changes at this stage were reversible. These features of the photo-thermal changes in the GO films are consistent with previous reports [START_REF] Qu | Enhanced Four-Wave Mixing in Silicon Nitride Waveguides Integrated with 2D Layered Graphene Oxide Films[END_REF][START_REF] Qu | Moss Analysis of Four-Wave Mixing in Silicon Nitride Waveguides Integrated With 2D Layered Graphene Oxide Films[END_REF]. For Stage III, when the input power was further increased to above 22 dBm, the results measured using low-power CW light also showed an obvious increase with input power. Since permanently reduced GO films did not show any obvious power dependence [START_REF] Lin | A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light[END_REF][START_REF] Lin | Structured graphene metamaterial selective absorbers for high efficiency and omnidirectional solar thermal energy conversion[END_REF], this reflects the fact that there were permanent changes in the GO films. In addition, the difference between the red dots and their corresponding blue dots indicates that there was still reversibly reduced GO and only part of the GO film was permanently reduced. We infer that there would be a new stage after Stage III at even higher powers, where the difference between the red and blue dots at the same power would vanish due to the full reduction of all the GO films. We could not observe this stage in our experiments since we had already applied the maximum experimentally available power to the DUT.

EPL = (IL -IL0)/Lw ( 1
)
where IL is the measured insertion loss of the hybrid waveguide in Figure 3a, IL0 is the insertion loss of the bare waveguide, and Lw is the GO film length. Figure 3c shows the ∆EPL extracted from Figure 3b, which is defined as the difference between the red and blue dots after exposure by the high-power CW source at the input power indicated on the x-axis. As can be seen, the ∆EPL remained zero at Stage I, and started to increase at Stage II. In Stage III, the ∆EPL first slightly increased and then decreased when the input power was above 24 dBm. This can be attributed to the hybrid nature of GO films at this stage due to the co-existence of the permanently and reversibly reduced GO. The corresponding experimental results for the hybrid waveguide coated with 2 layers of GO are shown in Figure 4. Figure 4a shows the measured insertion loss versus input CW power. Similar to the results for the device with 1 layer of GO, the evolution of the PTT of the device with 2 layers of GO can also be divided into three reduction stages with increasing input power. Compared to the results in Figure 3a, the power thresholds for Stage II and Stage III were lower, with Stage II starting at 13 dBm and Stage III starting at 18 dBm. This reflects the fact that the power endurance of the film with 2 layers of GO was lower than the film with 1 layer of GO.

Figure 4b shows the GO induced EPL extracted from Figure 4a. Compared to the results in Figure 3b, the EPL here increased more slowly with input power. At Stage I, the excess propagation loss induced in the film with 2 layers of GO is about twice that induced in the film with a single layer of GO. However, at Stage II and Stage III, the difference between the EPL induced in 1 and 2 layers of GO became smaller, particularly at higher powers above 20 dBm. This is because the EPL defined in Equation ( 1) is a parameter averaged over the GO film length, whereas the reduction of GO in practical hybrid waveguides induced by the photo thermal changes is nonuniform, i.e., the GO film at the beginning of the waveguide is more easily to be reduced, which absorbs more light power and so protects the GO film following it from being reduced. The film with 2 layers of GO absorbed more light than the film with 1 layer of GO, and so the light transmission was more attenuated over a shorter distance, resulting in a higher proportion of unreduced GO. The loss of the non-reduced 2 layers of GO was lower than the single layer of rGO, thus resulting in a lower EPL.

Figure 4c shows the ∆EPL extracted from Figure 4b. Unlike the trend in Figure 3c, the ∆EPL here increases with input power in Stages II and III without showing obvious decrease. This is because for the hybrid waveguide with 2 layers of GO, only a small length of the GO film near the waveguide input was permanently reduced, leaving significant lengths of GO films that were either non-reduced or only reversibly reduced. Although the ∆EPL increased to above zero at relatively low input power for the device with 2 layers of GO, it increased more slowly with input power, with the values at high input powers being smaller than those for the device with 1 layer of GO. This is because for the film with 2 layers of GO, the reversibly reduced GO experienced relatively lower power (14 -18 dBm), while the film exposed to higher power was permanently reduced and no longer exhibited ∆EPL. On the other hand, for the single layer GO film, the reversibly reduced GO experienced relatively higher powers (20 -22 dBm), thus yielding a higher ∆EPL.

Discussion

In section 3, the inhomogeneous GO reduction along the hybrid waveguides was used to explain several experimental phenomena. To verify the inhomogeneous nature of the GO reduction induced by the photo thermal changes, we characterized the Raman spectra of 2 layers of GO coated on an integrated waveguide after applying the maximum input power of 24 dBm. The results are shown in Figure 5, where representative D and G peaks of GO can be clearly identified. Near the waveguide input, the D and G peaks of the detected Raman signals are relatively small, with a D/G ratio being larger than 1. This is similar to that of graphene [START_REF] Yang | Graphene-Based Multilayered Metamaterials with Phototunable Architecture for on-Chip Photonic Devices[END_REF], indicating that the GO film here was deeply reduced. In contrast, for positions further away from the waveguide input, the D/G ratio decreased to become less than 1, together with an increased intensity for the detected Raman signal. These characteristics show agreement with Raman spectra of GO having fewer defects [START_REF] Loh | Graphene oxide as a chemically tunable platform for optical applications[END_REF][START_REF] Yang | Article: Enhanced fourwave mixing in waveguides integrated with graphene oxide[END_REF] and reflect the fact that the GO away from the waveguide input was reduced less. To compare the PTT induced by CW light versus optical pulses, we measured the EPLs of the hybrid waveguides with a single GO layer for both CW light and optical pulses having the same average power. The results are shown in Figure 6. The optical pulses had a repetition rate of ~60 MHz and a pulse width of ~3.7 ps, which corresponded to a peak power 4 × 10 3 times higher than the CW light with the same average power. As can be seen, both the CW light and the optical pulses induced measurable EPLs at high average input powers. The small difference between them indicates that the EPL was mainly a function of the average power rather than peak power. This is in agreement with observations in GO films arising from photo-thermal processes in Refs. [START_REF] Qu | Enhanced Four-Wave Mixing in Silicon Nitride Waveguides Integrated with 2D Layered Graphene Oxide Films[END_REF][START_REF] Chong | Photo-induced reduction of graphene oxide coating on optical waveguide and consequent optical intermodulation[END_REF][START_REF] Wu | 2D Layered Graphene Oxide Films Integrated with Micro-Ring Resonators for Enhanced Nonlinear Optics[END_REF], and further confirms the existence of the photo thermal changes. In contrast, the changes induced by ultrafast nonlinear optical processes such as four-wave mixing, two-photon absorption, and saturable absorption are dependent on the peak input light power [START_REF] Qu | Moss Analysis of Four-Wave Mixing in Silicon Nitride Waveguides Integrated With 2D Layered Graphene Oxide Films[END_REF][START_REF] Jiang | Ultrafast coherent nonlinear nanooptics and nanoimaging of graphene[END_REF][START_REF] Zhang | Moss Design and Optimization of Four-Wave Mixing in Microring Resonators Integrated With 2D Graphene Oxide Films[END_REF]. The slightly lower EPL induced by optical pulses compared to CW light can be attributed to saturable absorption in the GO films caused by the high peak powers, which was also observed in Refs. [START_REF] Zhang | Enhanced self-phase modulation in silicon nitride waveguides integrated with 2D graphene oxide films[END_REF][START_REF] Demongodin | Ultrafast saturable absorption dynamics in hybrid graphene/Si3N4 waveguides[END_REF]. We also measured permanent EPLs with low-power CW light (0 dBm) after turning off the high-power CW light and optical pulses. The permanent EPLs induced by the CW and optical pulses showed negligible difference, reflecting the fact that the permanent reduction of GO was mainly induced by the photo thermal changes. These results have significant implications for designing and engineering nonlinear photonic chips for applications such as microcombs.

