G Caravaca
email: gwenael.caravaca@univ-nantes.fr

Le Mouélic

V Ansan

F Civet

Le Deit

M Massé

& Mangold

High-resolution Digital Outcrop Modelling of terrestrial analogues for education on Planetary Geology

Keywords: Digital Outcrop Model, Virtual Reality, Photogrammetry, Virtual field-trip, Sedimentology, Planetary Geology

Teaching in Planetary Geology relies both on remote data gathered by various probes exploring the solar system (orbiters, landers and rovers), and on the study of terrestrial analogues sites. Usually, a field-trip on selected outcrops is the most widely used approach. However, this cannot always be possible for various reasons, such as a far distance of the site, safety or accessibility issues, cost, etc.

To overcome these problematics, a complementary solution is progressively emerging thanks to 3D reconstruction and Virtual Reality (VR) techniques. Virtual field-trips can be organized using highresolution 3D recreations of outcrops providing relevant analogues for Planetary Geology. Here, we specifically focus on the "Goldmine Beach" outcrop in western France (Pénestin, Morbihan), that displays a suite of fluvial siliciclastic sedimentary rocks and structures ( [START_REF] Van Vliet-Lanoë | Neotectonic and seismic activity in the Armorican and Cornubian Massifs: regional stress field with glacioisostatic influence[END_REF][START_REF] Brault | Le système fluvio-estuarien Pleistocène moyen-supérieur de Penestin (Morbihan): une paléo-Loire?[END_REF] used as an analogue to Martian fluvial valley systems. Our objectives are to: 1) Produce a highlyresolved 3D photogrammetric model of the outcrop, 2) Evaluate the accuracy of the 3D model reconstruction process by comparing it with ground-truth measurements, and in particular by evaluating the accuracy of the reconstruction computed with limited conditions similar to the ones available from Martian rovers; and 3) Integrate the model within a VR system to allow our students to roam over and characterize at real scale the entire outcrop.

We made two Digital Outcrop Models (DOMs) of the "Goldmine Beach" outcrop using Structure-from-Motion photogrammetry. The first model was obtained using a set of photos taken following the usual procedure for photogrammetric reconstruction (fixed optical parameters, homogeneous lighting, maximum overlapping and coverage). It provides the maximum accuracy to allow our students a close mm-scale inspection of the outcrop and its structures. The second model was made using a "degraded" set of photos, analogue to the photos taken by the Mars Science Laboratory Curiosity rover (varying optical parametersfocal length, frame resolution -, heterogenous lighting, lower overlapping, non-optimal coverage). This second model has a good accuracy despite the degraded observing conditions (Fig. 1) and thus validate the creation of Martian DOMs produced from Curiosity data (e.g., [START_REF] Caravaca | 3D Digital outcrop Model reconstruction of the Kimberley outcrop (Gale Crater, Mars) and its integration into Virtual Reality for simulated geological analysis[END_REF] in a controlled case.

The DOM was subsequently integrated within a VR environment (Fig. 2), using either SteamVR, Sketchfab online platform, or a game engine. In the VR environment, several students and a teacher can interact using real-time networked telepresence to observe, characterize and interpret the structures of the outcrop (Fig. 2a), including the most remote parts that are not accessible on the real outcrop (e.g., top of the cliff; Fig. 2b). Additionally, it is possible to "come back" to the virtual place at any time for further observations and get familiar with taught structures taking advantage of the online availability of the model on the Sketchfab platform (model available at: https://skfb.ly/6WJrW. VR has the potential to become a major part of our Geoscience lessons in the coming years for both remote planetary outcrops (Moon, Mars, etc.) and their terrestrial analogues.

Figure 1 :

 1 Figure 1: Preview of the Goldmine Beach outcrop high-resolution DOM produced under Agisoft Metashape photogrammetry software and using an MSL/Curiosity-analogue photoset. The reconstruction includes the wellexpressed fluvial sedimentary pattern on the upper part of the outcrop. DOM available on Sketchfab at: https://skfb.ly/6WJrW.

Figure 1 :

 1 Figure 1: Screen capture of the Virtual Reality environment featuring the Goldmine Beach outcrop; a) VR avatar of a teacher pointing a structure of interest on the DOM. The hammer is modelled for scaling; b) Same VR teacher avatar pointing another structure from a remote place on top of the cliff, where access is prevented on the real outcrop.


Joseph Sambasene Diatta

Christophe Couder

Christelle Harnois

Sylvain Marinel

Charles Manière
email: charles.maniere@ensicaen.fr

Modeling spark plasma sintering of zirconia with prediction of final stage high densification rate

Keywords: Spark Plasma Sintering, final stage sintering, zirconia, modeling

𝐴 0 Creep coefficient (Ks -1 Pa -n ) 𝑄 Creep activation energy (J.mol -1 ) R Gas constant 8.314 (J.mol -1 .K -1 ) T Temperature (K) 𝜑 Shear modulus 𝜓 Bulk modulus Pl Sintering stress (Pa) 𝛼 Surface energy (J.m -2 ) 𝑟 Particles radius (m) 𝑎, 𝑏, 𝜇 Fitting constants 𝜃 𝑐 Critical porosity I.

In this study, the SPS sintering of 0.1µm zirconia has been performed and shows high densification rate behavior in the final stage. This work consists of modeling the densification behavior of this powder Sintering modeling of processes like the spark plasma sintering (SPS) represents a key step for optimizing the thermal/pressure cycle optimization and also to be able to simulate the powder densification in finite element software (FEM) [1]. The continuum theory of sintering can be employed to simulate the SPS sintering analytically and identify sintering parameters easily implementable in FEM code [2]. Hot pressing (and SPS) solid-state sintering model is expressed after. This model generally assumes the applied stress is higher than the capillarity stress (𝜎 𝑧 ≫ 𝑃𝑙). However, if the powder is submicronic these forces are not negligible and should be taken into account 𝜎 𝑧 𝑛 → (𝜎 𝑧 -𝑃 𝑙 ) 𝑛 . Skorohod sintering stress expression is taken as it gives a reasonable approximation when compared to other theories [3,4], 𝑃 𝑙 =

-𝑛-1 2 (1 -𝜃) 1-𝑛 2 ) 1 𝑛
. The assessment of the sintering parameters requires to identify first the thermal behavior A(T,G) in a high porosity region where the grain growth is inactive. To do so, the master sintering curve or kinetic field methods that can be adapted to SPS equations can be done to identify independently the sintering activation energy [6,7]. With this information, the theoretical moduli can be adjusted by a linear regression equation and other parameters determined. This approach has been used for conventional sintering of zirconia [8], MgAl2O4 spinel [9] and requires less sintering tests than the full extensive approaches that identify both creep and moduli [START_REF] Nicolle | Mise En Forme de Poudre de Bore Par Compression Isostatique à Chaud: Determination Des Propriétés Rhéologiques et Simulation Numérique Du Procédé[END_REF][START_REF] Geindreau | [END_REF][12][13][14].

In this study the combined master sintering curve and moduli adjustment method is adapted to SPS of submicronic zirconia.

II. Materials and Method

The study has been performed with SPS FCT HP25 device and with a binderless 0.1µm Tosoh TZ-3Y-S zirconia powder. For the master sintering curve (MSC) and the simulation analysis study three sintering tests at 20, 50 and 100K/min have been performed at 50MPa of pressure up to 1350°C.

The sintering assessment method consists of three steps.

Step 1 is the independent determination of the sintering activation energy (via the MSC) by finding the activation energy that minimizes the three tests curves differences when plotting the relative density vs 𝑙𝑛 (∫ 𝑒𝑥𝑝(

-𝑄 𝑅𝑇 ) 𝑇 𝑑𝑡 𝑡 0
) [15].

