Petra Pelletier
email: petra.pelletier@gmail.com

Rubal Kanozia
email: rubal.kanozia@cup.edu.in

Ritu Arya
email: ritu.arya@cup.edu.in

Claire Lefort
email: claire.lefort@cnrs.fr

Cécile Mclaughlin
email: cecile.mc-laughlin@unilim.fr

Magali Boespflug
email: magali.boespflug@univ-poitiers.fr

Sophie Alain
email: sophie.alain@unilim.fr

Keywords: COVID-19, SARS-CoV-2 virus, mass media, images, perceptions The coronavirus disease

According to the latest The Global Risks Report (2022) of World Economic Forum, the large-scale coronavirus disease 2019 (COVID-19) threat creates various tensions that might lead to unexpected cascading impacts in various domains. Nevertheless, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, about 120 nm in diameter, remains invisible to people whose cognition, emotions, and healthrelated behaviors are driven primarily by the subjective perception of the virus. Mass media communicating information, symbols, beliefs, and codes of conduct to the population contribute widely to the socially constructed representations of the new SARS-CoV-2 virus. Thus, the aim of the current research is to investigate the impacts of the common COVID-19 mass media image of the "ball with spikes" representing the SARS-CoV-2 virus on older adults particularly vulnerable to the COVID-19 coronavirus disease and fake news dissemination. This research is based on an innovative mixed-methods research design that combines questionnaires (N = 144), semi-structured research interviews, and pictographic measures (N = 26). The primary results demonstrate that individuals' perceptions of and emotional reactions to the invisible SARS-CoV-2 virus are shaped by mass media exposure, as the "ball with spikes" became a familiar symbol of the COVID-19 virus, marked by the symbolism of dangerousness and mystery with a divisive aesthetic. The current research that aims to highlight the role of mass media as the vector of an icon image of the new SARS-CoV-2 virus provides additional elements that may contribute to improved crisis management effectiveness of future pandemic outbreaks.

Health Regulations Emergency Committee of the World Health Organization declared on January 30, 2020 that the COVID-19 outbreak of a new type of coronavirus in China was becoming a public health emergency of international concern, primarily due to extensive human-to-human transmission, while calling for solidarity and cooperation of the global community (World Health Organization, January 30, 2020). During the global COVID-19 pandemic, researchers rapidly pointed out related COVID-19 infodemics and their impacts on individuals' health and general well-being [START_REF] Brennen | Types, sources, and claims of Covid-19 misinformation[END_REF][START_REF] Gao | Mental health problems and social media exposure during COVID-19 outbreak[END_REF][START_REF] Pennycook | Fighting COVID19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]. In particular, negative mass media news has impacted individuals' emotions and overall psychological resilience during the COVID-19 pandemic [START_REF] Giri | A neglected reality of mass media during COVID-19: Effect of pandemic news on individual's positive and negative emotion and psychological resilience[END_REF].

Construction of Collectively Shared Representations of the New COVID-19 Virus

Regardless of the nature of crises, whether natural or man-made, extreme situations are inherent to the human condition. These low-probability and high-impact situations, whatever their origin or their consequences, refer to a temporal breakdown in the course of individuals' existence [START_REF] Pelletier | Crisis of COVID-19: Breakdowns and transformations of humans' trajectories in uncertain times[END_REF]. These extreme situations are commonly followed by a transformative pivot of the reconstruction of the situational meaning and reshuffling of existence that allows individuals to overcome the collective trauma (Pelletier & Drozda-Senkowska, 2019a;[START_REF] Pelletier | From Cosmos to Chaos: The Contribution of Social Sciences to an Analysis of Extreme Situations[END_REF][START_REF] Schippers | For the greater good? The devastating ripple effects of the COVID-19 crisis[END_REF]. Large-scale crises, such as the COVID-19 pandemic, oblige people and societies to deploy adaptive coping mechanisms [START_REF] Silver | Surviving the trauma of COVID-19[END_REF]. Thus, during the COVID-19 crisis, the population has tried to cope with this extraordinary situation by reconstructing its meaning (de Jong, Ziegler, & Schippers, 2020), allowing people to cope with and overcome the destabilizing circumstances of the sanitary crisis (Eisenbeck, Carreno, & Pérez-Escobar, 2021).

In facing the new severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus characterized above all by its invisibility, the representations of populations fall within the register of subjectivity underpinned by complex factors of the social construction of reality [START_REF] Berger | The social construction of reality[END_REF]. Thus, various representations, projections, and imaginations built by emotional, cognitive, and social processes contribute to the elaboration of a collectively shared representation of the new virus and the meaning of the COVID-19 crisis. In particular, the mass media has an important role in the social construction of reality during extreme societal situations. The seminal research of Moscovici (1961Moscovici ( /1976) pointed out that mass media diffusion refers to a particular communication system transmitting a message that represents common knowledge intended to be shared. Thus, the mass media constitutes a fundamental mediator between new and external objects, such as the new SARS-CoV-2 virus and the general public, consequently determining laypeople's emotions, cognition, and health-related behaviors during the COVID-19 pandemic.

In line with the postulation of [START_REF] Herman | Manufacturing consent: The political economy of the mass media[END_REF][START_REF] Herman | Manufacturing consent: The political economy of the mass media[END_REF], the mass media serves as a system for communicating information, various symbols, consensual beliefs, and codes of conduct to the population. Indeed, the mass media remains one of the most important vectors of the social construction of reality and, therefore, the construction of meaning that people have of actual societal threats, together with political, institutional, and interpersonal communications [START_REF] Orfali | La société face aux événements extraordinaires: Entre fascination et crainte[END_REF]Pelletier & Drozda-Senkowska, 2019b). Mass media information diffusion, which is above all factual, contributes to the construction of an "imaginary social world" (Rouquette, 1998, p. 93) and, therefore, cannot be apprehended without its relationship to ideology. By extension, mass media communication cannot be understood without its relationship to political power [START_REF] Wandhoefer | Politician2. 0 on Facebook: Information behavior and dissemination on social networking sites-gaps and best-practice. Evaluation results of a novel eParticipation toolbox to let politicians engage with citizens online[END_REF] because it irrevocably carries political and institutional influences and interests. Thus, the mainstream mass media is a powerful instrument that spreads societal interests, efficiently amplified by the Internet and various social media platforms. In particular, [START_REF] Lim | #mytweet via instagram: Exploring user behaviour across multiple social networks[END_REF] found that online users use social networks for personal and professional reasons. Furthermore, they observed that YouTube and Instagram act as source networks where users post to a sink network commonly found to be Twitter.