Conclusions

In this paper, we present detailed characterization of the PTT of GO films coated on integrated optical waveguides. Reversible and permanent GO reduction are observed by applying different CW laser powers to the devices with 1 and 2 layers of GO. The corresponding power thresholds are measured, with three reduction stages being identified. The Raman spectra at different positions of a hybrid waveguide with a permanently reduced GO film are characterized, which verifies the inhomogeneity of GO reduction. The photo-thermal changes induced by CW light and optical pulses with the same average power are also compared, which show negligible difference and confirms that the PTT mainly depends on the average input power. These results are useful for controlling and engineering the material properties of GO in hybrid integrated photonic devices.

Figure 1 .

 1 Figure 1. (a) Schematic illustration of a SiN waveguide coated with 1 layer of GO. (b) A micrograph showing the area around the opened window of the fabricated device corresponding to (a). (c) Schematic illustration of the cross-section of the hybrid waveguide. (d) TE mode profile corresponding to (c).

Figure 2 .

 2 Figure 2. Experimental setup for characterization of PTT of GO-coated integrated waveguides. EDFA: erbium-doped fiber amplifier. PC: polarization controller. DUT: device under test. CCD: charged-coupled device. VOA: variable optical attenuator. OPM: optical power meter.

Figure 3 .

 3 Figure 3. Experimental results for characterizing PTT of the hybrid waveguide coated with 1 layer of GO. (a) Insertion loss of the hybrid waveguide versus the input power of the highpower light source. The red dots show the loss of the high-power CW light source, and the blue dots show the loss measured with a low-power CW light source after exposure at the power level indicated on the x-axis. (b) GO-induced excess propagation loss (EPL) versus input power of the high-power light source. The red and blue dots show the results corresponding to the red and blue dots in (a), respectively. (c) ∆EPL extracted from (b) showing the difference between the red and blue dots.

Figure 3b depicts

  Figure 3b depicts the GO-induced excess propagation loss (EPL) extracted from Figure 3a. The EPL (dB/cm) is defined as

Figure 4 .

 4 Figure 4. Experimental results for characterizing PTT of the hybrid waveguide coated with 2 layers of GO. (a) Insertion loss of the hybrid waveguide versus the input power of the highpower light source. The red dots show the loss of the high-power CW light source, and the blue dots show the loss measured with a low-power CW light source after exposure at the power level indicated on the x-axis. (b) GO-induced excess propagation loss (EPL) versus input power of the high-power light source. The red and blue dots show the results corresponding to the red and blue dots in (a), respectively. (c) ∆EPL extracted from (b) showing the difference between the red and blue dots.

Figure 5 .

 5 Figure 5. Raman spectra of 2 layers of GO coated on an integrated waveguide after applying an input CW power of 24 dBm.

Figure 6 .

 6 Figure 6. Experimental results of the total and permanent EPL induced by a CW light and optical pulses versus average input power for the hybrid waveguides coated with 1 layer of GO.

Conflicts of Interest:

The authors declare no conflict of interest.


Cezar Mbiethieu
email: mbiethieucezar@gmail.com

Norbert Tsopze

Engelbert Mephu-Nguifo

CovSegNet: An Automated COVID-19 lesion segmentation from CT scans using Deep Learning Techniques

Keywords: COVID-19, CT scans, Deep Learning, U-net, SubSampling, Attention mechanism

The coronavirus disease (COVID-19) pandemic has led to a devastating effect on the global public health. Computed Tomography (CT) is an effective tool in the screening of COVID-19. It is of great importance to rapidly and accurately segment COVID-19 lesions from CT images to help diagnostic and patient monitoring. In this paper, we propose a U-net based segmentation network using attention mechanism. As not all the features extracted from the encoders are useful for segmentation, we propose to incorporate an efficient attention mechanism, to an U-Net architecture to re-weight the feature representation channel-wise to capture rich contextual relationships for better features representation while maintaining a better time complexity. In addition, a novel subsampling techniques for CNN is introduced to significantly increase the amount of information kept by feature maps through subsampling layers and we finally use a focal Tversky loss to deal with small lesion segmentation. The experiment results, evaluated on a COVID-19 CT scans segmentation dataset where 3250 CT slices are available, demonstrate the proposed method can achieve an accurate and rapid segmentation on COVID-19 segmentation. The method takes only a fraction of second to segment a single CT slice.

I INTRODUCTION

The COVID-19 pandemic caused by the virus named SARS-CoV-2 identified in 2019, has been spread all over the world and has caused a devastating effect on the global public health. Researches have shown that the coronavirus is spread through droplets and virus particles released in the air when an infected person breathes, talks, laughs, sings, coughs or sneezes. The traditional method used to diagnose and evaluate the disease is named real-time polymerase chain reaction (RT-PCR) which assays the sputum; it has a high specificity, but is time consuming, laborious and has been reported for high false negative rates Liang [START_REF] Liang | Handbook of covid-19 prevention and treatment[END_REF]. Chest Computed tomography (CT) and Chest X-ray are two imaging approaches used to detect certain characteristics manifestations in the lung infected by COVID-19. CT is more sensitive, especially for early stage of infection. Chest CT is considered as a low-cost, accurate and efficient method diagnostic tool for early screening and diagnosis of COVID-19. It can be used to evaluate how severely the lungs are affected, and how the patients disease is evolving, which is helpful in making treatment decisions. The evaluation of localization and geometric features of infection area could provide adequate information of disease progress and help doctors make better treatment.

One of the most widely used method to segment region of interest(ROI) in medical images is a deep learning system called U-net presented by Ronneberger, Fischer, and Brox [START_REF] Ronneberger | U-Net: Convolutional Networks for Biomedical Image Segmentation[END_REF] which has an architecture in "U" form based on encoder -decoder that captures low level and high level resolution features at the encoder phase and combines with the semantic features extracted at the decoder phase using skip connections. However, the features captured from the encoder part are not all useful for the segmentation task. Therefore, it is necessary to find an effective way to fuse features of the encoder and that of the decoder; we focus on the extraction of the most informative features for segmentation. Recently, incorporation of channel attention into convolution blocks has attracted a lot of interests, showing great potential in performance improvement of deep CNNs which extract the most informative features for segmentation. Some of the representative methods include squeeze-and-excitation networks (SENet) of Hu, Shen, and Sun [START_REF] Hu | Squeeze-and-Excitation Networks[END_REF] and it variants, which learns channel attention for each convolution block, bringing clear performance gain for various deep CNN architectures. Although these methods have achieved higher accuracy, more often, they bring higher model complexity and suffer from heavier computation burden due to complex architecture. Through the deep analysis of different types of layers in a deep learning architectures, we discovered that we usually skip some important features which could significantly increase the amount of information kept by the feature maps, therefore improving the models accuracy.