For step 2, the following Skorohod-Olevsky analytical SPS equation is used:

- 1 𝜌 𝑑𝜌 𝑑𝑡 = 𝐴(𝑇, 𝐺) (𝜓 + 2 3 𝜑) -𝑛-1 2 (1 -𝜃) 1-𝑛 2 (𝜎 𝑧 -𝑃 𝑙 ) 𝑛 (2)
In the latter, A(T) is isolated to obtain the regression equation giving A0, Q in the intermediate stage.

𝑌 = 𝑙𝑛 (𝑇|𝜃 ̇||𝜎 𝑧 -𝑃 𝑙 | -𝑛 (𝜓 + 2 3 𝜑) 𝑛+1 2 (1 -𝜃) 𝑛-3 2 ) = 𝑙𝑛(𝐴 0 ) - 𝑄 𝑅𝑇 (3)
Knowing the MSC activation energy (Q) and n=2 for a previous study [13], it is then possible to adjust the unknown parameters of Skorohod [5] moduli (𝜓 = 𝑎

(𝜃 𝑐 -𝜃) 𝑏 𝜃 𝑐 &𝜑 = (1 - 𝜃 𝜃 𝑐 ) 2
) to obtain the slope corresponding to the MSC value. These moduli calibration avoid the identified creep parameters (A0,Q) compensate an error in the theoretical moduli. Afterward, the A0 can be obtained by the origin the regression curve (exp(A0)).

All parameters determined, step 3 is the analytic simulation of the sintering curve based on equation (2).

III. Results and Discussion

Figure1(C)

shows the MSC performed on this powder in order to know its activation energy. The results of the MSC study gives an activation energy of797kJ. mol -1 . Close values of 630 kJ/mol [16] and 673kJ/mol with n~2.1 [17] were obtained for zirconia by SPS in the literature indicating a grain boundary sliding mechanism. As the MSC activation energy is determined by different heating rate independently from the stress intensification factor expression 𝜙(𝜌), the linear regression method described earlier can be used to correct the Skorohod moduli and determine A 0 with equation (3). Figure2(A) shows the results of this regression method after moduli correction. The regression for three heating rates (20, 50 and 100K/min) gives a value of the activation energy close to the MSC of790kJ. mol -1 and a preexponent constant In the final stage sintering, the high densification behavior observed in the curve in Figure2(A) makes a deviation after 1217°C. To model this, a transition switch is operated for a couple Q,A0 of 1400kJ/mol and 1.506E 35 Ks -1 Pa -n after 1217°C. This behavior is considered as a temperature-dependent regime transition (like Figure2(A) suggests) happening at the final stage sintering (where the sintering densification is not decreased).

A 0 of2.16E

IV. Conclusion

In this study, a 0.1µm zirconia powder was sintered by SPS. Three sintering tests at 20, 50 and 100K/min were performed at 50MPa up to 1350°C. The sintering behavior shows limited grain growth and no sigmoid densification behavior at the final stage. To model this sintering behavior of the powder, the Skorohod-Olevsky model was used. A new method has been developed to identify the sintering activation energy while correcting the Skorohod theoretical moduli by coupling a regression approach and a master sintering curve. Model the experimental curves with the continuous final stage densification requires regime transition after 1217°C.

  especially at the intermediate/final stage transition. To model this, a Master Sintering Curve (MSC) is combined with an analytic model to identify the activation energy and the sintering moduli. The modeling of the behavior of the powder during the sintering tests is done via the Skorohod-Olevsky model. It appears from this study that the modeling of final stage sintering requires a regime transition to model the exceptionally high densification rate of the powder. The final stage grain growth seems not to decrease the final stage sintering kinetics. Nomenclature θ Porosity 𝜌 Relative density 𝜎 𝑧 Applied stress (N.m -2 ) H A constant D Diffusion coefficient (m 2 .S -1 ) k Boltzmann Constant (1.380 649 × 10 -23 J.K -1 ) 𝜙 Stress intensification factor G Grain size (m) n Creep law stress exponent m Creep law grain size exponent A Creep deformability (s -1 Pa -n ) Introduction

Figure1(A)

  Figure1(A) shows the results of three experimental tests of SPS sintering at different heating rates

Figure 1 .

 1 Figure 1. Relative density curves at constant heating rate of 20, 50 and 100K/min (A), polished SEM images of the final microstructures (B) and sintering activation energy identification by the Master Sintering Curve (C), in the inset is the minimization graph, the error is the distance between the curves.

Figure 2 .

 2 Figure 2. Regression analysis using SPS data for extraction of activation energy (A) and shear and bulk viscosity moduli as a function of time (B)

Figure 3 .

 3 Figure 3. Simulated relative density as a function of time obtained by SPS at different heating rates, the simulation curves distinguish the identified model in "intermediate stage" without regime transition and the model including the final stage "regime transition".

Table 1 .

 1 14 Ks -1 Pa -n . The corrected moduli are plotted in Figure2(B). The modulus parameters are reported in Table1. Coefficients of adjustment of shear and bulk viscosity moduli

	𝜓 = 𝑎	𝜃 𝜇 (𝜃 𝑐 -𝜃) 𝑏	a	b	μ	θ c
	𝜑 = (1 -	𝜃 𝑐 𝜃	) 2	10	3	2.8	0.51

Acknowledgments

The help and support of Christelle Bilot and Jérôme Lecourt is gratefully acknowledged. This work was supported by: the French National Research Agency (ANR), project ULTRARAPIDE N°ANR-19-CE08-0033-01 and the project "région normadie" -00016601-20E02057_RIN RECHERCHE 2020 -Emergent -ULTIMODULUS.

V.


Pierre-Etienne Martin

Jordan Calandre

Boris Mansencal

Jenny Benois-Pineau

Renaud Péteri

Laurent Mascarilla

Julien Morlier

Sport Task: Fine Grained Action Detection and Classification of Table Tennis Strokes from Videos for MediaEval 2022

. This research is intended to build tools for coaches and athletes who want to further evaluate their sport performances.

Introduction

Action detection and classification is one of the main challenges in computer vision [START_REF] Martin | 3D Convolutional Networks for Action Recognition: Application to Sport Gesture Recognition[END_REF]. Throughout the last few years, datasets focusing on action classification have grown tremendously, along with their complexity [START_REF] Martin | Fine-Grained Action Detection and Classification from Videos with Spatio-Temporal Convolutional Neural Networks[END_REF]. There has been a significant number of studies devoted to the analysis of sports gestures using motion-capture systems. Nonetheless, sensors and markers attached to the body have the inherent tendency to interfere with the natural behaviour of the athletes. Therefore, this concern motivates the development of non-invasive methods using video recording from a camera.

The sports video classification project was initiated by the Sports Faculty of the University of Bordeaux (STAPS), the computer science laboratory LaBRI, and the MIA laboratory of the University of La Rochelle 1 . This project intends to develop artificial intelligence and multimedia indexing methods for table tennis stroke recognition. The ultimate goal is to evaluate the performance of individual athletes, especially students, and thereby develop optimal training strategies. For this purpose, we have recorded a video corpus TTStroke-21 with volunteer athletes.

Datasets like UCF-101 [START_REF] Soomro | UCF101: A dataset of 101 human actions classes from videos in the wild[END_REF], HMDB [START_REF] Kuehne | HMDB: A large video database for human motion recognition[END_REF][START_REF] Jhuang | Towards understanding action recognition[END_REF], AVA [START_REF] Gu | AVA: A video dataset of spatio-temporally localized atomic visual actions[END_REF] and Kinetics [START_REF] Kay | The kinetics human action video dataset[END_REF][START_REF] Smaira | A short note on the kinetics-700-2020 human action dataset[END_REF][START_REF] Li | The ava-kinetics localized human actions video dataset[END_REF] are used in the action recognition field, with an increasing number of video samples and number of classes covered over the years. There are very few datasets available that have a focus on fine-grained classifications in sports, such as FineGym [START_REF] Shao | Finegym: A hierarchical video dataset for fine-grained action understanding[END_REF] and TTStroke21 [START_REF] Martin | Fine grained sport action recognition with twin spatio-temporal convolutional neural networks[END_REF].