Mass Media as a Tool for Manufacturing Collectively Shared Representations

In particular, the mass media-generated images of the world in laypeople's cognition allow for constructing representations of major societal issues marked by uncertainty and novelty. These mass media images are of remarkable ingenuity primarily due to the invisibility of social construction processes [START_REF] Gamson | Media images and the social construction of reality[END_REF]. These images can take various forms, such as visual imagery, language, and sounds, and contain layers of meaning. Indeed, the mass media image of the invisible virus SARS-CoV-2 diffused by the mass media worldwide depicted as a "ball with spikes" offers clear visual information to the population. In particular, this generic mass media image of the "ball with spikes" offers a visual icon that embodies the very idea of a virus and therefore represents a common, intelligible, and familiar symbol of COVID-19 [START_REF] Pelletier | An optical visualization of free virions for revealing the first public enemy[END_REF]. Visuals in the form of images, pictures, photographs, and videos have been used in news and mass media for easy comprehension of and attraction to a news story or message. They are also used as powerful symbols that can develop or change people's interpretation of events and messages. Indeed, people understand, retain, and retrieve visuals more easily than text [START_REF] Bucher | The relevance of attention for selecting news content. An eye-tracking study on attention patterns in the reception of print and online media[END_REF] due to their vivid nature and greater occupancy of the mind than textual information. Hence, visuals impact a person's emotions, ideas, impressions, judgments, and even behaviors more than texts [START_REF] Gibson | Reading between the photographs: The influence of incidental pictorial information on issue perception[END_REF]. The mass media mainly used the picture of a "ball with spikes" since the start of the pandemic. Specifically, the Centers for Disease Control and Prevention (CDC) developed the famous red and gray "ball with spikes" image for the virus [START_REF] Li | Visual representations of SARS-CoV-2, emotions, and risk perception of COVID-19[END_REF]. This image became so popular that it could be regarded as one of the most important icons symbolizing the virus and the COVID-19 pandemic in general. Indeed, this inexact representation corresponds to a scientific reality of another type of virus: the capsid with proteins stuck inside, playing the role of a "key" to open the cells to be infected. In particular, this image has been revealed recently under an electron microscope on cryogenized slices [START_REF] Ke | Structures and distributions of SARS-CoV-2 spike proteins on intact virions[END_REF]. The scientific explanation behind the spikes was that they represented the virus' tools to attach to other cells, but these scientific explanations were missing in mass media platforms.

Furthermore, the meaning and context of the virus's actual existence and extremely contagious and harmful nature were lost due to the "beautiful and colorful" pictorial representation of the SARS-CoV-2 virus [START_REF] Sonnevend | A virus as an icon: The 2020 pandemic in images[END_REF]. The "ball with spikes" image has appeared in varying sizes, colors, and patterns across different media outlets as the primary representation of how the COVID-19 virus looked, although it was not the case in reality. This image was disseminated by news media as well as other media platforms. The widespread circulation and presence of the image across all the media platforms, coupled with the misleading or lacking explanation of the scientific structure of the virus, misled people to believe and embed in their minds the "ball with spikes" image as the accurate representation of the SARS-CoV-2 virus. As a result, throughout the pandemic and even today, people think about the virus as the mass media depicted representation without knowing how it truly appears under microscopy [START_REF] Pelletier | An optical visualization of free virions for revealing the first public enemy[END_REF].

Theory of Visual Framing in Mass Media

The theory of visual framing sheds light on how the media frames messages with the help of visuals.

Framing is an important concept in the mass media to understand how a message is constructed, and meaning is derived through its context [START_REF] Bock | Theorising visual framing: Contingency, materiality and ideology[END_REF]. [START_REF] Goffman | Frame analysis: An essay on the organization of experience[END_REF] first elaborated on the framing concept and argued that the construction and context of messages impact the subsequent thoughts and behaviors of the audience about these messages. Similarly, visual framing uses visuals in the message construction that are considered powerful since they are less intrusive and require less cognitive load than text. [START_REF] Rodriguez | The levels of visual framing[END_REF] analyzed how visuals can be used as denotative systems, stylistic-semiotic systems, connotative systems, and ideological representations.

According to [START_REF] Wischmann | Dying on the front page: Kent State and the Pulitzer Prize[END_REF], visuals are good framing tools to haze over issues while overwhelming the truth or facts. In the context of the COVID-19 pandemic, almost all news or messages have been framed using the "ball with spikes" image. The image has most often been used to cover anything related to pathogens. Indeed, it might have been used to instill fear among the audience about the virus. [START_REF] Li | Visual representations of SARS-CoV-2, emotions, and risk perception of COVID-19[END_REF] analyzed the impact of the representational images of SARS-CoV-2 on the emotions and risk perception of viewers and found that the images elicited different levels of fear and disgust. However, no association with risk perception was observed. Thus, these authors suggested being careful about using the representational images of the COVID-19 virus or other infectious pathogens as they can have potential cognitive and emotional impacts on the audience. Notably, the growth of predominantly visual social media platforms (e.g., YouTube, Instagram, and TikTok) has made online users more susceptible to visual information on such platforms (Marcella-Hood & Marcella, 2022).

Herman and Chomsky's (1988/2010) theory of manufacturing consent explains the impact of mass media on society as an important means of disseminating information, symbols, beliefs, and norms to the public. The mass media is also responsible for giving meaning to these messages, constructing common symbols and beliefs for the public while propagating them widely so that a common consent or commonality is reached among the masses. In particular, [START_REF] Gamson | Media images and the social construction of reality[END_REF] analyzed how media messages or images contribute to the social construction of reality by highlighting three main factors with a major role in its social construction: 1) hegemony, 2) framing, frame transformation, or manipulation by the media, and 3) the fragmentation effect. All these factors contribute to constructing a shared "reality" that is often distorted by society. Indeed, in the context of the COVID-19 pandemic, the common mass media image of the "ball with spikes" representing the SARS-CoV-2 virus tends to be perceived as clear visual information that is easily "targetable" by people and, therefore, less anxiety-eliciting compared to the scientific image of the virus [START_REF] Pelletier | An optical visualization of free virions for revealing the first public enemy[END_REF].

The aim of the current research is to investigate the impact of the mass media image of the "ball with spikes" on older adults' perceptions. We constructed an innovative mixed-methods research design protocol combining questionnaires, semi-structured research interviews, and pictographic measures. Indeed, older adults have been commonly designated by the French and international health authorities as a particularly vulnerable group to the COVID-19 coronavirus disease since the beginning of the pandemic (République Française, 2022). Moreover, older adults are the most affected by social isolation and loneliness in the context of the COVID-19 outbreak, which predicts poor physical and mental health outcomes [START_REF] Wu | Social isolation and loneliness among older adults in the context of COVID-19: A global challenge[END_REF]. While using social networks tends to reduce the negative impact of the COVID-19 pandemic on older adults' global health [START_REF] Rolandi | Loneliness and social engagement in older adults based in Lombardy during the COVID-19 lockdown: The long-term effects of a course on social networking sites use[END_REF], the use of social networks during the COVID-19 lockdowns underpinned the COVID-19 infodemic characterized by broad dissemination of various fake news and misleading images [START_REF] Kanozia | Infodemic during the COVID-19 lockdown in India[END_REF][START_REF] Rocha | The impact of fake news on social media and its influence on health during the COVID-19 pandemic: A systematic review[END_REF]. Recent research has demonstrated that older adults are particularly vulnerable to fake news dissemination in the context of the COVID-19 pandemic [START_REF] Sun | Factors influencing rumour re-spreading in a public health crisis by the middleaged and elderly populations[END_REF], and older adults share fake news seven times more than young adults on social networks [START_REF] Guess | Less than you think: Prevalence and predictors of fake news dissemination on Facebook[END_REF].

Method

The current research protocol, based on a mixed-methods research design combining research questionnaires (N = 144), semi-structured research interviews, and pictographic measures (N = 26), aimed to investigate the specificities and societal impacts of the COVID-19 mass media image of the "ball with spikes." Participants of this study were recruited by snowball sampling focused on an older adult recruitment pool living in the Nouvelle-Aquitaine region of France. Specifically, two sets of research protocols comprised an online questionnaire administered to the participants during the strict COVID-19 pandemic lockdown in France due to the lack of other solutions between February and June 2021. Immediately after the COVID-19 lockdown, an additional investigation was conducted utilizing semi-structured research interviews in July 2021. These semi-structured research interviews with older participants aimed to thoroughly investigate the specificities and impacts of the COVID-19 mass media image of the "ball with spikes" on older adults' perceptions.

Participants

The current mixed-methods research protocol participants were French adults 60 years and older. Indeed, older adults are particularly vulnerable to the COVID-19 coronavirus disease and fake news dissemination. All participants were recruited by random snowball sampling during the COVID-19 pandemic lockdown in France during the first half of 2021 in the French region of Nouvelle-Aquitaine. The participants that completed the online questionnaire were a sample of older adults (N = 144), aged from 60 to 84 years (M = 70.22, SD = 5.63), and the participants that were interviewed during research interviews were a sample of older adults (N = 26), aged from 63 to 86 years (M = 74.05, SD = 6.41), living the region of Nouvelle-Aquitaine in France.