To address the above issues, we focus our research on finding a method which will establish a tradeoff between a better performance and a low model complexity cost. In this paper, we propose CovSegNet (Covid-19 Segmentation Network), a deep learning based segmentation system made with improved convolution and pooling layers to significantly increase the amount of information kept by the feature maps; we also proposed to used an improved channel attention mechanism which reduces the complexity of the segmentation models while maintaining their accuracy to segment the covid-19 lesions. We revisit the existing layers in deep architectures which perform subsampling and the existing attention mechanism in order to tackle their limitations in medical image segmentation. Our contributions include:

1. The proposition of a novel subsampling technique in encoder-decoder models to significantly increase the amount of information kept by the feature maps. 2. We propose a novel attention mechanism based Deep CNN architecture to segment COVID-19 CT scans. 3. We built a new U-net based architecture which integrates our proposed subsampling and attention mechanism in the classical skip connection, and also we replace the classical subsampling by our proposed lighter subsampling module. The rest of this paper is organized as follows. In section 2, we provide an overview of the segmentation models and some related literature using attention mechanism. Section 3 represents our proposed CovSegNet. Section 4 will describe the dataset and the experiments to demonstrate the potential power of our proposed method. Finally, we will present the conclusion in section 5.

II RELATED WORK

Most cutting-edge segmentation algorithms are based on deep learning approaches, which are algorithms that feature powerful fitting capacity and require no laborious preprocessing on input data. For example, U-Net of Ronneberger, Fischer, and Brox [START_REF] Ronneberger | U-Net: Convolutional Networks for Biomedical Image Segmentation[END_REF] and its variants were used to segment lung tissues in chest CT scans. However, those models suffer from the fact that, not all the features extracted from the encoder are useful for segmentation task at hand. Thus, attention mechanisms guide the model to emphasize the most salient features, avoiding useless features that are not beneficial.

With the development of deep neural networks, attention mechanism has been widely used in diverse application domains. It is a module added at the top of a convolution layer in order to guide the model to emphasize the most salient features, avoiding useless feature that are not beneficial for the given task. Related algorithms typically refine feature maps in spatial dimension, channel dimension or both. To focus on the most informative features for segmentation using U-Net, researchers proposed to insert attention module in the skip connection of U-net. For example, Oktay et al. [START_REF] Oktay | Attention U-Net: Learning Where to Look for the Pancreas[END_REF] proposed attention gate modules (AG) that are incorporated into the skip connections of the encoder-decoder network, using the information of the decoder feature to better guide information to the encoder feature. Hu, Shen, and Sun [START_REF] Hu | Squeeze-and-Excitation Networks[END_REF] introduced a Squeezeand-Excitation module, where global average pooling is performed on input features to produce channel-wise attention which highlight useful channels and that outperforms the methods in ILSVRC 2017 image classification. Roy, Navab, and Wachinger [START_REF] Roy | Concurrent Spatial and Channel 'Squeeze & Excitation' in Fully Convolutional Networks[END_REF] introduced to use both spatial and channel block (scSE), which concurrently recalibrates the feature representations spatially and channel-wise, and then combines them to obtain the final feature representation. Some of the above mentioned methods have been adjusted to segment COVID-19 infections. Zhou, Canu, and Ruan [START_REF] Zhou | Automatic COVID-19 CT segmentation using U-Net integrated spatial and channel attention mechanism[END_REF] segmented COVID-19 from CT to help diagnostic and patient monitoring while incorporating spatial and channel attention mechanism to U-Net architecture to capture rich contextual relationships for better feature representation. Li et al. [START_REF] Li | Using Artificial Intelligence to Detect COVID-19 and Community-acquired Pneumonia Based on Pulmonary CT: Evaluation of the Diagnostic Accuracy[END_REF] developed a COVID-19 detection neural network (COVNet) to extract visual features from volumetric chest CT exams for distinguishing COVID-19 from Community Acquired Pneumonia (CAP).

III METHOD

In this section, we will explain in detail the proposed CovSegNet.

Overview of CovSegNet architecture

The figure 1 shows the general architecture of the network, which is basically the U-net architecture with additional blocks including the attention mechanism module which replaces the classical skip connection. The traditional subsampling blocks (convolutional layers with stride, pooling layers) are replaced by their corresponding multisampling blocks. In figure 1, Multi_conv2 represents the improved version of 2D convolution layer with stride of 2 and a kernel of size k=3; Multisample Maxpooling is the improved version of maxpooling layer; EATT is the attention mechanism block.

Novel Subsampling technique: Multisampling

Deep learning architectures employ subsampling techniques to scale down spatial dimension lengths of the feature maps in order to increase the global receptive field of neurons in proceeding layers. Some subsampling layers include: pooling layers, convolution layers with stride, dropout, normalization. The spatial resolution r t of a feature map after passing through a CNN layer is: r t = r t-1 /k d where r t-1 is the resolution of the feature map before the subsampling layer is applied, k is the stride length, and d is the dimensionality of the CNN (1D, 2D or 3D) . A two dimensions convolution layer (2D CNN) with a stride length of 2 reduces spatial resolution by a ratio of 4, bottlenecking the capacity of proceeding feature maps. By implementing the following subsampling strategy, we preserve the benefits of traditional subsampling layers while generating a more informative forward pass producing higher-resolution feature maps, better gradient updates for deep layers during training. We increase the number of samples taken from feature maps at subsampling layers and therefore preserve more information for late layers in the network. In the above figure 2(a), with the traditional subsampling, the feature map is divided into k × k sampling windows, then a convolution or pooling operation is lined up with the top left element of the window and the result is a single 2 × 2 feature window. Our idea is not to limit to lining up the convolution or pooling operation only to the top left element, but we have k 2 possibilities (representing all the elements of the k ×k window) of subsampling. One can decide to choose n samples of the k 2 , generalizing the spatial resolution of the feature map r t to higher dimension: r t = n. r t-1 k d . In figure 2(b), we show an example of 2D subsampling with kernel size of 2x2 where our choice of samples is made on the top left and bottom right element of the window. A 2x2x2 size feature map is then generated with n = 2. The multisampling is applied to all the subsampling layers and the output of the final convolution layer is made of many different submaps giving room to the post processing operations to generate feature vector (3D convolution can be used to combine features across the submap dimension).

Attention mechanism module

Description

The channel attention block of Hu, Shen, and Sun [START_REF] Hu | Squeeze-and-Excitation Networks[END_REF] (Squeeze Excitation block named SENET) is performed through Equation 1 below which shows that there is a dimensionality reduction which can reduce the model complexity, but it destroys the direct correspondence between channels and its weights. Equation 1 first projects channel features into a low-dimensional space and then maps them back, making correspondence between channel and its weight to be indirect.

z ′ = W 1 (δ(W 2 z)) (1)
with W 1 ∈ R C×C/r , W 2 ∈ R C/r×C being weights of two fully-connected layers and the ReLU operator δ(.). Wang [START_REF] Wang | ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks[END_REF] demonstrates that avoiding dimensionality reduction helps to learn effective channel attention.

Inspired by Wang [START_REF] Wang | ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks[END_REF], we propose to solve the above problem by avoiding the dimensionality reduction. The idea is to consider the following: Z = δ(W y) where W is a matrix with C × C parameters allowing to model cross-channel (C channels) interaction which is proven to be beneficial to learn channel attention, each row i of the matrix models the relation between the channel i and the remaining C-1 channels . Proceeding as such requires mass of parameters (C × C) leading to high model complexity, especially when the number of channel C is large.