To address the increasing complexity of datasets, some classification methods exploit temporal information as much as possible. For example, [START_REF] Liu | Spatiotemporal relation networks for video action recognition[END_REF] learns spatio-temporal dependencies from videos using only RGB data. Alternatively, some methods integrate other modalities extracted from videos, e.g., optical flow [START_REF] Carreira | Quo vadis, action recognition? A new model and the kinetics dataset[END_REF][START_REF] Varol | Long-term temporal convolutions for action recognition[END_REF][START_REF] Martin | Optimal choice of motion estimation methods for fine-grained action classification with 3d convolutional networks[END_REF]. Moreover, in the TTStroke-21 dataset, stroke classification is challenging, because movements between two strokes share strong visual similarities.

The following sections present the Sport task and its substasks for this year, along with the dataset and the specific terms of use when downloading the dataset. Complementary information on the task may be found on the dedicated page from the MediaEval website2 .

Task description

The Sport task is based on the TTStroke-21 database [START_REF] Martin | Sport action recognition with siamese spatio-temporal cnns: Application to table tennis[END_REF][START_REF] Martin | Fine grained sport action recognition with twin spatio-temporal convolutional neural networks[END_REF]. This database is a corpus of table tennis recordings with players performing in natural conditions. The dataset delivered through this task focuses on videos acquired with GoPro cameras at a recording speed of 120 frames per second and annotated by professional players. This task offers researchers an opportunity to solve a fine-grained classification problem with videos and annotations of high quality in the sports domain. Compared to the Sport task from MediaEval 2021's edition [18], the dataset has been enriched and the data organization and distribution differ. The task has two subtasks: stroke classification from trimmed videos and stroke detection from untrimmed videos. Each subtask has its own dataset.

Researchers can participate in one or both subtasks and submit up to five runs for each subtask. The participants must fill in the provided XML files dedicated to the test set of the subtask for each run. The content of the XML file varies according to the subtask. The runs have to be submitted in an archive (zip file), with each run in a different directory for each subtask. Participants should also submit a working notes paper, which describes their method and indicates if any external data, such as other datasets or pre-trained networks, was used to compute their runs. The use of pre-trained models on the Sport task dataset TTStroke-21 of the previous years is however forbidden. The task is considered fully automatic: once the videos are provided to the system, results should be produced without any human intervention. Participants are encouraged to release their code publicly with their submission. This year, similarly to the 2021 edition, a baseline for both subtasks is shared publicly3 [START_REF] Martin | Baseline method for the sport task of mediaeval 2022 benchmark with 3d cnns using attention mechanism[END_REF].

Subtask 1 -Stroke Classification

For this subtask, the participants are required to classify a set of trimmed videos containing only one table tennis stroke, or possibly no stroke at all. There are 20 possible stroke classes and an additional non-stroke class. For this purpose, two annotated sets are provided: a training and a validation set with respectively 807 and 230 trimmed videos. A non-annotated test set comprising 118 trimmed videos has to be classified. The trimmed videos in the different sets may have been retrieved from the same untrimmed videos but at different moments in time without overlapping. Specifically, the participants are invited to fill an XML file and replace the default label "Unknown" with the stroke class assigned by the participants' method. All submissions will be evaluated in terms of global accuracy for ranking, and detailed with per-class accuracy.

In last year edition, the best global accuracy reached 74.2% [START_REF] Qian | Learning unbiased transformer for long-tail sports action classification[END_REF] using SWIN-Transformers, followed closely by ResNet-50 models (68.8%) beating by a large margin last year baseline (20.4%) [21]. Methods effectiveness seem to be linked to the model architecture, but also the taking into account of both stroke class similarity and class imbalance during training. This year, the task uses the same split of the TTStroke-21 database as in [START_REF] Martin | 3d attention mechanisms in twin spatio-temporal convolutional neural networks. application to action classification in videos of table tennis games[END_REF][START_REF] Martin | Fine-Grained Action Detection and Classification from Videos with Spatio-Temporal Convolutional Neural Networks[END_REF] allowing better comparison with previous works outside the MediaEval benchmark scope.

Subtask 2 -Stroke Detection

For this subtask, the participants are required to segment a set of untrimmed videos with the aim to retrieve strokes whatever the stroke class. For this purpose, two annotated sets are provided: a training set and a validation set, with respectively 16 and 6 untrimmed videos. A non-annotated test set consisting of 6 untrimmed videos has to be temporally segmented. The videos are not shared across the training, the validation, and test sets; however, the same player may appear in the different sets.

Specifically, the participants have to fill the provided test set XML files with the stroke temporal boundaries (frame index of the videos). All submissions will be evaluated in terms of mean Average Precision (mAP) and temporal Intersection over Union (IoU). Both are usually used for image segmentation but are adapted for this task:

• mAP: each stroke represents an object to be detected temporally. Detection is considered

True when the temporal IoU between prediction and ground truth is above an IoU threshold. 20 thresholds from 0.5 to 0.95 with a step of 0.05 are considered, similarly to the COCO challenge [START_REF] Lin | Microsoft COCO: common objects in context[END_REF]. This metric will be used for the final ranking of participants. • IoU: the frame-wise overlap between the ground truth and the predicted strokes across all the videos.

For last year's edition, only two participants submitted runs for this difficult subtask [START_REF] Zahra | Two stream network for stroke detection in table tennis[END_REF][START_REF]YOLOV5 for stroke detection and classification in table tennis[END_REF]. They did not improve the baseline result in terms of mAP but [START_REF]YOLOV5 for stroke detection and classification in table tennis[END_REF] reached an IoU of 0.247 against 0.144 for the baseline, using YOLOv5 model.

Dataset description

The dataset was recorded at the Sports Faculty of the University of Bordeaux. It is constituted of player-centred videos without markers or sensors, recorded in natural conditions using GoPro cameras (see Figure 1). Professional table tennis teachers designed a dedicated taxonomy to describe all the possible strokes. The dataset includes 20 table tennis stroke classes: 8 services, 6 offensive strokes, and 6 defensive strokes. The strokes may also be divided in two super-classes: Forehand and Backhand. The dataset was annotated by professional players using a crowd-sourced annotation platform. Non-stroke samples are inferred from the stroke annotations.

In order to be able to share the dataset, we blurred the faces of the players for each original video frame using OpenCV deep learning face detector, based on the Single Shot Detector (SSD) framework with a ResNet base network. A tracking method has been implemented to decrease the false positive rate. The detected faces are blurred, and the video is re-encoded in MPEG-4.

Compared with last year's edition, the classification dataset is enriched this year with new and more diverse video samples. The source videos were trimmed, sorted in class folders and

Specific terms of use

Although faces are automatically blurred to preserve anonymity, some faces are misdetected, and thus some players remain identifiable. In order to respect the personal data of the players, this dataset is subject to a usage agreement, referred to as Special Conditions.

These Special Conditions apply to the use of videos in the scope of the MediaEval workshop task "Sport Task: Fine Grained Action Detection and Classification of Table Tennis Strokes from Videos. ". They correspond to the specific usage agreement referred to in the Usage agreement for the MediaEval 2022 Research Collections, signed between the user and the University of Delft. The complete acceptance of these Special Conditions is a mandatory prerequisite for the provision of the videos as part of the MediaEval 2022 evaluation campaign. A complete reading of these conditions is necessary and requires the user, for example, to obscure the faces (blurring, black banner) in the video before use in any publication and to destroy the data by January 30th, 2023.

Discussions

As last year, the MediaEval Sport task offers two subtasks: i) Classification and ii) Detection of strokes. Classification methods performance has increased since the launch of the task. We hope to have more participation in the detection subtask in order to also improve in the domain of moment of interest in sports. The participants are encouraged to share their difficulties and their results even if they seem not sufficiently good. All the investigations, even when not successful, may inspire future methods.