Measures

Online Questionnaire

Mass media impacts on the lay population have been assessed by an online questionnaire during the COVID-19 pandemic lockdown in France, during the first half of 2021. An advertisement has been made on various internet platforms and university websites to invite older participants living in the region of Nouvelle-Aquitaine to complete the questionnaire. The online questionnaire aimed to assess primarily the mass media exposure of the participants. Participants were asked to report the frequency of use of social networks (e.g., Facebook, Twitter, and Instagram) since the beginning of the COVID-19 pandemic, the Likert scale of this item ranged from 1 (I never use social networks) to 5 (I use social networks several times per day). Also, participants were asked for what aim they use social networks: "Since the Coronavirus COVID-19 pandemic, what are you using social media for?" The Likert scale of this item ranged from 1 (The most frequent) to 4 (The less frequent). The participants were 50.00% males and 50.00% females, and their answers to these mass media-related questions were collected and analyzed by the statistical software IBM SPSS Statistics version 26.

Research Interviews

In order to investigate more thoroughly specificities and impacts on laypeople's representations of the COVID-19 mass media image of the "ball with spikes," semi-structured research interviews were conducted by three interviewers, experienced, and trained to conduct research interviews. First, the participants were invited to sign a consent to participate in the research interview and an agreement to record the audio of their interview. The totality of research interviews was based on an interview guide in order to standardize rigorously the research procedure. The research interviews aimed primarily to investigate how participants are spontaneously depicting the COVID-19 virus and what the target mass media image of the "ball with spikes" elicits to them on the basis of free association. All interviews took place individually, face-to-face with an interviewer in a calm individual office, specifically designed for research interviews. First, the interviewer gave a white sheet of paper to the participant and asked the participant to spontaneously draw the COVID-19 virus as he or she think it looks like. Then, the participant was invited to describe thoroughly his or her spontaneously painted image of the COVID-19 virus. Second, the interviewer showed the participant the target mass media image of the "ball with spikes" (cf., Appendix) and asked the participant what representations the current target image spontaneously elicits to him or her? Then, the interviewer asked the participant, the following questions to further elaborate his or her discourse: What do you see? What do you think it is? What do you think about this image? What inspires you with this image? What are your feelings and emotions? What does that make you think of? The totality of interviews was recorded and thoroughly analyzed afterward by the method of semiotic analysis that allows deriving meaning of an object from participants' narratives.

Sociodemographic Data

The final part of the questionnaire and research interviews requested participants to indicate their basic sociodemographic characteristics, namely their age, gender, family situation, postcode of residence, and their usual daily activities.

Power Analysis

The data that support these findings for reproducing statistical analyses are provided on Open Science Framework: https://osf.io/bq2vn/. We conducted a post hoc power analysis with the software G*Power 3 [START_REF] Faul | G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences[END_REF] to retrospectively estimate the statistical power of an observed effect, based on the sample size. A post hoc power analysis for the goodness of fit tests demonstrated that with power (1 -β) set at 0.87, α = 0.05 (two-tailed), and critical χ 2 = 7.82, a sample size of 144 participants allows reaching an effect size of 0.30, which corresponds to a conventional medium size effect of the study results.

Results

The results in percentages reported the mass media exposure of the older participants, such as the frequency of use of social networks by the participants since the beginning of the COVID-19 pandemic (Figure 1) and the primary aim of participants' use of social networks since the beginning of the COVID-19 pandemic (Figure 2), examples of the most frequently spontaneously painted image by 59% of participants, representing the COVID-19 virus as a "ball with spikes" (Figure 3), and the most representative participants' verbatims of the target mass media image representing the COVID-19 virus as a "ball with spikes." It can be observed in Figure 1 that the majority of the participants, 45.10%, never used any social media platforms. The older adults who used social media several times a day constituted 23.60% while 13.20% used it only once a day. Few participants, 10.40%, used social media only once a week, and the least number of older adults, 7.60%, used it several times a week.

Figure 2 shows that there are mainly four aims for the use of social media by older adults since the beginning of the pandemic. It can be observed that the majority of the participants used social media to play online games, followed by work. Comparatively, a smaller number of participants used social media more frequently to search for mass media and information or to discuss with others. Additionally, the Chi-square independence test has been conducted to assess whether the frequency of use of social networks since the beginning of the COVID-19 pandemic and the purpose of use of social networks by the participants were associated. The results demonstrated that the frequency of use and the use of social networks for mass media and information search, χ 2 (12, N = 144) = 8.09, p = 0.778, Cramer's V = 0.137, and for work, χ 2 (12, N = 144) = 19.62, p = 0.075, and Cramer's V = 0.213, were not associated. However, the results demonstrated that the frequency of use of social networks and the use of social networks to discuss with others, χ 2 (12, N = 144) = 20.96, p < 0.05, and Cramer's V = 0.220, and to play online games, χ 2 (12, N = 144) = 34.44, p < 0.001, and Cramer's V = 0.282, were associated.

In the second step of the research protocol, participants were asked to paint their depiction of the COVID-19 virus on a sheet of paper during the research interviews. The most of participants spontaneously depicted the image of the COVID-19 virus as a spike mine, a chestnut bug, as a sphere with prickly protruding contours, which can detach and disperse in the air to attack the humans' respiratory tract. The imagined COVID-19 virus is made up of a fairly mobile central core, which multiplies and increases its dangerousness. This most common representation of a "ball with spikes" for 59% of participants corresponds to the largely diffused mass media image of the COVID-19 virus that highlights the unequivocal dangerousness of the new virus. The examples of the most frequently spontaneously painted image of the COVID-19 virus by the participants are reported in Figure 3. The research protocol was followed by the step where the interviewers showed the participants the target mass media image of the "ball with spikes" (cf., Appendix) and asked participants what they think about the image, as described in Section 4. The target mass media image allows constructing a generic narrative of the virus. It is a well-recognized and familiar image that is rather consistent with spontaneous spherical representations diffused by mass media news channels. However, the target mass media image does not necessarily represent the real shape of the COVID-19 virus, because this inexact representation corresponds to a scientific reality of another type of virus: the capsid with proteins stuck inside, playing the role of a "key" to open the cells to be infected [START_REF] Ke | Structures and distributions of SARS-CoV-2 spike proteins on intact virions[END_REF].

The most representative participants' narratives of the target mass media image of the "ball with spikes," a symbol of the COVID-19 virus, demonstrated that the mass media image corresponds to the participants' general representation of the virus, because the mass media mainly used the picture of a "ball with spikes" since the start of the pandemic:

• "I must have seen it on TV, it's the representation I had of the virus" (Female, 76 years)

• "It reminds me of TV health podcasts, we've seen it in certain diseases, like cancer" (Male, 74 years)

• "It's what they show us in the TV, we see it every day. It is a big hedgehog, except that the hedgehog isn't mean, and there we wouldn't want to have him in his garden, it is a bit of a threat" (Female, 75 years) • "It matches the picture science makes of it" (Male, 78 years)

• "It's the virus I recognize it with its big red spikes" (Female, 72 years)

• "A small circle with small peaks like on TV" (Female, 72 years)

• "A red star with lots of thorns sticking out, like the dandelion flower. It's volatile, we don't catch it" (Male, 71 years) • "It's a virus that you see in the labs. A kind of virus, a bug, our bug" (Female, 84 years) • "It is an international symbol, we know what we are talking about by seeing the image" (Male, 73 years)