An efficient and effective method to cross-channel interaction consists of modelling the relation between the channel i and its k neighbors, making an abstraction with other channels. This can be done by equation 2 proposed by Wang [START_REF] Wang | ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks[END_REF]:

w = δ(C1D k (y)), (2)
where C1D indicates 1D convolution and k is the kernel size of the convolution.

The equation 2 is graphically represented by figure 3 named efficient attention mechanism (EATT) module, which only involves k parameters. The objective of the EATT module is to approximately capture local cross-channel interaction, the coverage of the interaction k can be determined automatically. A high value of k also increases the model complexity. After aggregating convolution features using global average pooling without dimensionality reduction, EATT module first performs 1D convolution then followed by a Sigmoid function to learn channel attention. Our EATT module is applied in U-net by replacing the skip connection by the EATT module as it is done by Hu, Shen, and Sun [START_REF] Hu | Squeeze-and-Excitation Networks[END_REF]. The architecture of our proposed attention module is shown in Figure 3.

IV EXPERIMENTATIONS

Dataset

We used a publicly available COVID-19 CT scans dataset published by Jun et al. [START_REF] Jun | Towards Efficient COVID-19 CT Annotation: A Benchmark for Lung and Infection Segmentation[END_REF], which contains 20 labeled COVID-19 CT lung scans volume ( with 3520 slices of 630x630 gray scale

Implementation details

In the medical community, the Dice Score Coefficient (DSC) is the most widespread metric to measure the overlap ratio of the segmented region and the ground truth, and it is widely used to evaluate segmentation performance. The Focal Tversky Loss function (FTL) addresses the limitation of Dice loss (DL) that penalizes false positive (FP) and false negative (FN) equally, which results in segmentation maps with high precision but low recall especially true and disadvantageous in the case of COVID-19 lesions which have small regions of interests. To this end, we used FTL to train the network to help segment the small COVID-19 regions.

The models are optimized with the Adam optimizer with learning rate of 5e-4 and batch size of 8. The models are trained until they cannot achieve further improvement and we use Early stopping strategy of size 15 to avoid model overfitting. The evaluation metrics used to validate the effectiveness of the proposed method are Dice similarity coefficient, Precision and Recall.

The execution is been done on a GPU Tesla P100-PCIE machine, with a memory size of 16GB.

The number of output channel is respectively 32, 64, 128, 256, and 512 at each level of the downsampling phase. We compared the performance of the proposed network with two publicly available models namely spatial -channel attention gate U-Net (scAG-U-net) Khanh, Dao, Ho, Yang, Baek, Lee, Kim, and Yoo [START_REF] Khanh | Enhancing U-Net with Spatial-Channel Attention Gate for Abnormal Tissue Segmentation in Medical Imaging[END_REF] and spatial-channel squeeze-excitation U-net (scSE-U-net) Roy, Navab, and Wachinger [START_REF] Roy | Concurrent Spatial and Channel 'Squeeze & Excitation' in Fully Convolutional Networks[END_REF] executed on the same computing platform. The evaluation metrics include both efficiency (i.e., network parameters, floating point operations per second and training speed) and effectiveness(Dice loss, recall and precision). Table 1 presents the evaluation metrics of different algorithms (our proposal and some state of art algorithms). The results presented in Table 2 show that the computer resources needed to execute CoviSegNet is lower than the the state-of-the-art counterpart.

Quantitative analysis

Detailed comparison among different models in our experiments is shown in Table 1. Our proposed model outperforms scSE-U-net and scAG-U-net in terms of training time, Dice, recall and precision metrics. As these models are identical in model encoder, it appears that the proposed attention mechanism contributes very well in lesion segmentation. The utilization of attention mechanism helps to accurately detect and segment infected tissues and ignore non infected tissues. The number of false positive is reduced, increasing the rate of the recall. The CovSegNet captures both the large and tiny visual structures which is useful to segment infection lesion with different size. It is noted that the number of parameters of our proposed model is lower than that of others attention U-net models presented in this work. More to that the computation cost is considerably reduced due to lower number of operations. The CovSegNet executed without the proposed subsampling techniques is fastest in terms of training time because of it low number of operations, but it is less accurate comparing to CovSegNet+Novel subsampling, which shows the efficiency of the novel subsampling techniques used in efficient features extractor.

Qualitative analysis

From the visualization of our results in Figure 5, we notice that our model outperforms other models. The models scSE-U-net and scAG-U-net provide good results but there are limited in segmenting lesions with non-smooth borders. Our proposed method is sensitive to non-smooth and tiny lesions as shown in Figure 4. Additionally, others methods tend to provide some segments which don't exist in the ground truth image.

VI CONCLUSION

We have presented in this paper, a novel segmentation network CovSegNet to efficiently segment COVID-19 lesions. The multisampling technique and the EATT module can easily be integrated into the popular U-Net architectures while minimizing the computational cost and increasing the performance of the model. By taking advantage of the information of the encoder and decoder features, our proposed attention mechanism captures efficient information about the location and the shape of the lesion. Experiments results show that the proposed method improves the segmentation results while reducing the model parameters and computation cost. We limited our study to the channel attention mechanism while expecting further works to be carried on the spatial attention mechanism that will allow to focus on the salient region that are beneficial to find the location of the object and determine the target structure of the of the object.

Figure 1 :

 1 Figure 1: Architecture of the proposed network. A CT slice is taken as input and the COVID-19 infected region is displayed as output

Figure 2 :

 2 Figure 2: Subsampling strategies

Figure 3 :

 3 Figure 3: Efficient attention mechanism

Figure 5 :

 5 Figure 5: Representative results from our dataset using different U-Net architectures.

Table 1 :

 1 Quantitative analysis of infection regions on our dataset. scAG-U-net refers to the model

	CoviSegNet +	90.73 ± 0.06 96.91± 0.02	95.90± 0.04
	Subsampling

proposed in Khanh, Dao, Ho, Yang, Baek, Lee, Kim, and Yoo

[START_REF] Khanh | Enhancing U-Net with Spatial-Channel Attention Gate for Abnormal Tissue Segmentation in Medical Imaging[END_REF]

and scSE-U-net is the model proposed in Roy, Navab, and Wachinger [4] Model Dice Recall Precision scAG-U-net 90.67 ± 0.06 96.54 ± 0.022 94.86 ± 0.05 scSE-U-net 90.55 ± 0.07 96.83 ± 0.02 94.97 ± 0.05 CoviSegNet 90.57 ± 0.06 96.03 ± 0.02 95.02 ± 0.04 image) of patients diagnosed with COVID-19 as well as segmentations of lungs and infections made by experts. Left lung, right lung, and infections are labeled by two radiologists and verified by an experienced radiologist. Each slice has it corresponding infection mask.

Table 2 :

 2 Comparison of different attention methods on Covid-19 in terms of network parameters (Param.), floating point operations per second (FLOPs), training speed (per second)

	Model	Time #Param. #FLOPS
	scAG-U-net	56.47 8.65M 16.47 G
	scSE-U-net	47.48 8.98M 16.44 G
	CoviSegNet	42.49 8.63M 16.43 G
	CoviSegNet +	43.82 8.63M 16.42 G
	Subsampling
	V EXPERIMENT RESULTS

A ANNEX 1

See Figure 4.