Figure 1 :

 1 Figure 1: Key frames of a same stroke from TTStroke-21

https://multimediaeval.github.io/editions/2022/tasks/sportsvideo/

https://github.com/ccp-eva/SportTaskME22

Acknowledgment

The authors would like to thank the players, coaches, and annotators who contributed to TTStroke-21.

This research is supported by the New Aquitania Region's CRISP project -ComputeR vIsion for Sports Performance and the MIRES Federation.


est destinée au dépôt


Jean-Baptiste Pavani

Desirée Colombo

Trait Hedonism and the Distribution of Savoring and Positive Emotion States in Everyday Life

Keywords: positive emotions, savoring, hedonism, orientation to happiness, quantile regression, emotion dynamics

  L'archive ouverte pluridisciplinaire

Introduction

Individuals durably differ from each other on their wish to maximize pleasure in their daily lives [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Vanderlande | Understanding positive emotion deficits in depression: From emotion preferences to emotion regulation[END_REF]. These differences in hedonism have received considerable attention, as they are thought to engender between-individuals differences in other important life domains, such as wellbeing and health [START_REF] Martin-Krumm | French adaptation of the Orientation to Happiness scale and its relationship to quality of life in French students[END_REF]Yang et al., 2017). In particular, depending on their level of trait hedonism, individuals have robustly been shown to differ from each other on the intensity of the positive emotions they experience in their daily lives [START_REF] Anić | Orientations to happiness, subjective well-being and life goals[END_REF]Chan, 2013;Yang et al., 2017). Despite these studies examining the trait hedonism-positive emotions relationship, there are many unresolved questions.

First, the strength of the trait hedonism-positive emotions relationship may vary, depending on which part of the distribution of positive emotions is considered. [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF] recently observed this for the extraversion-positive emotion relationship. The intensity of the positive emotions individuals felt during their worst times1 (i.e., times of their lives marked by very weak positive emotions compared with their usual experience of positive emotions) was virtually the same, whatever their level of extraversion. By contrast, the intensity of the positive emotions they felt during their best times (i.e., the times of their lives marked by far more intense positive emotions than usual) differed. More specifically, the most extraverted individuals experienced the greatest intensity. These individuals therefore seem capable of experiencing intense feelings of positive emotions that their more introverted counterparts struggle to achieve. Theoretical arguments led us to assume that there is a similar difference between individuals with different levels of trait hedonism.

Second, little is known about the mechanism linking individuals' levels of trait hedonism to their actual experiences of positive emotions, thus hindering our understanding of the reasons why individuals with greater trait hedonism feel more positive emotions. In particular, although the use of emotion regulation strategies has frequently been shown to mediate the link between personality traits and the experience of one type of emotion or another [START_REF] Kobylińska | The mediational role of emotion regulation in the relationship between personality and subjective well-being[END_REF][START_REF] Vaughan | Exploring emotion regulation as a mediator of the relationship between resilience and distress in cancer[END_REF][START_REF] Wang | Neuroticism, extraversion, emotion regulation, negative affect and positive affect: The mediating roles of reappraisal and suppression[END_REF], to our knowledge no study has examined whether the use of strategies to upregulate positive emotions mediates the link between trait hedonism and positive emotions.

The present study was designed to address both issues. More specifically, by assessing trait hedonism with a traditional self-report questionnaire (i.e., Orientation To Happiness Questionnaire; [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Peterson | Strengths of character, orientations to happiness, and life satisfaction[END_REF], and by repeatedly assessing positive emotions and the savoring emotion regulation strategy over a 32-day period using an experience sampling method [START_REF] Hektner | Experience sampling method: Measuring the quality of everyday life[END_REF], we sought to pinpoint the relationship between trait hedonism and the distribution of positive emotions and savoring in everyday life. We tested the hypothesis of a mediated moderation, whereby the effect on positive emotion intensity of the interaction between trait hedonism and the part of the distribution being considered is mediated by savoring.

Trait Hedonism, Positive Emotions, and Savoring

Trait hedonism is a motivational attribute. It corresponds to the degree to which individuals pursue the goal of maximizing pleasure and minimizing pain [START_REF] Chen | Validating the Orientations to Happiness Scale in a Chinese sample of university students[END_REF][START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF].

Although it is conceptually close to traits related to approach temperament (e.g., extraversion, approach motivation; Quilty et al., 20134), trait hedonism is commonly assessed using the Orientation to Happiness Questionnaire [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Peterson | Strengths of character, orientations to happiness, and life satisfaction[END_REF], with items such as "In choosing what to do, I always take into account whether it will be pleasurable".

Consistent with the idea that valuing a goal increases the likelihood of attaining it [START_REF] Austin | Goal constructs in psychology: Structure, process, and content[END_REF], individuals' level of trait hedonism has robustly been shown to relate positively to their emotional wellbeing (i.e., intense experience of positive emotions and/or nonintense experiences of negative emotions). More specifically, it appears to relate to their experiences of positive emotions rather than their experiences of negative emotions [START_REF] Anić | Orientations to happiness, subjective well-being and life goals[END_REF]Chan, 2013;[START_REF] Vella-Brodrick | Three ways to be happy: Pleasure, engagement, and meaning-Findings from Australian and US samples[END_REF]Yang et al., 2017).

To our knowledge, no study has so far examined the main processes that may mediate the relationship between trait hedonism and the experience of positive emotions, thus hindering an indepth understanding of this relationship. The use of emotion regulation strategies could be one such mediating process, for two main reasons. First, at the theoretical level, emotion regulation strategies are defined as the means through which individuals attempt to attain their emotional goals [START_REF] Gross | Emotion regulation: Current status and future prospects[END_REF][START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF][START_REF] Quoidbach | Positive interventions: An emotion regulation perspective[END_REF]. Second, at the empirical level, the use of such strategies has already been shown to mediate the relationship between personality traits and emotional experiences [START_REF] Kobylińska | The mediational role of emotion regulation in the relationship between personality and subjective well-being[END_REF][START_REF] Vaughan | Exploring emotion regulation as a mediator of the relationship between resilience and distress in cancer[END_REF][START_REF] Wang | Neuroticism, extraversion, emotion regulation, negative affect and positive affect: The mediating roles of reappraisal and suppression[END_REF]. In the present study, we chose to focus specifically on the emotion regulation strategy of savoring (also labelled appreciation by some researchers; [START_REF] Adler | Appreciation: Individual differences in finding value and meaning as a unique predictor of subjective well-being[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF], as recent studies suggest that this is the most effective strategy for upregulating positive emotions [START_REF] Colombo | Savoring the present: The reciprocal influence between positive emotions and positive emotion regulation in everyday life[END_REF][START_REF] Jose | Does savoring increase happiness? A daily diary study[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF].

Savoring consists in focusing on and appreciating those positive aspects of life that one might otherwise overlook or rush through [START_REF] Bryant | Savoring: A New Model of Positive Experience[END_REF][START_REF] Seligman | Positive psychotherapy[END_REF]. Engaging in this emotion regulation strategy requires individuals to focus on the present moment and the immediate experience, and either concentrate on the positive aspects of their environment, or reappraise seemingly neutral events by considering their possible positive features [START_REF] Smash Smash Erisman | A preliminary investigation of the effects of experimentally induced mindfulness on emotional responding to film clips[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF]. Cross-sectional, longitudinal, and experimental studies converge to suggest that engaging in this strategy moderately to strongly increases the intensity of the positive emotions that are experienced [START_REF] Adler | Appreciation: Individual differences in finding value and meaning as a unique predictor of subjective well-being[END_REF][START_REF] Colombo | Savoring the present: The reciprocal influence between positive emotions and positive emotion regulation in everyday life[END_REF][START_REF] Jose | Does savoring increase happiness? A daily diary study[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Seligman | Positive psychotherapy[END_REF]. In addition, the mean tendency to engage in this strategy has been shown to relate positively to some personality traits that, like trait hedonism, are implicated in the value assigned to positive emotional experiences (e.g., extraversion and emotional stability; [START_REF] Fagley | Appreciation uniquely predicts life satisfaction above demographics, the Big 5 personality factors, and gratitude[END_REF]. Nevertheless, as detailed below, restricting our attention to individuals' mean tendency to engage in savoring has potential limitations. More specifically, depending on the part of the distribution of an individual's savoring behaviors (e.g., first vs. tenth decile) that is considered, trait hedonism may relate differently to savoring. This reasoning may also apply to the experience of positive emotions, for the reasons set out below.