Participants' narratives illustrate the fact that the mass media image of the "ball with spikes" elicits the very idea of the dangerousness of the virus due to its warrior symbolism and multidirectional spikes that are harmful to the body and, hence, elicit different emotions and reactions. The dialectic that is specific to pandemics is manifested in participants' narratives by the "war metaphor," and these narratives reflect also humans' primordial primary fears and the symbolism of a war:

• "It's like a missile, it's the bomb that's going to explode, like in the 7th company. it's scary" (Female, 67 years) • "An underwater mine. When you touch it, it explodes" (Male, 71 years)

• "A sea urchin with its spines, I wouldn't put my hand on it" (Male, 78 years)

• "The virus is a bit like a bomb with spikes. He doesn't need guns to kill" (Female, 63 years)

• "It's a soft bullet, much like a jellyfish, that can be deadly" (Male, 65 years)

• "It's a picture of danger, it is sly" (Female, 84 years) However, the aesthetically "vivid and beautiful" representation of the virus as a red and blue "ball with spikes" that creates an "identity" for the COVID-19 virus remains tainted by a divisive aesthetic, ranging from appreciating its beauty to feeling fear, apprehension, or disgust, expressed by the following narratives:

• "It's pretty, I like it. it makes you think of a planet" (Female, 78 years)

• "It's kinda pretty; the colors are nice, it's nice to look at" (Female, 72 years)

• "The less I see of it, the better off I am, it saps my spirits." These red dots are everywhere, it disgusts me.

It's colorful but it's not beautiful" (Male, 80 years) • "I see him aggressive because of the spikes, it's scary" (Female, 79 years) • "It is not handsome, it is mean and vicious, it is not an attractive image" (Female, 63 years)

• "Red is aggressive, midnight blue is the unknown. it disgusts me" (Female, 84 years) Furthermore, participants' narratives express the search for meaning, that is recurrent in crisis situations, related in particular to the biological functioning of the COVID-19 virus, and the modes of action of the virus that remain a mystery for most of the participants:

• "How does it act?" How does it feed? It pumps oxygen…" (Female, 78 years) • " It falls like a chestnut bug" (Female, 71 years)

• "I don't know how it goes about attacking, it has to reach the lungs with the suction cups" (Female, 72 years) • "It enters the body by contact, the spikes play a role in entering the cells" (Male, 73 years) • "It enters through the mouth into the body" (Female, 79 years)

• "With its little spikes, it injects something to infect the cells where it multiplies" (Female, 63 years)

• "It floats in the air, it tries to enter the cells to spread inside and it can kill me" (Male, 65 years)

• "It's a total mystery how it enters the cells" (Female, 84 years)

Discussion

The current research investigated the impacts of the common COVID-19 mass media image of the "ball with spikes" representing the SARS-CoV-2 virus on older adults particularly vulnerable to COVID-19 disease and fake news dissemination. The primary results of the current research demonstrated that mass media images are a powerful vector of the social construction of reality. Indeed, 36.80% of older adults use social networks daily. In our study, most participants used social networks to play online games or for work, while fewer older adults used them to search for information or discuss with others. Furthermore, 59% of the older adults spontaneously depicted the representation of the new SARS-CoV-2 virus as the generic mass media image of the "ball with spikes." Therefore, older adults' imagery of the invisible SARS-CoV-2 virus has been shaped by mass media exposure: the "ball with spikes" that became a familiar symbol of the COVID-19 virus. Furthermore, the image elicited different emotions in older adults, marked by the symbolism of deadliness, mystery, and disgust, with a divisive aesthetic.

The main results of this research showed that 36.80% of the older participants used social media at least once daily for different reasons, mostly playing games and working. The COVID-19 pandemic was accompanied by several lockdowns and, consequently, work from home across countries. This situation might have resulted in increased usage of social networks for work. Inside their homes, people also had more free time to indulge in indoor activities like playing online games. Furthermore, people used social networks to access information related to the pandemic and discuss with others because the lockdowns forced them to remain indoors, so they used online means to acquire information and communicate. During the COVID-19 pandemic, people accessed information about the virus and the disease through several media platforms.

At the start of the pandemic, the CDC created the famous red and gray "ball with spikes" pictorial representation of the virus [START_REF] Giaimo | The spiky blob seen around the world: How the CDC medical illustrators created the coronavirus pandemic's most iconic image[END_REF] depicted by the mass media and popular science broadcasts, such as the broadcast about the origin of COVID-19 virus primarily diffused by the international TV channel TV5 Monde (2021, June 9). Major mass media outlets used this image along with many other similar images. Considering the first factor, hegemony [START_REF] Gamson | Media images and the social construction of reality[END_REF], it could be understood that the powerful and big media houses have more resources, money, and power at their disposal to investigate the latest news or information. The first filter of the propaganda model within [START_REF] Herman | Manufacturing consent: The political economy of the mass media[END_REF][START_REF] Herman | Manufacturing consent: The political economy of the mass media[END_REF]) manufacturing of consent explains that due to this concentration of power and resources among a handful of big media organizations, smaller organizations have become dependent on them for the latest news, leading to a lack of news heterogeneity. This concentration led to all online media outlets and social media platforms, even those disseminating mis/disinformation about the pandemic, using the "ball with spikes" image as a representation of the COVID-19 virus. This constant representation since 2019 has made it one of the most identifiable icons defining the pandemic, leading to the cultivation of this mediated representation of the virus in peoples' minds as posited by [START_REF] Gerbner | Cultivation analysis: An overview[END_REF] cultivation theory that found that messages or images transmitted by media heavily influence people's perceptions of the real world.

In this present research, most (59%) of the participants depicted the image of the COVID-19 virus as a bug or mine having protrusions that detach and disperse in mid-air, thereby multiplying to harm humans. The depicted image was similar to the representational image of the mass media for the virus. Hence, it is clear that the mass media profoundly impacted older adults' perception and depiction of the COVID-19 virus. The results of this present study showed that older adults perceived the "ball with spikes" image as a symbol of war, like an explosive mine, missile, or bomb, due to multidirectional spikes that are harmful to the body and, hence, elicit various emotions and reactions, such as fear, mystery, apprehension, and disgust. However, given its divisive aesthetic, some people liked the image for its aesthetic beauty, as Sonnevend (2020) argued. The aesthetically "vivid and beautiful" representation of the virus as a red and gray "ball with spikes" was designed by the CDC, where two medical illustrators were tasked to create an "identity" for the virus [START_REF] Giaimo | The spiky blob seen around the world: How the CDC medical illustrators created the coronavirus pandemic's most iconic image[END_REF]. Thus, instead of instilling fear and wariness about the virus and disease among the public, this image possibly incited a different approach due to the seemingly harmless and attractive representation, thereby thwarting the application of public health policies and other healthrelated behaviors.

While we may not clearly define the boundary between threatening and reassuring responses concerning the "ball with spikes," we may conclude that the mass media images continuing to exist in laypeople's heads elicit specific emotions while thinking about the COVID-19 pandemic or similar future pandemics. The mass media images allow laypeople to be continuously aware of the current developments of the crisis while the mass media warns of possible consequences for their health. [START_REF] Weldon | An" urban legend" of global proportion: An analysis of nonfiction accounts of the Ebola virus[END_REF], in her study on the media representation of the Ebola virus as an urban legend, observed that media representations of any disease can impact the quality of reporting and the diagnosis and treatment of the disease. The misrepresentation of the virus can also lead to poor adherence to appropriate health behaviors among health workers and the public. Therefore, the targeted mass media image is saturated with feelings of pessimism, uncertainty, fear, anxiety, and threat. Indeed, these negative emotions may have a detrimental effect on people's mental health and well-being, contributing to lowering an individual's resilience during the COVID-19 crisis. Hence, people must be shown real images of the virus to relate to the crisis more and understand the seriousness of the situation during the pandemic when many might not have followed the rules and guidelines for COVID-19 appropriate health-related behaviors. Although the image of the virus in the mass media presents a synthesis of scientific reality, it is not an image resulting from an accurate scientific recording because, at present, there is no scientific tool capable of providing this level of detail to the image, whatever the method.