RELATIVE AGE EFFECT IN SHOOTING SPORTS Is There an Influence of Relative Age on Participation in Non-Physical Sports Activities? The Example of Shooting Sports

Keywords: Relative Age Effect, Discrimination, Dropout, Shooting sports

Abstract

The aim of this study was to test the presence of the Relative Age Effect (RAE) on the overall male (n = 119,715) and female (n = 12,823) population of the shooting sports federation, and to see if it has an impact on discontinuance. For the boys as for the girls, the results show a uniform distribution of discontinuance. Concerning the girls, a RAE was not found, showing that in female shooting sports this effect is not operating. Looking at the males, a significant statistical RAE was not detected in "18-20 years old" and "13-14 years old" categories. However, this effect was found in "adults", "11-12 years old" and "under 11 years old" categories. A significant "inverse" RAE was found for the "15-17 years old". If the rejection of the null hypothesis in some male age groups of a non-physical sports activity is of interest, further qualitative research is needed in order to clearly understand which factors contribute to this asymmetric distribution of birth dates in French male shooting sports.

Is There an Influence of Relative Age on Participation in Non-Physical Sports Activities? The Example of Shooting Sports.

In competitive sports, players are grouped according to age. The goal of these age categories is to make competition more equal between participants. Despite this, in a system which has the 1 st of January as the cut-off date, for example, a child born in January can have an advantage of physical and cognitive maturity of 12 months compared to a child born in December in that same year, although the two will find themselves in the same age group. In terms of relative age, there can be a large difference between the young players in the same age category. This gap is noticeably apparent in terms of physical development [START_REF] Tanner | Clinical longitudinal standards for height, weight, height velocity and weight velocity and the stages of puberty[END_REF] and also in cognitive development [START_REF] Bisanz | Effects of age and schooling on the acquisition of elementary quantitative skills[END_REF]. This advantage (or disadvantage) of relative age will reach its climax at the point of puberty.

Thus, Delorme and Raspaud (2009) have shown that in all French youth basketball age categories, the children born at the beginning of the competitive year (i.e., the oldest relative age) are always significantly taller on average than those born at the end of the year. The greatest difference in average size of the two groups is at the beginning of puberty (La [START_REF] Rochebrochard | Age at puberty of girls and boys in France: measurements from a survey on adolescent sexuality[END_REF], with 4.53 centimetres for the girls at 10 years old, and 5.21 centimetres for the boys at 13 years old. The consequence of relative age is called "Relative Age Effect" (RAE). [START_REF] Grondin | Trimestres de naissance et participation au hockey et au volleyball[END_REF] were the first to discuss the possible relationship between the trimester of birth and achieving a high sporting level. In analysing the data of the National Hockey League, it reveals an over-representation of players born at the start of the year and a significant under-representation of those born at the end of the year. They suggest that this biased distribution was the consequence of the 1 st of January cut-off date, which was used to determine the age categories for minor hockey.

Since this first study, an increasing amount of work has been published on RAE in the sporting domain. The research on professional sports mainly focuses on football and ice hockey [START_REF] Musch | Unequal competition as an impediment to personal development: A review of the Relative Age Effect in Sport[END_REF]; however, there are also numerous studies of baseball [START_REF] Thompson | Born to play ball': The relative age effect and major league baseball[END_REF][START_REF] Stanaway | Lack of a season of birth effect among American athletes[END_REF], basketball [START_REF] Daniel | More on the relative age effect[END_REF][START_REF] Côté | When ''where'' is more important than ''when'': Birthplace and birthdate effects on achievement of sporting expertise[END_REF]Delorme, Boiché & Raspaud, in press), American football [START_REF] Daniel | More on the relative age effect[END_REF][START_REF] Stanaway | Lack of a season of birth effect among American athletes[END_REF] and tennis [START_REF] Edgar | Season of birth distribution of elite tennis players[END_REF]. Such investigations are also carried out at the youth level and the youth elite level. Here too, ice hockey and football are most often studied [START_REF] Musch | Unequal competition as an impediment to personal development: A review of the Relative Age Effect in Sport[END_REF]. There are also some studies on baseball [START_REF] Thompson | Baseball performance and the relative age effect: Does little league neutralize birthdate selection bias?[END_REF], basketball (Delorme & Raspaud, 2009), gymnastics (Baxter-Jones, 1995), swimming [START_REF] Baxter-Jones | Growth and development of young athletes. Should competition levels be age related?[END_REF], tennis [START_REF] Dudink | Birth date and sporting success[END_REF][START_REF] Edgar | Season of birth distribution of elite tennis players[END_REF] and volleyball [START_REF] Grondin | Trimestres de naissance et participation au hockey et au volleyball[END_REF].

With a few rare exceptions [START_REF] Daniel | More on the relative age effect[END_REF][START_REF] Baxter-Jones | Growth and development of young athletes. Should competition levels be age related?[END_REF][START_REF] Stanaway | Lack of a season of birth effect among American athletes[END_REF][START_REF] Côté | When ''where'' is more important than ''when'': Birthplace and birthdate effects on achievement of sporting expertise[END_REF]Delorme et al., in press) most of the studies report a significant RAE, especially in sports where height, weight and strength are considered as assets [START_REF] Musch | Unequal competition as an impediment to personal development: A review of the Relative Age Effect in Sport[END_REF]. Activities such as dance and gymnastics, where physical attributes are ineffective, or even disadvantageous, RAE is not present. The work of [START_REF] Baxter-Jones | Effects of training at young age: a review of the Training of Young Athletes (TOYA) study[END_REF] and [START_REF] Malina | Growth, maturation and physical activity[END_REF] show that late puberty is an advantage for gymnasts and dancers. In addition, it has been observed that a positive correlation exists between late puberty and the practice of gymnastic at a high level [START_REF] Baxter-Jones | Growth and development of young athletes. Should competition levels be age related?[END_REF][START_REF] Baxter-Jones | Growth and development of male gymnasts, swimmers, soccer and tennis players: A longitudinal study[END_REF][START_REF] Van Rossum | Relative age effect revisited: findings from the dance domain[END_REF], the presence or absence of RAE is a function of motor skills. Thus, the author argues that a RAE should not be imposed in activities where physicality is not important.

The unequal distribution of athletes at a professional level is explained by others using a model of selection giving value to premature physical development which leaves sportsmen/women born late in the competitive year behind [START_REF] Sherar | Do physical maturity and birth date predict talent in male youth ice hockey players[END_REF]. The athletes born early in the competitive year possess significant assets in terms of their development (i.e., size, weight and force) which influence their perceived potential [START_REF] Helsen | The relative age effect in youth soccer across Europe[END_REF]. These adolescents being more easily identified as talented or promising and are thus more easily selected to enter professional team training centres or sports institutes for youth national teams and thus have a greater possibility of a professional career. This early exposure to high level training gives them a decisive advantage in terms of skills and game knowledge (Williams, 2000;Ward & Williams, 2003). Thus, RAE is considered a discriminatory effect in the junior categories because it disadvantages the players born late after the cut-off date, as it reduces their chances of selection to elite groups [START_REF] Musch | The relative age effect in soccer: Cross-cultural evidence for a systematic discrimination against children born late in the competition year[END_REF]. Given the lucrative nature of certain professional sports, this discrimination requires particular attention.

Parallel to this phenomenon, it can be equally noted that certain activities dissuade the youngest players in relative age from taking up a sport. Indeed, Delorme and Raspaud (2009) report a significant RAE in the entire youth categories of French basketball for girls and boys.