Trait Hedonism and the Distribution of Positive Emotions and Savoring Behaviors

When a state variable (e.g., positive emotion intensity) is repeatedly assessed over time (e.g., several times a day over a 1-month period), the distribution of this variable, from its minimum value to its maximum value through all the quantiles, can be computed for each individual. These withinindividual distributions can sometimes be subject to very complex between-individuals differences [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF][START_REF] Koenker | Regression quantiles[END_REF][START_REF] Lee | Are value-behavior relations stronger than previously thought? It depends on value importance[END_REF]. For instance, two individuals can have the same minimum value of positive emotion intensity (e.g., 5/100), the same median value of positive emotion intensity (e.g., 55/100), but very different maximum values of positive emotion intensity (e.g., 70/100 for one individual and 90/100 for the other).

In addition, depending on which part of the distribution is considered, the relationship between the state variable of interest (e.g., positive emotion intensity) and another variable can vary considerably [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF][START_REF] Lee | Are value-behavior relations stronger than previously thought? It depends on value importance[END_REF]. This observation inspired the development of so-called quantile regression techniques [START_REF] Koenker | Regression quantiles[END_REF]. To give but one example, when [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF] examined between-individual differences on the fifth centile of individuals' distribution of positive emotion states, the relationship they found between positive emotion intensity and extraversion was negligible and nonsignificant. However, this relationship became stronger and significant when they examined between-individual differences on the 95 th centile. In other words, individuals experienced the same low levels of positive emotions during their worst times regardless of their level of extraversion. By contrast, during their best times, extraverted individuals 2 felt more intense positive emotions than their more introverted peers.

In the present study, we supposed that the relationship between trait hedonism and the distribution of positive emotion states and savoring behaviors would follow the same pattern as the extraversion-positive emotions relationship found by [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF]. Our hypotheses were mainly inspired by theoretical arguments, based on the two main forces that drive emotion and emotion regulation dynamics according to [START_REF] Kuppens | Emotion dynamics[END_REF]see also Garland & Fredrickson, 2010;[START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF].

The first force can be described as regulatory. It is the force that brings individuals' emotional states closer to their emotional goals, partly through the emotion regulation strategies that individuals use to attain these goals [START_REF] Kuppens | Emotion dynamics[END_REF]. In other words, individuals who have different emotional goals are also likely to differ in their actual emotional experiences and emotion regulation behaviors. For instance, individuals who value intense experiences of positive emotions more than others do are supposed to generally feel more intense positive emotions, and generally make more intense use of strategies (e.g., savoring) to upregulate their positive emotions.

As between-individual differences in emotional goals are known to be relatively stable over time (e.g., [START_REF] Martin-Krumm | French adaptation of the Orientation to Happiness scale and its relationship to quality of life in French students[END_REF][START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Peterson | Strengths of character, orientations to happiness, and life satisfaction[END_REF], those individuals who value intense positive emotional experiences more than others are likely to report more intense positive emotion feelings and greater use of savoring regardless of whether they are having a bad time or a good time. By definition, individuals with high levels of trait hedonism value intense positive emotion experiences more than individuals with low levels of trait hedonism do. Therefore, the regulatory 2 Between-individual differences in extraversion cannot be reduced to the introverted versus extroverted distinction. Rather, they are distributed along a continuum running from a high level of introversion to a high level of extraversion. We nevertheless used this distinction for clarity's sake. We did the same for trait hedonism, referring to individuals with high or low levels, even though they actually differ from one another along a continuum of trait hedonism.

force should lead them to display more intense positive emotions and greater savoring behaviors than individuals with low levels of trait hedonism, regardless of which part of the distribution is considered.

The second force can be described as self-perpetuating, in line with Garland and Fredrickson (2010; see also [START_REF] Kuppens | Emotion dynamics[END_REF], who label this force inertia). It refers to the tendency of an individual's emotions and behaviors (e.g., use of emotion regulation strategies) to mutually reinforce each other over time, leading both to upward spirals (i.e., an emotional state and a behavior mutually increasing each other) and downward spirals (i.e., the lack of this emotion and the lack of this behavior mutually reinforcing their absence). The strength of this force has been shown to differ between individuals [START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF], leading some to display more variable emotional states and emotion regulation behaviors than others [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF]. Compared with an individual who is less prone to them, an individual who is more prone to the abovementioned upward and downward spirals will, by definition, experience both lower (during bad times) and higher (during good times) levels of the relevant emotion or emotion regulation behavior. To the best of our knowledge, no study has so far examined how mutual relationships between positive emotions and savoring differ between individuals according to their level of trait hedonism. Nevertheless, studies of personality traits that assign value to pleasant experiences (e.g., extraversion, behavioral activation system), albeit less directly than trait hedonism, have already been conducted, and all suggest that the higher the level of such traits, the stronger an individual's self-perpetuating force with regard to positive emotions and positive emotion regulation behaviors [START_REF] Fulford | Pushing and coasting in dynamic goal pursuit: Coasting is attenuated in bipolar disorder[END_REF][START_REF] Hirsh | Positive mood effects on delay discounting[END_REF][START_REF] Johnson | The behavioral activation system and mania[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF].

By simultaneously considering these two forces, we were able to propose the following expectations. During individuals' worst times (e.g., first decile of their distributions of positive emotions and savoring), the regulatory force would, as mentioned above, lead individuals with high levels of trait hedonism to display more intense positive emotions and more savoring behaviors than their peers with lower levels of trait hedonism. However, their heightened sensitivity to the selfperpetuating force, and the greater downward spirals, would lead them to display less intense positive emotions and fewer savoring behaviors. Therefore, during these bad times, the two forces would cancel each other out, leading to few differences between individuals according to their level of trait hedonism. By contrast, during individuals' best times (i.e., highest deciles of the distributions of positive emotions and savoring), the effects of the regulatory and self-perpetuating forces would go in the same direction. Once again, the regulatory force would lead individuals with a high level of trait hedonism to experience more intense positive emotions than peers with a low level of this trait. Furthermore, their heightened sensitivity to the self-perpetuating force, and the accompanying upward spirals, would produce the same effect, heightening the difference between individuals with high versus low levels of trait hedonism.

The Present Study

The present study was designed to deepen current understanding of the relationship between trait hedonism and positive emotion experiences. To this end, we examined (1) whether this relationship is moderated by the part of the distribution (i.e., centile) of the state variable being considered, and (2) whether the effect on the intensity of positive emotion of the interaction between trait hedonism and the centile being considered is mediated by savoring. To capture each individual's distribution of savoring behaviors and positive emotion experiences, we implemented an experience sampling method [START_REF] Hektner | Experience sampling method: Measuring the quality of everyday life[END_REF]) over a 32-day period. By contrast, trait hedonism was assessed using a standard self-report questionnaire.

Based on the arguments reported above, we formulated three hypotheses. First, we predicted that the relationship between individuals' level of trait hedonism and the intensity of their experiences of positive emotions would be moderated by the centile of the distribution of their positive emotions, such that the higher the centile, the stronger the relationship between trait hedonism and positive emotion intensity (Hypothesis 1). Second, the relationship between individuals' level of trait hedonism and the intensity of their engagement in savoring would be moderated by the centile of the distribution of savoring, such that the higher the centile, the stronger the positive relationship between trait hedonism and savoring (Hypothesis 2). Third, the interaction effect of trait hedonism and the centile considered for positive emotions would be mediated by savoring (Hypothesis 3).