For further consideration, the role of the scientific image of these free viral particles named "virions" on the population's trust in the scientific community, including scientists and medical doctors, should be tested. Therefore, a specific experimental protocol of nonlinear optics with multiphoton microscopy assisted numerically should be established through the mathematical estimation of the instrumental response function [START_REF] Lefort | FAMOUS: A fast instrumental and computational pipeline for multiphoton microscopy applied to 3D imaging of muscle ultrastructure[END_REF]. The images resulting from such an innovative protocol must then be confronted with images delivered with the electron microscope. Moreover, conducting research in pandemic contexts that constitute a risk of human-to-human transmission remains complex. In particular, an online questionnaire appears as a hardly reachable research tool for older adults which caused the relatively small sample size. Also, future qualitative investigations of older adults' social network use should be conducted to avoid bias related to self-reported measures. However, the mixed methods research design of the current study, and research interviews in particular, allows increasing the ecological validity of applied research [START_REF] Flick | Triangulation revisited: Strategy of validation or alternative?[END_REF][START_REF] Flick | Triangulation in data collection[END_REF], conducted in complex societal contexts, such as the COVID-19 pandemic lockdowns. Additionally, future research should strive for replication and extension of the current study with other age groups, and large-scale cross-country research projects should be conducted.

Future research should investigate why the mass media did not provide a real explanation of the "ball with spikes" image, as the image was circulated even by public health authorities without a scientific explanation. Perhaps, miscommunication, a lack of communication between the media, health authorities, and scientists, or negligence by mass media actors and public health officials were reasons behind the public's misleading belief about the virus's accurate representation.

Additionally, future research should deepen the understanding of the precise nature of the individual and collective processes contributing to the social construction of reality during critical collective upheavals, such as the COVID-19 global pandemic. The current interdisciplinary and multimethodological analysis, which aims to shed light on the different aspects of mass media influences during the COVID-19 sanitary pandemic, can attract scientific interest and the current research bears useful elements for crisis decision-making by public authorities and institutions. Indeed, a better understanding of the specificities of the mass media influences during the health pandemic situation would provide concrete elements for a better consideration of human aspects in managing current and future health crises similar to the COVID-19 pandemic.

Conclusion

In-depth knowledge, understanding, care, and caution are required when making such visual representations that can immensely impact people's emotions, attitudes, and behaviors during global crises of any sort. Therefore, in times of health crisis, experts from health sciences, psychology, crisis communication, and mass media must work hand in hand to aware the public about the problem. Thus, developing critical public thinking represents one of the best challenges for crisis management effectiveness of future global pandemic outbreaks. Furthermore, in pandemic situations, production and diffusion of real scientific images of the virus are essential to build public trust in the scientific discourse and to enable the public to identify the risk as a reality. These images, used in collaboration with mass media and public policy experts, will be essential for the information and awareness of the general population during major pandemics.

Figure 1 :

 1 Figure 1: Frequency of use of social networks since the beginning of the COVID-19 pandemic.

Figure 2 :(Figure 3 :

 23 Figure 2: Primary aim of participants' use of social networks since the beginning of the COVID-19 pandemic.

COVID-19 in Mass Media  3

 Petra Pelletier et al.

COVID-19 in Mass Media  11

COVID-19 in Mass Media  15

Acknowledgements: We would like to thank Aurore Marcellaud and Virginie Magadoux for conducting and analyzing research interviews of the current study. Funding information: This research was conducted as a part of the interdisciplinary research program CoviZion "Storytelling of a Virus: Representations, Images and Imaginations. Represent and Understand in Order to Act Better and Live with it," funded by AMI FLASH Research and Innovations COVID of Nouvelle-Aquitaine, France.

Data availability statement: The data that support these findings for reproducing statistical analyses are provided on Open Science Framework: https://osf.io/bq2vn/.

Conflict of interest:

The authors state no conflict of interest.

Appendix

The targeted mass media image presented to the participants semi-structured research interviews was downloaded from the official website of the government of Québec, Canada. In particular, this image has been used to illustrate COVID-19 information, entitled "Science in the Fight Against COVID-19: Stay Well Informed," related to the diffusion of research projects conducted on the COVID-19 pandemic and official COVID-19 information websites: https://www.scientifique-en-chef.gouv.qc.ca/impacts/covid-19/.


R Mattéoli

J P Dalmont

S Maugeais

S Terrien

C Vergez
email: vergez@lma.cnrs-mrs.fr.

ONE PEDAL NOTE CAN HIDE ANOTHER

Keywords: pedal note, ghost note, brass musical instrument, bifurcation diagram

. We show here that using advanced numerical methods for nonlinear dynamical systems allows us to finally demonstrate that standard models of sound production in brass instruments explain the emergence of pedal notes. This analysis also explains why pedal notes are played preferably at fortissimo level rather than pianissimo. Finally, we show how most recent studies have revealed, for certain brass instrument geometries like the tuba family, the existence of so-called ghost notes lying between the pedal note and the second register.

INTRODUCTION

"Take a tenor trombone, substitute its usual mouthpiece with a tenor saxophone mouthpiece, the adaptation isn't perfect but it's good enough (...) And surprise, the lowest note obtained, in the first position, will be the D, i.e. the D0 pedal 1 below the usual B♭ pedal, so beware : one pedal can hide another."

The paragraph above is translated from the very first paper of Joël Gilbert in a journal for trombone players [START_REF] Gilbert | Une note pédale peut en cacher une autre[END_REF]. At that time, he has just completed his internship after his master degree in acoustics, and is not even a PhD student. This highlights that trying to shed light on the question of the pedal note produced by brass instruments was one of his scientific goals from the outset. A goal that will remain with him for the rest of his career. In this article, we outline the milestones in his work on this subject.

A MYSTERIOUS REGIME

The experiment described in the introduction above is mentioned as early as the beginning of the 20 th century by [START_REF] Bouasse | Instruments à Vent. Delagrave[END_REF], who mentions "strange peculiarities in the low register"2 for brass instruments. However Joël Gilbert proposed with Aumond a refined version of this experiment [START_REF] Gilbert | Pedal notes of brass instruments, a mysterious regime of oscillation[END_REF]: the input impedance of each instrument is measured, and the sounding frequencies are quantitatively compared to the resonance frequencies of the impedance peaks. Moreover, the experiment is reproduced numerically by carrying out time domain simulations of ele-mentary physical models of the sound production. This is done either when the trombone is played with a brass mouthpiece (vibrating lips) or with a clarinet mouthpiece (vibrating reed). Even if both experimental and numerical results are conclusive, there is still a long way to go before an explanation for the observed phenomena is proposed. However, the authors already conclude their paper by an intuition -decisive for the next 15 years -that a modal formulation of the models could be the key to a better understanding of the phenomena: "This method could be used to do a numerical morphing from a resonator having a set of harmonic resonances (saxhorn-like resonator) to a set of incomplete harmonic peaks (trombone-like resonator) by slightly moving down the first resonance frequency out of the harmonic series."