Their results show that the children born late in the competitive year suffer from a significant disadvantage in size and as a consequence have a lesser tendency to take up this sport. This explains their systematic under-representation. In addition to this auto-elimination at the entry level, [Authors] note that young players born early in the competitive year are significantly under-represented in the statistics of those who quit basketball, whilst their counterparts born at the end of the year are largely over represented.

The unequal distribution of the month of birth of high level athletes is explained by the joint action of the two mechanisms described above; on one side, the youngest players participate less and /or discontinue more easily sports which require strong physical attributes, and on the other side, the oldest players enter more easily into elite training programs. These two phenomena (i.e., auto-elimination/discontinuance and recruitment) thus facilitate the entry of children born just after the cut-off-date into a professional sporting career.

Despite the now substantial literature on RAE, [START_REF] Musch | Unequal competition as an impediment to personal development: A review of the Relative Age Effect in Sport[END_REF] observe that the effect of an athlete's gender on this phenomenon still remains neglected in the literature. The rare research carried out has led to contradictory results. [START_REF] Baxter-Jones | Growth and development of young athletes. Should competition levels be age related?[END_REF] studied elite gymnasts in Britain and observed no RAE for girls or boys. [START_REF] Van Rossum | Relative age effect revisited: findings from the dance domain[END_REF] arrived at the same conclusion for professional dancers in the Netherlands. In the same way, Vincent and Glamser's study (2006) compared the RAE of 1344 male and female footballers considered by the US Olympic Development Program. The results reveal a marginal RAE for the girls at a regional and national level and no RAE for those at a state level. However, a strong RAE has been noted for the males at a regional, state and national level. Delorme et al.

(2009) also do not find a RAE among high level French female soccer players, basketball players and handball players.

Contrary to these results, Delorme and Raspaud (2009) observed a significant RAE in the entire youth female and male categories in French basketball. This phenomenon is even more pronounced with girls than with boys, despite Musch and Grondin's (2001, 162) assertion that "stronger RAEs in male youth sports can be predicted." Indeed, Baxter-Jones (1995) suggested that the stronger RAE among male players is the result of the earlier maturation of girls and the higher variance of the maturity status of boys. During the period of selection, there would thus be more important differences between boys than between girls. Vincent and Glamser (2006, p. 412) argued that social pressures to conform to a socially constructed gender role (i.e., stereotyped definition of femininity) 'could make early maturing females less motivated to achieve excellence in competitive sport because of a perception that society does not value female athletic accomplishments in the same way it does those of males'. [START_REF] Shakib | Female basketball participation. Negotiating the conflation of peer status and gender status from childhood through puberty[END_REF] provided an illustration of this phenomenon in her study about female basketball participation, showing that before and after puberty, girls' peer statuses and gender statuses are conflated. Girls have to renegotiate a tension between popularity (i.e., peer status) and athleticism. Thus, early maturing females are more subject to leave competitive sports than later maturing females. The physical advantage provided by an early maturation to excel more early in certain sports would thus be more profitable among boys than among girls.

It is noted that up until present, the entire body of literature on RAE has been carried out on sports where the physical attributes of participants have a decisive advantage either because they are very developed (e.g., ice-hockey, football) or because they are not yet developed (e.g., gymnastics, dance). Thus it seems useful to take interest in a sporting activity in which physical attributes have a priori no impact, in order to observe how RAE functions. Our attention is therefore turned to a non physical discipline: shooting sports. The French Federation for Shooting Sports (FFT) manages ten disciplines covering numerous arms (e.g., pistols, rifles) over numerous distances (i.e., 10 to 300 metres). Within these disciplines, there are eight events which are in the males' Olympic program and seven events for the women's Olympic program.

Due to the fact that the morphological and muscular characteristics of children do not allow them to hold classic arms, intended for adults, the FFT has incited the fabrication of adapted arms, which use compressed carbon dioxide. These adapted arms are also smaller, lighter and offer greater manoeuvrability. The FFT has also put in place a progression system, allowing the children to use adjustable aids, in function with their age and level. Thus even in the youth categories, the differences in physical development due to relative age remain ineffective.

The study will examine the entire membership body of the federation during the 2006-2007 season, which will allow a diachronic analysis of this phenomenon. In light of the contradictory results obtained concerning the sex of athletes and RAE, women and men will be separated to assess if there is an impact on the RAE. We will also focus on the members of the 2006-2007 season who did not renew their memberships for the 2007-2008 season; thus we will observe whether RAE affects discontinuance of membership, just as [Authors] suggest.

Given that it concerns an activity in which physical attributes are not operating, the hypothesis is that there will be an absence of RAE for girls and for boys, in youth and adult categories. For the same reasons, it can be hypothesised that a uniform distribution of those discontinuing the sport across all categories for girls and boys will be seen.

Methodology Data Collection

For the needs of this current study, the dates of birth of the entire membership body, will be taken from the FFT database for girls (n = 12,823) and boys (n = 119,715). The federation has also given the dates of birth of those who did not renew their memberships for the 2007-2008 season. We also waited for the end of the 2007-2008 season to ensure that some members had not renewed their license later during the year. The identification of people who discontinued this sport can be identified by the fact that the FFT attributes a lifelong number to members.

At the youth level, the FFT has five different age categories: "under 11 years old", "11-12 years old", "13-14 years old", "15-16 years old" and "18-20 years old". The cut-off date used to determine the categories is the 1 st January. The FFT competition year cut-off date is the same as the French school year one. Furthermore, shooting sports are not a discipline included in the French physical education programs. Thus, given that there are not inconsistencies in school and competition cut-off dates, the present RAE study results cannot be confounded (see O'Donoghue, [START_REF] O'donoghue | Season of birth in elite cricket and netball[END_REF].

Data Analysis

In the current literature, the presence of RAE is determined by testing if a significant statistical difference exists between the expected number of players born per month or per quarter (i.e., three consecutive months) and the observed number. In relation to FFT, the cutoff date is 1 st January. Thus, the birth month of members are classed in four quarters, starting with the period January-March (Q1) and ending with the period October-December (Q4).

Next, a chi-square test is used to determine if the observed distribution differs significantly from the expected distribution. Similar to previous works, the expected distribution is calculated from statistics of the distribution of birth months, by gender and by year, for the national population, using weighted means. These data have been obtained from the National Institute of Statistics and Economic Studies.

As pointed by [START_REF] Musch | The relative age effect in soccer: Cross-cultural evidence for a systematic discrimination against children born late in the competition year[END_REF] a chi-square test cannot shed light on the existence of trends in the data. Consequently, for each significant chi-square test, the predicted linear relationship between month of the competition year and the distribution of members was examined by calculating the Kendall tau rank correlation coefficient between the month of the competition year and the difference between the expected and observed number of members for each month. These tests were conducted one-tailed according to the direction of the investigated effect. Consequently, a negative sign of the correlation will indicate that members born at the beginning of the competition year are overrepresented.

In relation to discontinuance, the expected distribution is calculated from the statistics of birth month, by gender and by year for the population of FFT members, using weighted means. For this type of analysis, it is more precise to take the statistics of all the members as the expected distribution, rather than the national population statistics (Delorme & Raspaud, 2009).

Results

Tables 1 and2 Concerning the females, a significant statistical RAE is not found , for the "adults", for the "18-20 years old", for the "13-14 years old", for the "11-12 years old" or for the "under 11 years old". In contrast, a significant biased distribution can be observed for the "15-17 years old" with an over-representation of members in Q1 and an under-representation in the other quarters.