Method Participants

A total of 84 French adults (79% female, 21% male) aged 19-63 years (M = 33.81, SD = 12.55) took part in the study on a voluntary basis. Their education levels varied widely (i.e., 4% had no diploma, 5% had a vocational high-school diploma, 15% had a general high-school diploma, 46% had completed 2 or 3 years of higher education, and 30% had completed more than 3 years of higher education). The study was introduced to potential participants as a scientific inquiry into emotions in everyday life. Experimenters recruited participants via their own social media, and by posting advertisements on social media pages devoted to emotions, wellbeing, and personal growth.

Participants had to be aged at least 18 years, and not to have any disorder that might impact their emotion regulation (e.g., major depressive disorder, generalized anxiety disorder, autism spectrum disorder). The present study's sample size may appear to be small, however it was decided on the basis of a statistical power analysis. As the main analyses performed in this study were linear mixed-effects models, we computed power analysis using the R package simr [START_REF] Green | simr: an R package for power analysis of generalised linear mixed models by simulation[END_REF]. Moreover, as the present study's data analytic strategy was innovative, the parameters on which it was based were computed on data collected from our first 20 participants. Simulations performed with simr suggested that, for our effect of interest that required the strongest power to be statistically significant at the p < 0.05 threshold, 80% of power was reached with n = 80.

Procedure

The present study was conducted in accordance with the 1964 Declaration of Helsinki and its later amendments, and the 2016 APA Ethical Principles of Psychologists and Code of Conduct.

Written informed consent was obtained from each participant.

The procedure comprised two phases. In the first phase, participants were asked to complete a questionnaire battery that included a sociodemographic questionnaire about their sex, age and education level, a questionnaire assessing trait hedonism, and a more original questionnaire. This original questionnaire was intended to control for the considerable differences between individuals on emotion labeling, as done in previous studies [START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF]. It was motivated by the ideas advanced by Nesselroade and Molenaar (2017), about the importance of tailoring a construct to each individual, all the while leading all the individuals to assign the same core meaning to that construct. More specifically, for each positive emotion-related item, as well as the savoring item we wanted to include in the brief questionnaire of the second phase (see below), participants were each given three wording options, and asked to choose the wording they felt best described the item. These choices were stored and subsequently used to create the individualized brief questionnaire that each participant would subsequently be invited to complete in the second phase.

In the second phase, participants were submitted to an experience-sampling method. To cover a sufficiently long period, the protocol lasted approximately 1 month (i.e., 32 consecutive days).

During this period, participants received the above-mentioned brief questionnaire twice a day (i.e., at noon and at 7 p.m.). A hyperlink to this questionnaire was sent by SMS or e-mail, according to participants' preferences. In the brief questionnaire, participants were asked to provide information about their immediate emotional feelings, and the intensity with which they had engaged in savoring since the previous assessment point. Participants were asked to respond to this questionnaire within 2 hours of receiving the link (i.e., before 2 p.m. for the first questionnaire of the day, and before 9 p.m. for the second questionnaire of the day), so that the two consecutive daily assessments were neither too close nor too far apart. Participants responded to 4604 of the 5376 brief questionnaires sent (i.e., 86%). At each assessment, participants were asked to indicate the intensity with which they currently felt each of the five types of emotions, on visual analogue scales yielding scores ranging from 0 to 100. A number of previous studies had provided evidence supporting the factorial and criterion validity of the above-mentioned items for assessing positive emotions (e.g., Le [START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF]. On this basis, we computed an indicator of positive emotions by averaging scores on the five items (α = 0.81 at the within-individual level, and 0.93 at the betweenindividual level). Internal consistency at the within-individual level was computed on the items after person mean centering them (N = 4604), whereas internal consistency at the between-individuals level was computed on the items after averaging them across individuals (N = 84).

Materials

Savoring Behaviors. Participants' engagement in savoring was assessed with a single item in the brief experience-sampling questionnaire 3 . The wording options given to participants for 3 Although single items are suboptimal as they prevent the control of measurement errors, they reduce the burden that repeated measurements place on participants. This is the reason why they are frequently used in studies pertaining to emotion regulation strategy implementation in everyday life (e.g., [START_REF] Brans | The regulation of negative and positive affect in daily life[END_REF][START_REF] Brockman | Emotion regulation strategies in daily life: Mindfulness, cognitive reappraisal and emotion suppression[END_REF]Colombo et al., 2021). In the present study, to reduce the risk of this single item being contaminated by major measurement the savoring-related item are contained in an open-access file available at https://osf.io/m5ebj/?view_only=f3330b1ca3434498a262ffc00a2afd02. At each assessment, participants were asked to indicate the intensity with which they had engaged in this behavior on a visual analogue scale yielding scores of 0-100. The criterion validity of the chosen item had been verified in previous research (e.g., [START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF].

Trait Hedonism. Participants' level of trait hedonism was assessed in the initial questionnaire battery with the Orientation to Happiness Questionnaire [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Peterson | Strengths of character, orientations to happiness, and life satisfaction[END_REF]. The French validation of this questionnaire [START_REF] Martin-Krumm | French adaptation of the Orientation to Happiness scale and its relationship to quality of life in French students[END_REF] contains four items assessing trait hedonism. Participants are asked to indicate the degree to which they agree with each item on a 5-point Likert scale ranging from 1 (Very much unlike me) to 5 (Very much like me). Scores on these items were averaged to yield the indicator of trait hedonism used in this study (α = 0.70).

Data Analysis Strategy

Data were analyzed using R, (R Core Team, 2020). The R code used, as well as the data on which our analyses were based, are available at https://osf.io/m5ebj/?view_only=f3330b1ca3434498a262ffc00a2afd02. To take account of the data's hierarchical structure (i.e., several assessments nested within several individuals), all the models reported below were linear mixed-effects models, fitted with maximum likelihood estimation. These models shared two characteristics. First, they all contained one random intercept per participant, to take into consideration the above-mentioned hierarchical nature of the data.

Second, they all contained the same sociodemographic control variables as predictors, namely sex errors, we used one savoring-related item that had already shown evidence of its criterion validity [START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF][START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF].

(dichotomous variable), age (grand-mean-centered numerical variable), and education level (grandmean-centered ordinal variable with the five modalities described above).

A three-step data analysis strategy was applied. The first step was designed to test Hypothesis 1.

More specifically, it tested whether the relationship between trait hedonism and positive emotion intensity depends on the part of the distribution of positive emotions considered, using the quantile regression strategy recently implemented by [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF]. First, a centile variable, reflecting the part of the distribution considered, was created. To this end, scores for positive emotions were assigned a rank for each individual. For example, for an individual having responded to 62 assessments, the time where he or she reported the least intense positive emotions was assigned a score of 1, the penultimate time where he or she reported the least intense positive emotions was assigned a score of 2, and so on until the time where he or she reported the most intense positive emotions which was assigned a score of 62. To convert these ranks into centiles, they were divided by the number of assessments to which the individual responded, and multiplied by 100 (e.g., 62 / 62 * 100 = 100 th centile). Second, a linear mixed-effects model was calculated, using the lmerTest R package [START_REF] Kuznetsova | lmerTest package: Tests in linear mixed effects models[END_REF]. This contained positive emotions score as the outcome, and trait hedonism, centile, and the interaction between these two variables as predictors. Like [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF], to capture possible complex effects, we examined the linear and quadratic effects of centile, by including polynomials of degrees 1 and 2 among the predictors. For clarity's sake, these variables are referred to hereafter as linear centile and nonlinear centile4 .

The second step served to test Hypothesis 2. It tested whether the relationship between trait hedonism and savoring depends on which part of the distribution of savoring is considered, with a strategy identical to that used in the first step. A second linear mixed-effects model was calculated, with savoring as outcome variable. It contained the same predictor variables as the first linear mixed-effects model.