THE BEGINNING OF AN EXPLANATION

Significant progress was made when the possible solutions of such a modal model were analyzed with the tools of nonlinear dynamical systems. Indeed, a few years later, [START_REF] Velut | How well can linear stability analysis predict the behaviour of an outward-striking valve brass instrument model?[END_REF] demonstrated that in the case of the trombone, the emergence of a note well above the frequency of the first impedance peak (the pedal note), could be explained by a linear stability analysis (LSA) of the equilibrium solution 3 : "LSA clearly indicates that for low enough acoustic resonance frequencies in the bore input impedance, the frequency of the emerging oscillation is far beyond the resonance frequency of the instrument (...) This result from LSA is quite unexpected: the pedal note of the trombone seems to result from a coupling between the lips and the nearest acoustic mode below the playing frequency, just like for the other oscillation regimes". Thus, higher bore resonances are not necessary to explain the emergence of the pedal note, which is an unexpected result given the speculations made in previous studies [START_REF] Benade | The physics of brasses[END_REF]. However, this approach raises a new mystery when applied to instruments of the saxhorn family, since it suggests the production of a new regime called the "ghost note" (verified experimentally since then), but not the pedal note.

A DEEPER UNDERSTANDING OF PHENOMENA THANKS TO THE BIFURCATION ANALYSIS

The most recent answers to date concerning pedal notes and ghost notes regimes have been proposed in [START_REF] Mattéoli | Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments[END_REF][START_REF] Mattéoli | Diversity of ghost notes in tubas, euphoniums and saxhorns[END_REF].

Bifurcation diagrams of a modal model of brass instrument including the action of the player are computed. To do so, periodic solutions are represented using a collocation approach, and solution branches are computed using a prediction-correction continuation approach [START_REF] Doedel | AUTO 97: Continuation and bifurcation software for ordinary differential equations (with homcont)[END_REF].

It has been found that in the case of the trombone, the pedal note corresponds to a branch of periodic solutions emerging from the equilibrium branch through an inverse Hopf bifurcation (see figure 1). The solutions on the branch close to the equilibrium are unstable, and stable solutions exist only beyond a finite amplitude. This corresponds to the musician's feeling that the pedal note is played more preferably in the forte nuance than in the piano nuance. Moreover, the oscillation frequencies of the accessible stable regimes differ by less than a semitone. As such, it is considered that only one note is accessible to the musician.

The picture is more complex in the case of the saxhorn family (see figure 2 in the case of the B♭ contrabass tuba). Indeed, the branch of periodic solutions emerging from the equilibrium (grey line) is not the pedal note anymore. This is shown in the lower subplot, where the oscillation frequency is higher than the expected frequency of the note B♭0 (29.1 Hz in the tempered scale). This branch corresponds to the ghost note. The pedal note, however, corresponds to the stable part of the lime green line. It can be noted that this branch is not connected to the "principal branch" (namely the branch arising from the Hopf point H1 which marks the loss of stability of the equilibrium). This explains why it was not possible for previous authors using only linear stability analysis to predict a pedal note for this family of instruments, but only the ghost note (for instance [START_REF] Velut | How well can linear stability analysis predict the behaviour of an outward-striking valve brass instrument model?[END_REF]).

As a summary, the bifurcation diagrams are in accordance on many points with the musicians' experience:

• For instruments with a predominantly cylindrical bore profile like the trombone, the pedal note is the only playable note around the expected frequency.

[6]

• The ghost note can be played exclusively on bass brass instruments with a predominantly-expanding bore profile such as tubas, euphoniums or saxhorns.

In that case, it stands between the pedal note -the lowest natural note playable, or first regime -and the instrument's second regime. More precisely, for the different instruments of the saxhorn family, the ratio between the frequency of the recorded pedal note and ghost note has been found in accor- the blowing pressure in the case of a trombone. The line thickness indicates whether the branch portion is stable (thick line) or unstable (thin line). The expected note is B♭1 whose frequency is 58.27 Hz in the tempered scale. Figure from [START_REF] Mattéoli | Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments[END_REF].

dance with the value predicted by the bifurcation diagram [START_REF] Mattéoli | Diversity of ghost notes in tubas, euphoniums and saxhorns[END_REF]. This agreement between the picture displayed by bifurcation diagrams and the experiments is all the more interesting as the physical model used is very simple, with a single degree-of-freedom model for lips.

CONCLUSION

Bifurcation analysis provides a global view of the dynamics of a musical instrument. It appears to be a suitable tool for understanding the production of the pedal note by brass instruments. Top and bottom plots represent respectively the maximum amplitude of the periodic oscillation and their oscillation frequency with respect to the blowing pressure. The line thickness indicates whether the branch portion is stable (thick line) or unstable (thin line). The point H1 corresponds to the Hopf bifurcation point at which a stable oscillation regime arises from the equilibrium. This corresponds to the ghost note. S1 corresponds to the saddle-node bifurcation point at which the stable regime arising from the Hopf point destabilises. S1 ′ corresponds to the saddle-node bifurcation point beyond which periodic solutions become stable again. S1 ′′ corresponds to the saddle-node bifurcation point at which the stable regime of the pedal note arises from the isolated branch (lime green). Figure from [START_REF] Mattéoli | Diversity of ghost notes in tubas, euphoniums and saxhorns[END_REF]. This tool also makes it possible to revisit earlier work and understand why approaches based on time integration or linear stability analysis, although they provided some interesting insights, could only lift one corner of the veil on these "strange peculiarities" mentionned a century ago by Bouasse [START_REF] Bouasse | Instruments à Vent. Delagrave[END_REF].

IN MEMORIAM

In memory of Joël Gilbert (1963[START_REF] Mattéoli | Diversity of ghost notes in tubas, euphoniums and saxhorns[END_REF] and his careerlong efforts to advance this research topic.

Figure 1 .

 1 Figure 1. Typical partial bifurcation diagram for the physical model of a bass trombone around the first Hopf bifurcation. Top and bottom plots represent respectively the maximum amplitude of the periodic solutions branches and their oscillation frequency vs.the blowing pressure in the case of a trombone. The line thickness indicates whether the branch portion is stable (thick line) or unstable (thin line). The expected note is B♭1 whose frequency is 58.27 Hz in the tempered scale. Figure from[START_REF] Mattéoli | Minimal blowing pressure allowing periodic oscillations in a model of bass brass instruments[END_REF].

Figure 2 .

 2 Figure2. Typical partial bifurcation diagram of a B♭ contrabass tuba around the first Hopf bifurcation. Top and bottom plots represent respectively the maximum amplitude of the periodic oscillation and their oscillation frequency with respect to the blowing pressure. The line thickness indicates whether the branch portion is stable (thick line) or unstable (thin line). The point H1 corresponds to the Hopf bifurcation point at which a stable oscillation regime arises from the equilibrium. This corresponds to the ghost note. S1 corresponds to the saddle-node bifurcation point at which the stable regime arising from the Hopf point destabilises. S1 ′ corresponds to the saddle-node bifurcation point beyond which periodic solutions become stable again. S1 ′′ corresponds to the saddle-node bifurcation point at which the stable regime of the pedal note arises from the isolated branch (lime green). Figure from[START_REF] Mattéoli | Diversity of ghost notes in tubas, euphoniums and saxhorns[END_REF].

The pedal note is the lowest note that can be played on a brass instrument.

Original version in french: "les instruments à embouchure de cor présentent d'étranges particularités dans le grave".

i.e. when the player blows into the instrument without any resulting self-sustained oscillation (no sound produced)


Florian Baud Liris
email: florian.baud@visiativ.com

Villeurbanne Visiativ

Alex Aussem
email: alexandre.aussem@liris.cnrs.fr

Non-Parametric Memory Guidance for Multi-Document Summarization

Multi-document summarization (MDS) is a difficult task in Natural Language Processing, aiming to summarize information from several documents. However, the source documents are often insufficient to obtain a qualitative summary. We propose a retriever-guided model combined with non-parametric memory for summary generation. This model retrieves relevant candidates from a database and then generates the summary considering the candidates with a copy mechanism and the source documents. The retriever is implemented with Approximate Nearest Neighbor Search (ANN) to search large databases. Our method is evaluated on the MultiXScience dataset which includes scientific articles. Finally, we discuss our results and possible directions for future work.