Looking at the males, a significant statistical RAE is not detected in the "18-20 years old" and in the "13-14 years old". However, conforming to the RAE theory, there is a strong over-representation of members in Q1 and a strong under-representation in Q3 and Q4 for the "adults" (τ = -.39, p<.05), the "11-12 years old" (τ = -.36, p<.05) and the "under 11 years old" (τ = -.67, p<.01). Finally a significant "inverse" RAE is found for the "15-17 years old" (τ = .36, p<.05), with an over-representation in Q4 and an under-representation in the other quarters. **** Table 3 near here **** For all the youth boy and girl categories, it can be stated that there is a high level of discontinuance during or at the end of the season studied. The rate of discontinuing however, is higher amongst the girls than the boys. For females, the age categories "15-17 years old" and "18-20 years old" have the highest level of discontinuance. For males, the highest levels of discontinuance are seen in the "11-12 years old", "13-14 years old" and "15-17 years old" categories. For the two sexes, it is noted that in the "adults" are least likely to discontinue, with a rate nevertheless higher for women than for men.

Tables 4 and5 5 near here **** Concerning the girls discontinuing, a statistically biased distribution is not found in "adults", nor in "18-20 years old", nor in "15-17 years old", nor in "13-14 years old", nor in "11-12 years old" and nor in "under 11 years old".

The distribution is uniform for the males, just like their female counterparts, in every age categories.

Discussion

Since the body of research on RAE concerns sports in which physical attributes have a significant impact on performance, we turn our attention to a discipline in which these attributes seem a priori to be inoperative; thus we aim to test the presence of this effect on participation and abandonment. Given that shooting sports are non physical, we hypothesize that there will be an absence of RAE and that there will be consistent discontinuance for boys and for girls, and in all age categories.

In relation to the girls, a biased distribution is not found, except for the "15-17 years". Despite this, this distribution does not correspond with the usual distribution observed in cases where RAE operates: there is an over-representation in Q1, yet an under-representation is not noted in Q4. While, in the RAE theory, an over-representation in the first six months of the year and an under-representation in the last six months is generally seen [START_REF] Musch | Unequal competition as an impediment to personal development: A review of the Relative Age Effect in Sport[END_REF]. A new analysis was then carried out, by grouping together Q1 with Q2 and Q3 with Q4, however, this analysis still did not show a significant RAE (χ 2 = 1.128, d.f.= 1, P<0.288). It can therefore be concluded that RAE is not found in French female shooting sports, conforming to our initial hypothesis.

In the category of women discontinuing, it is noted that for all the age categories, the distribution observed does not differ from that of the expected distribution. Contrary to French female youth basketball study by [Authors], an over-representation of girls born in Q4 discontinuing this sport is not noticed, nor an under-representation of those born in Q1.

These results support our initial hypothesis that in female shooting sports, a difference in terms of relative age is not operating. Auto-elimination at the entry level of those born in Q4, as described by Delorme and Raspaud (2009) is not found. Neither is the overrepresentation of discontinuance seen by those same individuals. Thus, in relation to females, this study confirms the proposition of [START_REF] Van Rossum | Relative age effect revisited: findings from the dance domain[END_REF], that is to say, that the presence or absence of RAE seems tied to the motor skill characteristics. In the case of non-physical sports, the differences in physical and cognitive development of participants, do not come into play.

For the boys, the initial hypothesis of an absence of RAE in all age categories has not been verified. Numerous scenarios in function with the age of members can be distinguished.

First of all, it is noticed that a significant statistical RAE exists in the "under 11 years old" and "11-12 years old" categories. This asymmetrical distribution is not due to discontinuance, as there is uniform distribution across the two age categories. The unevenness of the distribution of members therefore comes from a stronger recruitment of young boys born in Q1, whilst those born in Q3 and Q4 are less likely to get involved in this sport. Given the young age of children, it is reasonable to think that becoming involved in this discipline is decided primarily by parental authorisation. As noted in the introduction, children born in Q3 and in Q4 are less physically and cognitively developed than are their counterparts born in Q1. Taking note of the social representations of danger and associated violence of firearms and their utilisation, it can be thought, that parents may have less hesitation to authorise their children participating in this sport, if they are among the older children in their age groups. This reasoning can therefore explain the asymmetry observed.

The work carried out on RAE in the scholarly domain, shows that the children having the youngest relative age (i.e., those born late in relation to the cut-off date) are more likely to fail (e.g., [START_REF] Diamond | The birthdate effect -A maturational effect[END_REF] and succeed significantly less than the students born just after the cut-off date (e.g., [START_REF] Davis | Does age of entrance affect school achievement?[END_REF][START_REF] Uphoff | Pupil age at school entrance -How many are ready for success[END_REF][START_REF] Sweetland | Age of entry, sex, and academic achievement in elementary school children[END_REF]. Perhaps this scholarly success contributes to the child projecting a 'serious' essence which facilitates parental agreement. The diachronical evolution of distribution seems to support this interpretation; the strongest RAE is observed amongst the "under 11 years old", then decreases in "11-12 years old" and finally disappears in "13-14 years old". Nevertheless, we must remain careful with this interpretation. A qualitative study about young members' parents is needed in order to clearly determine which reasons/factors led them to allow their children to practice this sport.

Secondly, a significant statistical "inverse" RAE appears amongst the "15-17 years old", whilst there is a uniform distribution of birth dates for the "13-14 years old". Thus, an over-representation of those born in Q4 and an under-representation of those born in Q1 is noted. This asymmetry is not a result of discontinuance, as the results are distributed in a uniform manner across the quarters. The "inverse" RAE observed here is therefore the result of a greater participation in this activity by children born in Q4 than those born in Q1. This phenomenon could be explained by weak players who changed sports after failing in disciplines in which developed physical attributes are determinant. Indeed, Delorme and Raspaud (2009) reveal that within French basketball, it is in the "13-14 years old" category where the greatest difference in size is found. Thus, the players born in Q1 are on average 4.88 centimetres taller than their team-mates born in Q4. It is also amongst the basketball players in the "13-14 years old" category, where [Authors] find the greatest overrepresentation of those discontinuing (in Q4), whereas those born in Q1 are clearly underrepresented. The basketball players born in Q4 exhibit less physical maturity on average, and thus have a greater tendency to discontinue this activity. It is therefore reasonable to venture that they enrol in sporting activities in which physical attributes are inconsequential.

Therefore, this could explain the over-representation noted in Q4. Even if the work of Delorme and Raspaud (2009) and [Authors], supports this interpretation, we must remain careful. Only a qualitative analysis carried out concerning the new members of this age category, would confirm the reality of this transfer.