The third step served to test Hypothesis 3. It tested whether the effect of the interaction between trait hedonism and centile on positive emotions was mediated by the effect of the interaction between these two variables on savoring, in a prototypical case of mediated moderation [START_REF] Muller | When moderation is mediated and mediation is moderated[END_REF]. We therefore ran a mediated moderation analysis using the lavaan R package [START_REF] Rosseel | lavaan: An R package for structural equation modeling[END_REF]. In this analysis, the outcome variable was positive emotions, the mediator variable was savoring, the predictor variables were the interaction effect between trait hedonism and linear centile, and the interaction effect between trait hedonism and nonlinear centile.

Results

Descriptive Statistics

Descriptive statistics are set out in Table 1. Trait hedonism was moderately correlated with the mean of individuals' distribution of positive emotion and savoring states. The following analyses examined whether these relationships changed if other parts of the distributions were considered.

(Insert Table 1 about here)

Effect of Trait Hedonism on Positive Emotions Depending on the Centile Considered

Results of the linear mixed-effects model calculated to test Hypotheses 1 and 2 are set out in Table 2. Consistent with our hypothesis, trait hedonism was significantly related to positive emotions (β 5 = 0.24, p < 0.001) and savoring (β = 0.28, p < 0.001). Thus, the higher the individuals' level of trait hedonism, the more intense their positive emotions and engagement in savoring in 5 Row variables were on very different scales (i.e., trait hedonism on a scale of 1-5, positive emotions on a scale of 0-100). To make the relationships easier to grasp, all these variables were standardized (M = 0, SD = 1) in the models reported here.

general during the experience-sampling period. More importantly, linear centile and nonlinear centile significantly moderated the relationship between trait hedonism and positive emotions (β = 0.07 and β = -0.04, ps < 0.001), as well as the relationship between trait hedonism and savoring (β = 0.06 and β = -0.07, ps < 0.001). To make these relationships easier to understand, predictions were made on the basis of the coefficients estimated by the models for a fictitious individual with a low level of trait hedonism and a fictitious individual with a high level of trait hedonism (i.e., one standard deviation below and above the mean). These predictions are depicted in Figure 2.

(Insert Table 2 and Figure 2 about here)

Figure 2a shows that at the points in the experience-sampling period where individuals experienced far less intense positive emotions than usual (i.e., Centiles 0-10) 6 , individuals with low versus high trait hedonism differed very little from each other on the intensity of their positive emotions. Within this part of the distribution, the intensity of the positive emotions felt by individuals with low trait hedonism was approximately equal to 20, while the intensity of the positive emotions felt by individuals with high trait hedonism was approximately equal to 23.

Greater differences between these individuals were observed within the subsequent centiles, continuing to increase up to approximately the 50 th centile, after which they plateaued. Figure 2b shows a similar pattern for savoring.

Put differently, during the times in their daily lives where individuals experienced far less intense positive emotions than usual or engage far less in savoring than usual (e.g., first centiles), a high level of trait hedonism did not appear to prevent individuals from reaching low levels of 6 There were no qualitative differences between the phenomena observed within the first ten centiles and the phenomena observed within the following centiles. We chose to highlight these first centiles solely for clarity's sake, as it allowed us to clearly explain that differences between individuals with low versus high trait hedonism became increasingly small toward the left part of the distribution.

positive emotions or savoring. By contrast, at better times in their daily lives (i.e., when they showed slightly less intense or more intense positive emotions or savoring than usual), a high level of trait hedonism was accompanied by more intense positive emotion experiences and savoring.

Consequently, individuals with high trait hedonism seemed to cross a boundary of positive emotions and savoring that individuals with lower levels of trait hedonism struggled to cross.

Effect of Trait Hedonism on Positive Emotions Depending on the Centile Considered via

Savoring

Results of the multilevel mediated moderation analysis performed to test Hypothesis 3 are set out in Table 3. These results were consistent with our hypothesis. The interaction between trait hedonism and linear centile predicted positive emotion intensity (β = 0.07, p < 0.001). Furthermore, 41% of this relationship was mediated by the effect of the interaction between trait hedonism and linear centile on savoring (β = 0.03, p < 0.001). The interaction between trait hedonism and nonlinear centile also predicted positive emotion intensity (β = -0.04, p < 0.001), and 78% of this relationship was mediated by savoring (β = -0.03, p < 0.001.

(Insert Table 3 about here)

Discussion

Interpretation of Results

Results were consistent with our hypotheses. For a start, the trait hedonism-positive emotions relationship varied according to the part of the distribution of positive emotions considered.

Similarly, the trait hedonism-savoring relationship varied according to the part of the distribution of savoring considered. Interestingly, in both cases, the relationship of interest was negligible for the first centiles of the distribution, and nonlinearly increased across the centiles. In other words, in the worst times (i.e., times in their daily lives where they displayed far less intense positive emotions and savoring behaviors than usual), a higher level of trait hedonism did not appear to prevent participants from experiencing low levels of positive emotions and savoring behaviors. By contrast, in the best times (e.g., when their positive emotion experiences and savoring behaviors were higher than usual), a higher level of trait hedonism was accompanied by more intense levels of these variables. Consequently, in their experience of positive emotions and engagement in savoring, participants with high trait hedonism seemed to be able to attain levels of intensity that participants with lower trait hedonism struggled to attain. Finally, consistent with previous findings suggesting that emotion regulation behaviors can partly mediate the relationship between personality traits and emotional experiences [START_REF] Kobylińska | The mediational role of emotion regulation in the relationship between personality and subjective well-being[END_REF][START_REF] Vaughan | Exploring emotion regulation as a mediator of the relationship between resilience and distress in cancer[END_REF][START_REF] Wang | Neuroticism, extraversion, emotion regulation, negative affect and positive affect: The mediating roles of reappraisal and suppression[END_REF], the above-mentioned effect on positive emotions of the interaction between trait hedonism and the part of the distribution examined was mediated by its effect on savoring.

Until recently (e.g., [START_REF] Pavani | Between-individual differences in baseline wellbeing and emotion regulation strategy use moderate the effect of a self-help cognitive-behavioral intervention for typical adults[END_REF][START_REF] Lee | Are value-behavior relations stronger than previously thought? It depends on value importance[END_REF], the idea that the relationship between two variables can vary, according to the part of the distribution of one of the two variables being considered, has received little attention in psychology research. Thus, to our knowledge, no theory has specifically been developed to attempt to explain this variation. For this reason, the abovementioned results may, at first glance, seem hard to interpret. Nevertheless, these results are consistent with the hypotheses we formulated on the basis of our understanding of trait hedonism, as well as the two forces that mainly drive emotion and emotion regulation dynamics, according to [START_REF] Kuppens | Emotion dynamics[END_REF]see also Garland & Fredrickson, 2010;[START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF].

The first force is goal-driven. By definition, compared with individuals with low trait hedonism, individuals with high trait hedonism wish to feel more intense positive emotions [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Peterson | Strengths of character, orientations to happiness, and life satisfaction[END_REF]. Such emotional goals generally lead them to use more strategies that enable them to attain this goal (e.g., savoring), and consequently experience more intense positive emotions than peers with low levels of trait hedonism. If this force were considered on its own, individuals with different levels of trait hedonism would differ in their use of savoring and their experiences of positive emotions, whichever part of the distribution of these variables was considered.

However, as suggested earlier (e.g., [START_REF] Hirsh | Positive mood effects on delay discounting[END_REF][START_REF] Johnson | The behavioral activation system and mania[END_REF][START_REF] Pavani | A network approach to affect regulation dynamics and personality trait-induced variations: Extraversion and neuroticism moderate reciprocal influences between affect and affect regulation strategies[END_REF], compared with individuals with low trait hedonism, individuals with high trait hedonism may also be more sensitive to the second force identified by [START_REF] Kuppens | Emotion dynamics[END_REF]. This force refers to the tendency to experience self-perpetuating relationships (i.e., downward or upward spirals; Garland & Fredrickson, 2010) between some emotions and behaviors. Heightened sensitivity to this force may lead these individuals to have more variable positive emotions and positive emotion regulation behaviors than their counterparts with lower trait hedonism. In other words, if this second force were considered on its own, individuals with high trait hedonism would display lower levels of positive emotions and savoring behaviors at their worst times than peers with lower levels of trait hedonism, and higher levels of positive emotions and savoring behaviors at their best times.