Introduction

Multi-document summarization is performed using two methods: extractive [START_REF] Wang | Heterogeneous graph neural networks for extractive document summarization[END_REF][START_REF] Liu | HETFORMER: Heterogeneous transformer with sparse attention for long-text extractive summarization[END_REF] or abstractive [START_REF] Hanqi | Multi-granularity interaction network for extractive and abstractive multi-document summarization[END_REF][START_REF] Xiao | PRIMERA: Pyramid-based masked sentence pre-training for multi-document summarization[END_REF]. So-called extractive methods rank sentences from source documents that best summarize them. These methods reuse important information well to construct a good summary but they lack coherence between sentences. To overcome this issue, abstractive methods are studied to imitate human writing behavior. They show great performance in human writing style but they often miss key information.

To make abstractive models aware of essential information, [START_REF] Dou | GSum: A general framework for guided neural abstractive summarization[END_REF] guides their model with additional information like a set of keywords, graph triples, highlighted sentences of source documents, or retrieved similar summaries. Their method, which uses every guidance previously mentioned, improves summary quality and controllability compared with unguided models. However, guidances require specific training data, especially for keywords, graph triples, and highlighted sentences.

Our proposal is that by guiding with pre-existing summaries, the model can draw inspiration from the summary as a whole. But also be able to extract keywords and phrases using a copy mechanism. Consequently, this work focuses on guidance by similar summaries extracted from a knowledge base using a similarity metric between source documents and pre-existing summaries. The model, inspired by RAG [START_REF] Lewis | Retrieval-augmented generation for knowledge-intensive nlp tasks[END_REF], is fully differentiable. In addition, the model generator uses a copy mechanism on the candidates returned from the knowledge base, inspired by [START_REF] Cai | Neural machine translation with monolingual translation memory[END_REF]. The findings of these two studies motivated the development of our model for the multi-document text summarization task.

We demonstrate the potential of our method on MultiXScience [START_REF] Lu | Multi-XScience: A large-scale dataset for extreme multidocument summarization of scientific articles[END_REF]. This dataset gathers scientific articles where we have to generate the "related work" part with the "abstract" of the source article and the "abstracts" of the citations. In the case of scientific articles, we believe that the source documents are insufficient to generate the "related work" part because external knowledge is necessary to write such a paragraph.

In this work, we investigate a sequence-tosequence model guided by a memory retriever of similar summaries. Specifically, source documents are the input of the memory retriever, which returns the top k similar summaries from a potentially large database using an approximate nearest neighbor search. Then, the decoder generates the summary taking into account the source and retrieved summaries and is trained to identify interesting texts for the targeted summary. The code of our work is available on GitHub1 .

Rebuilt every n steps Source Documents

Query Encoder

Knowledge Base

Memory Encoder

MIPS Retrieved Encoder

Copy Mechanism Summary

Candidates Encoded Database

Memory Encoder

Recomputed Scores

Source Encoder Decoder

Figure 1: In the first step, the knowledge base is built by encoding all documents with the memory encoder. Then the source documents are transformed with a query encoder and with a source encoder, the query encoder is used to search the knowledge base. The encoded source is used to represent the source documents for the generation of the summary. After retrieving the top-k of the search, they are encoded with the retrieved encoder and again with the memory encoder to recalculate the relevance score for back-propagation. Then, the decoder takes as input the source documents and the relevant documents for the generation of the summary.

Our contribution is twofold: firstly, we integrate a retriever to retrieve candidates for the generation of the summary, and secondly, we make use of a copy mechanism to incorporate these candidates into the generation procedure.

Related Work

We start with a brief review of related work. (Cohan et al., 2018) proposes to capture the structure of the document to better represent the information of the source document. Their method is applied to scientific articles from Arvix and Pubmed which are long documents. For the same purpose, (Cohan and Goharian, 2018;[START_REF] Yasunaga | Scisummnet: A large annotated corpus and content-impact models for scientific paper summarization with citation networks[END_REF] propose to generate a summary from the articles that cite the article to be summarised. The disadvantage of these methods is that they cannot be used when writing an article. In this work, we use references and not the papers that cite the documents to be summarised. More recently, [START_REF] Xiao | PRIMERA: Pyramid-based masked sentence pre-training for multi-document summarization[END_REF] proposed a pre-training strategy dedicated to multi-document text summarisation, their masking strategy showed significant improvement for the MDS task. They applied their method to the MultiXScience dataset.

The models using guidances are close to our work, indeed [START_REF] Cao | Retrieve, rerank and rewrite: Soft template based neural summarization[END_REF][START_REF] Dou | GSum: A general framework for guided neural abstractive summarization[END_REF] use retrieved summaries to better control the summary generation. However, they use information retrieval systems such as ElasticSearch to find candidates for summary generation. Also, [START_REF] An | Retrievalsum: A retrieval enhanced framework for abstractive summarization[END_REF] has introduced dense search systems for text summarization, but they do not train the retriever with the summary generator. In our case, the re-triever is dense and trainable to find the most relevant candidates for the generation of the summary.

In addition, retrieval-augmented models share commonalities with our work. RAG, [START_REF] Lewis | Retrieval-augmented generation for knowledge-intensive nlp tasks[END_REF] which introduced this type of model, is used for the question-answering task, where a context is given to answer the question. The model retrieves several contexts with a retriever and then answers the question using each of the retrieved candidates. These types of models are also used in the translation task, where [START_REF] Cai | Neural machine translation with monolingual translation memory[END_REF] translates a sentence with a pre-established translation base. Their model searches this base for translations close to the sentence to be translated and then incorporates them into the generation of the translation through a copy mechanism. This approach shares some similar intuition with our proposed approach because our architecture is based on an augmented retriever that incorporates the memory by means of a copy mechanism. It is interesting to investigate whether the encouraging success of the copy mechanism recently obtained in translation carries over to the MDS task.

Proposed Method

Inspired by [START_REF] Cai | Neural machine translation with monolingual translation memory[END_REF], we propose a model composed of a memory retriever and a copy generator. Figure 1 illustrates our framework, where we start by encoding the entire knowledge base. After an arbitrary number of steps during the training, the encoded knowledge base is updated. Then, the forward pass encodes source documents and finds similar documents. Retrieved documents are encoded and fed to the generator with the source documents.

Our memory retriever has multiple encoders, one for encoding the query, one for the knowledge base, one for the sources documents, and one for the retrieved candidates. Our copy generator is a decoder with a cross-attention mechanism on source document embeddings and a copy mechanism on retrieved candidates, which is placed at the top of the decoder. We begin describing the retriever and then show how our generator works.

Memory Retriever

The retrieval approach consists of source documents as query and documents from a knowledge base denoted respectively by q and c. Documents are often too long to be encoded with a Transformer [START_REF] Vaswani | Attention is all you need[END_REF], so we used a LongFormer [START_REF] Beltagy | Longformer: The long-document transformer[END_REF] model. LongFormer has a Transformer-like architecture that can deal with long input sequences by attending tokens with windowed attention and global attention on a few tokens. We encode source documents and candidates documents with a pretrained LongFormer model separated by a special token ([DOC]) :

h q = LED q enc (q) h m = LED m enc (m)
where the LongFormer encoder is denoted by LED enc . All documents in the knowledge base are encoded and stored in an index. For retrieving candidates, we take the [CLS] token of encoders output that we normalize and we define a relevance function :

h q cls = norm(h q cls ) h m cls = norm(h m cls ) score(x, y) = x ⊤ • y
We then calculate the relevance score on normalized tokens, which represents the cosine similarity between source documents q and candidate documents m that fall in the interval [-1, 1].