Finally, in the "adults" category, our initial hypothesis has not been verified, given the presence of a significant RAE in the results. Indeed, as there is an over-representation of members in Q1 and an under-representation of members in other quarters, this distribution is typical of RAE, given that in grouping together Q1 with Q2 and Q3 with Q4, this allows an over-representation amongst the first group to appear, and under-representation amongst the second group, which is statistically significant (χ 2 = 5.796, d.f.= 1, P<0.016). The overrepresentation of members in Q1 is not explained by discontinuance, as these are distributed in a uniform manner across the different quarters. This asymmetry could be explained by a transfer of sportsmen born in Q1 who find themselves in the situation of failure in the sports privileging developed physical attributes. In fact, in Bäumler's study (1996) carried out on the Germany Professional Football Championships, the author has shown a negative correlation between age and RAE; the more the age increases, the more RAE declines. Thus the author notes that amongst the "18-22 years old", 68% of players are born in the first six months of the competitive year. This proportion will diminish continually until reaching a uniform distribution at "33-35 years old". [START_REF] Bäumler | The relative age effect in soccer and its interaction with chronological age[END_REF] concludes that the physical advantage of players born in Q1 and Q2 is reduced with time and that the reduction of RAE corresponds to a shift in direction of players possessing the best technical attributes, who have suffered from disadvantages in terms of relative age in their youth. The recent work of [START_REF] Ashworth | Selection bias and peer effects in team sports: The effect of age grouping on earnings of German soccer players[END_REF] confirms this analysis. Basing their research on the German Football Championships, they find a significant RAE. However, they note that although being underrepresented, the players born in Q3 and Q4 are more competitive and reach a better salary than their team-mates born just after the cut-off date. The authors put forward two explanations for this phenomenon. Firstly they suggest that players born late after the cut-off date, who are still participating in the sport, have survived the recruitment process which normally discriminates against them. For the authors, "to succeed in such survival is possible only if they are of above-average talent" (p. 372). Secondly, they suggest that the players born in the second half of the year have benefited from a greater quantity of training due to the systematic confrontation with their counterparts with more developed physical attributes. In fact, "the age grouping creates a systematic advantage for late-born players who receive their soccer education together with players who, though equally talented, are better than themselves (just because they are a few months older)" (p. 372). Thus, the adults born in Q1, who find themselves failing, as a result of the progressive reduction of the initial disadvantage due to relative age of their counterparts born in Q4, could thus lead them to switch to sports where physical attributes are not operating. Once again, we must be careful with this interpretation, which must be supported by a qualitative study about the new adult members of the FFT with the goal of drawing up a history of their old sporting practices, to determine the reasons of their new participation in this activity.

Conclusion

For [START_REF] Van Rossum | Relative age effect revisited: findings from the dance domain[END_REF], the presence or absence of RAE is a function of motor skills. Thus, the author argues that a RAE should not be imposed in activities where physicality is not important. While our results about French female shooting sports confirm this hypothesis, the results of the male shooting sports make it invalid. Indeed, although male sport shooting seems to be a discipline where physical attributes do not play a priori a determining role in the decision to participate or discontinue this activity, our results suggest that some exogenous factors deriving from relative age (e.g., parental authorisation, failure in another sport) might explain the biased distribution in some age groups.

However that may be, we must remain very careful with the varied proposed interpretations. Indeed, if the rejection of the null hypothesis in some male age groups of a non-physical sports activity is of interest, further qualitative research is needed in order to clearly understand which factors contribute to this asymmetric distribution of birth dates in French male shooting sports.

  respectively present the distribution per quarter and by age category for girls and boys discontinuing during the 2006-2007 season. **** Table 4 near here **** **** Table

  respectively present the distribution per quarter and per category of boy and girl members during 2006-2007 season.

**** Table 1 near here **** **** Table 2 near here ****

Table 3

 3 presents the percentages of those discontinuing, by age category and by sex, for the 2006-2007 season.

Table 1 .

 1 Distribution of female license holders(2006)(2007).

		Q1(%) (expected)	Q2(%) (expected)	Q3(%) (expected)	Q4(%) (expected)	Total	χ 2	P
	Adults	2,498 (24.56) (2,498)	2,674 (26.29) (2,673)	2,606 (25.62) (2,565)	2,393 (23.53) (2,435)	10,171 1.399 0.706
	18-20	156 (26.71) (141)	146 (25.00) (151)	145 (24.83) (148)	137 (23.46) (144)	584	2.231 0.526
	15-17	227 (28.44) (193)	184 (23.06) (203)	192 (24.06) (206)	195 (24.44) (196)	798	8.501 0.037
	13-14	128 (25.10) (121)	136 (26.67) (130)	124 (24.31) (132)	122 (23.92) (127)	510	1.256 0.739
	11-12	118 (24.79) (113)	119 (25.00) (120)	120 (25.21) (123)	119 (25.00) (120)	476	0.268 0.966
	< 11	72 (25.35) (68)	79 (27.82) (72)	68 (23.94) (73)	65 (22.89) (71)	284	1.737 0.629
	TOTAL	3,199 (24.95) (3,149	3,338 (26.03) (3,370)	3,255 (25.38) (3,234)	3,031 (23.64) (3,070)	12,823 1.738 0.628

Table 2 .

 2 Distribution of male license holders(2006)(2007).

	Q1 (%) (expected)	Q2 (%) (expected)	Q3 (%) (expected)	Q4 (%) (expected)	Total	χ 2	P

Table 3 .

 3 Discontinuance during 2006-2007 season .

			Females			Males
		Total	Dropouts	%	Total	Dropouts	%
	Adults	10,171	2,729	26.83	108,257	19,501	18.01
	18-20	584	282	48.29	1,925	919	47.74
	15-17	798	369	46.24	3,236	1,775	54.85
	13-14	510	206	40.39	2,773	1,518	54.74
	11-12	476	190	39.92	2,199	1,195	54.34
	< 11	284	112	39.44	1,325	637	48.08
	Total	12,823	3,888	30.32 119,715	25,545	21.34

Table 4 .

 4 Distribution of discontinuance for females(2006)(2007).

		Q1 (∆)	Q2 (∆)	Q3 (∆)	Q4 (∆)	Total	χ 2	P
	Adults	655 (-15)	711 (-7)	683 (-16)	680 (+ 38)	2,729	3.012	0.390
	18-20	75 (-1)	74 (+ 4)	77 (+ 7)	56 (-10)	282	2.430	0.488
	15-17	113 (+ 8)	79 (-6)	82 (-7)	95 (+ 5)	369	1.830	0.608
	13-14	51 (-1)	51 (-4)	59 (+ 9)	45 (-4)	206	2.252	0.522
	11-12	42 (-6)	47 (0)	54 (+ 6)	47 (0)	190	1.340	0.720
	< 11	28 (0)	37 (+ 6)	25 (-2)	22 (-4)	112	1.739	0.628

Note : ∆ is the difference between observed distribution and theoretical expected distribution.

Table 5 .

 5 Distribution of discontinuance for males(2006)(2007).

		Q1 (∆)	Q2 (∆)	Q3 (∆)	Q4 (∆)	Total	χ 2	P
	Adults	4,900 (+ 17)	5,184 (+ 81)	4,808 (-44)	4,609 (-54)	19,501	2.346	0.504
	18-20	207 (-3)	225 (-25)	238 (+ 13)	249 (+ 15)	919	4.175	0.243
	15-17	400 (-8)	442 (-7)	442 (+ 5)	491 (+ 10)	1,775	0.520	0.914
	13-14	326 (-18)	407 (+ 3)	383 (+ 1)	402 (+ 14)	1,518	1.381	0.710
	11-12	311 (-8)	302 (-1)	278 (-3)	304 (+ 12)	1,195	0.690	0.876
	< 11	184 (+ 3)	174 (0)	148 (-7)	131 (+ 4)	637	0.470	0.925

Note : ∆ is the difference between observed distribution and theoretical expected distribution.

 Ward, P. & Williams, A. M. (2003). Perceptual and cognitive skill development in soccer:

The multidimensional nature of expert performance. Journal of Sport and Exercise Psychology, 25, 93-111. Williams, A. M. (2000). Perceptual skill in soccer: Implications for talent identification and development. Journal of Sports Sciences, 18, 737-740.