The present study's findings confirmed predictions about what would happen were the two forces simultaneously considered. During their worst times, the wish to experience more intense positive emotions and the increased probability of experiencing downward spirals of positive emotions would cancel each other out in individuals with high levels of trait hedonism, meaning that they would not differ from individuals with lower levels. By contrast, during more favorable times, their wish to experience more intense positive emotions and their increased probability of experiencing upward spirals of positive emotions would have an additive effect, leading them to differ substantially from individuals with lower levels. This is what we identified in this study.

Implications

Taken together, the above-mentioned results may have both theoretical and practical implications. At a theoretical level, regarding the relationship between personality traits and wellbeing states, the results we obtained encourage the construction of more complex theories than those that are currently available. In particular, although this idea is overlooked in positive psychology research, differences between one individual and another on personality traits (e.g., trait hedonism) may be related to differences between these individuals on some parts, but not all, of the distribution of the relevant variable of interest (e.g., intensity of positive emotions).

At a practical level, it appears that some of the content of wellbeing-enhancing interventions is inspired by the personality traits displayed by the happiest individuals, in that it is designed to encourage individuals to engage in the ways of thinking and acting that are exhibited by these very happy individuals [START_REF] Lyubomirsky | How do simple positive activities increase wellbeing?[END_REF][START_REF] Seligman | Positive psychotherapy[END_REF], including those with the highest levels of trait hedonism (e.g., anticipating and seeking pleasant outcomes; [START_REF] Schueller | Preferences for positive psychology exercises[END_REF].

By so doing, these interventions may enable individuals to reach more intense levels of positive emotions in general, as well as in their best times, although they may not prevent individuals from experiencing very weak levels of positive emotions in their worst times. This should be investigated, and if it is indeed observed, it should be explained to individuals who wish to follow a positive psychology intervention. Providing this information might avoid individuals concluding that any moment of low positive emotion is a sign that the intervention is not effective, and thus quitting an intervention that could otherwise have helped them achieve their emotional goals.

Limitations

A first limitation relates to generalizability. The size of our sample, albeit based on statistical power analyses and comparable to those in previous studies of emotions in everyday life (e.g., [START_REF] Brans | The regulation of negative and positive affect in daily life[END_REF][START_REF] Colombo | Savoring the present: The reciprocal influence between positive emotions and positive emotion regulation in everyday life[END_REF] could be perceived as relatively small. Furthermore, it was mainly made up of female participants. The female majority was not judged to be an urgent problem requiring resolution, as there are currently no theoretical arguments to suggest that our variables of interest display different relationships according to sex. However, further investigations of this issue with more balanced sex ratios would serve to establish the robustness of our findings.

A second limitation concerns the restricted scope of our hypotheses. For instance, although the use of various emotion regulation strategies can mediate the link between personality traits and emotional experiences [START_REF] Kobylińska | The mediational role of emotion regulation in the relationship between personality and subjective well-being[END_REF][START_REF] Vaughan | Exploring emotion regulation as a mediator of the relationship between resilience and distress in cancer[END_REF][START_REF] Wang | Neuroticism, extraversion, emotion regulation, negative affect and positive affect: The mediating roles of reappraisal and suppression[END_REF], we only analyzed savoring. We focused on savoring in this initial study because of its considerable effectiveness in helping individuals to upregulate the intensity of their positive emotions [START_REF] Colombo | Savoring the present: The reciprocal influence between positive emotions and positive emotion regulation in everyday life[END_REF][START_REF] Jose | Does savoring increase happiness? A daily diary study[END_REF], but each individual has many more emotion regulation strategies to upregulate positive emotions [START_REF] Livingstone | Up-regulating positive emotions in everyday life: Strategies, individual differences, and associations with positive emotion and well-being[END_REF][START_REF] Quoidbach | Positive interventions: An emotion regulation perspective[END_REF]. Examining multiple emotion regulation strategies in future studies might therefore allow us to deepen our understanding of the processes that mediate the phenomenon examined in the present study.

Moreover, although nonintense experiences of negative emotions represent an important component of emotional wellbeing, only positive emotions were examined in the present study. This choice was based on previous findings suggesting that trait hedonism is negligibly related to negative emotions [START_REF] Anić | Orientations to happiness, subjective well-being and life goals[END_REF]Chan, 2013;[START_REF] Vella-Brodrick | Three ways to be happy: Pleasure, engagement, and meaning-Findings from Australian and US samples[END_REF]Yang et al., 2017). This negligible relationship is nonetheless surprising, given that trait hedonism is defined as the wish not only to maximize pleasure, but also to minimize pain [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF][START_REF] Peterson | Strengths of character, orientations to happiness, and life satisfaction[END_REF]. Further studies may thus be needed to assess the link between individuals' level of trait hedonism and the whole distribution of their negative emotions in their daily lives, to understand these surprising findings.

The third limitation is our focus on trait hedonism. Hedonism is not the only pathway to wellbeing that individuals can follow. Eudemonic pathways are also available [START_REF] Peterson | Orientations to happiness and life satisfaction: The full life versus the empty life[END_REF]. Importantly, trait hedonism and eudemonism are positively related, with moderate effect sizes (e.g., [START_REF] Anić | Orientations to happiness, subjective well-being and life goals[END_REF]Chan, 2013). Consequently, if it is not controlled for, eudemonism can be a possible confounding variable in findings about hedonism. Studies simultaneously examining trait hedonism and eudemonism should therefore be conducted to determine their respective contributions to the distribution of positive emotion and savoring states in everyday life.

Conclusion

Three main findings emerged in the present study. First, the trait hedonism-positive emotions relationship varied according to the part of the distribution of positive emotions that was considered. More specifically, this relationship was negligible for the first centiles of the distribution, and increased nonlinearly across the centiles. Second, the trait hedonism-savoring relationship also varied as a function of the part of the distribution of savoring that was considered.

The shape of this moderation effect was similar to that observed for the trait hedonism-positive emotions relationship. Third, a mediated moderation effect was identified, whereby the effect on positive emotions of the interaction between trait hedonism and the part of the distribution of the relevant state variable was partly mediated by savoring.

State

  Positive Emotions. Participants' positive emotion experiences were assessed with five items in the brief experience-sampling questionnaire. These items were designed to cover the five types of positive emotions identified in the 12-point circumplex model (Yik et al., 2011), namely, highly activated, activated, neither activated nor deactivated, deactivated, and highly deactivated positive emotions. The wording options given to participants for the five positive emotion-related items are contained in an open-access file available at https://osf.io/m5ebj/?view_only=f3330b1ca3434498a262ffc00a2afd02.

The informal expressions worst times and best times are used here and in other sections for clarity's sake. Although they suggest the existence of distinct categories, the different intensities of the positive emotion states felt by an individual over a period of time are actually distributed along a continuum running from the least intense moment of positive emotions to the most intense moment through all the quantiles. A more rigorous alternative expression would be the higher the centile of positive emotion examined, the stronger its relationship with extraversion.

Formulated with the language used in the lmerTest R package[START_REF] Kuznetsova | lmerTest package: Tests in linear mixed effects models[END_REF], the model was as follows.Positive emotions ~ Trait hedonism * (Linear Centile + Nonlinear centile) + (1 | Participant), where "(1 | Participant)" corresponds to a random intercept per participant.

Conflicts of interest/Competing interests: The authors did not receive support from any organization for the submitted work. In addition, the authors have no relevant financial or nonfinancial interests to disclose. Studies,18(6), 1747-1762. https://doi.org/10.1007/s10902-016-9794-1 Yik, M., Russell, J. A., & Steiger, J. H. (2011). A 12-point circumplex structure of core affect. Emotion, 11, 705-731. https://doi.org/10.1037/a0023980

Journal of Happiness