For fast retrieval, we retrieve the top-k candidates m topk = (m 1 , . . . , m k ) using the maximum inner product search (MIPS) implemented with FAISS [START_REF] Johnson | Billion-scale similarity search with gpus[END_REF]. At each training step, we calculate the actual embedding of candidates {h m cls,i } k i=1 and compute their relevance scores {s i = score(h m cls,i , h q cls )} k i=1 for back-propagation as in [START_REF] Cai | Neural machine translation with monolingual translation memory[END_REF][START_REF] Lewis | Retrieval-augmented generation for knowledge-intensive nlp tasks[END_REF]. The recalculated score biases the decoder copy mechanism , which we detail in section 3.2.

The memory encoder does not re-encode all the knowledge base at each training step because this would be expensive computation. Instead, the knowledge base and the MIPS index are updated at regular intervals defined arbitrarily. On the other hand, we encode the retrieved top-k candidates and the source documents with two encoders, LED r enc and LED s enc , as shown below:

h s = LED s enc (q) h r topk = LED r enc (m topk )
These two results are forwarded to the copy generator, which we detail in the next section.

Copy Generator

In the generation part of our model, we use the decoder from LongFormer and apply a copy mechanism to previously retrieved candidates. Formally, we have :

h d = LED dec (y, h s )
where LED dec corresponds to the decoder part of the LongFormer model, and y is the targeted summary. The decoder attends over source documents h s and previous tokens y 1:t-1 , producing a hidden state h d t at each time step t. The probability of the next token is calculated with a sof tmax function:

P dec (y t ) = sof tmax(W d • h d t + b d ) (1)
where W d is a hiddens size × vocab size matrix and b d is the bias; both are trainable parameters. Then, we incorporate the top-k candidates m topk with a copy mechanism by calculating a cross attention between h d t and h r topk . To this end, we reuse the cross-attention part of LongFormer to add it after its original decoder. This new layer has only one attention head in order to use the attention weights as the probability to copy a word from top-k candidates.

Given k documents encoded in h r topk , then we can construct a set of token embedding {r i,j } L i j=1 where i ∈ [1, k], j ∈ [1, L i ] and L i is the length of document i. Formally, the attention weight of the jth token in the ith relevant document is expressed as,

α ij = exp(h d⊤ t W a r i,j + βs i ) k i=1 L i j=1 exp(h d⊤ t W a r i,j + βs i ) c t = W c k i=1 L i j=1 α ij r i,j
where α ij is the attention weight of the jth token in the ith relevant document, W a and W c are learnable parameters, c t is a weighted representation of top-k candidates and β is a learnable scalar that controls the relevance score between the retrieved candidates and the decoder hidden state, enabling the gradient flow to the candidates encoders as in [START_REF] Cai | Neural machine translation with monolingual translation memory[END_REF][START_REF] Lewis | Retrieval-augmented generation for knowledge-intensive nlp tasks[END_REF]. Equation 1may be rewritten to include the memory:

P dec (y t ) = sof tmax(W d • (h d t + c t ) + b d ) (2)
Thus the next token probability takes into account the attention weights of the top-k candidates. The final next token probability is given by:

P (y t ) = (1 -λ t )P dec (y t ) + λ t k i=1 L i j=1 α ij 1 r ij =yt
where λ t is a gating scalar computed by a feedforward network λ t = g(h d , c t ). The model is trained with the log-likelihood loss L = -log P (y * ) where y * is the target summary.

Training Details

Our model is composed of several encoders and one decoder based on the LongFormer [START_REF] Beltagy | Longformer: The long-document transformer[END_REF] large model. Therefore, the size of our model attains 1.9B of trainable parameters. Then we used the DeepSpeed [START_REF] Rasley | Deepspeed: System optimizations enable training deep learning models with over 100 billion parameters[END_REF] library for the training. Our model uses the LongFormer pretrained models available on HuggingFace2 .

The training of the model makes use of MultiX-Science data comprising 30,369 scientific articles for training, 5,066 validation, and 5,093 test articles. The objective is to generate the related work using the abstract of the article and the abstracts of the cited articles. This is an interesting dataset to experiment with because writing a related work part requires knowledge beyond the scope of the source documents.

Cold start problem At the beginning of the training, the weights are randomly initialized. Therefore the retriever selects low-quality candidates that don't send out a good signal for training. Under these conditions, the retriever cannot improve, and the model will ignore the retriever's candidates. To overcome this cold start problem, we pre-trained the retriever on the MultiXScience data to improve the quality of the retriever. The objective is to maximize the similarity between the abstract and the related work section. These two sections are encoded with the two encoders of the retriever to calculate the cosine similarity.

In concrete terms, pre-training works as follows. For a batch size equal to N , we have N "abstract" sections encoded with A = {LED q enc (a i )} N i=1 and N "related work" sections encoded with B = {LED m enc (b j )} N j=1 , in order to obtain a cosine similarity equal to 1 when j = i corresponds to positive examples and -1 otherwise for negative examples. We calculate for each element in A, the following errors:

L i (A, B) = -log exp (score(A i , B i )/τ ) N j=1 exp (score(A i , B j )/τ )
where τ is an arbitrarily chosen temperature parameter. The final error is L = N i=1 L i backpropagated in the two encoders of the retriever.

Experiments

In this section, we report on the experiments performed on the MultiXScience dataset to evaluate our model. Training the full model is more difficult due to its size but also due to the cold start problem. The latter corresponds to the fact that the similar summaries retrieved are not sufficiently relevant to help the model. In addition, we have trained two other methods adapted to text summarisation as a comparison, Bart [START_REF] Lewis | BART: denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension[END_REF] and T5 [START_REF] Raffel | Exploring the limits of transfer learning with a unified text-to-text transformer[END_REF]. We detail the training procedure for each of them. All models use the beam search method to generate summaries. We chose a beam size of 4, a length penalty of 1.0, and limited the repetition of tri-grams. The rouge scores [START_REF] Lin | ROUGE: A package for automatic evaluation of summaries[END_REF] The ROUGE score (R-1/R-2/R-L) of our preliminary results on the MultiXScience test dataset. The * symbol means that the results have been borrowed from [START_REF] Xiao | PRIMERA: Pyramid-based masked sentence pre-training for multi-document summarization[END_REF].

Reduced model To reduce the computational burden, we used a reduced model where the knowledge base is not reconstructed. In addition, the memory encoder parameters were frozen in order to reduce the complexity of the training. These two modifications reduced the training time considerably. Indeed, the burden of reconstructing the knowledge base was overwhelming. The reduced model has fewer trainable parameters (1.4B). The model was trained for 12.000 steps on four v100 GPUs with Adam optimizer and a learning rate of 3e -5, a batch size of 64, a top-k of 5 for the retriever, and with 2.000 warmup steps and linear decay. Despite its reduction in size, we observe that the model is competitive with the state of the art.

Bart We fine-tuned a Bart-large model on the MultiXScience dataset using a single v100 GPU over two days. The model weights were updated for 20,000 steps with a learning rate of 3.0e-5. A linear warmup for 2,000 steps was applied to the learning rate. We also limited the norm of the gradient to 0.1. The training aims to minimize cross-entropy with a smoothing label of 0.1. The MultiXScience articles have been concatenated using the '\n\n' separator. The results show that Bart is competitive with the state of the art.

T5

The T5-large model was fine-tuned on the same dataset as before. The training lasted 4 days on a single v100 GPU, this model is slightly larger and was trained in fp32 precision. As T5 is a textto-text model, we have used the prefix 'summarize:' for the input documents, which are separated by the separator '\n\n'. The model was trained for 7,000 steps with a learning rate of 1.0e-4 and a batch size of 64. A linear warm-up of up to 2000 steps and a gradient norm limitation of 0.1 was applied. The error to be minimized is the cross-entropy with a label smoothing of 0.1.

Conclusion and Future Work

This paper presents an architecture for multidocument text summarization inspired by retrievalaugmented models. This architecture includes a retriever that searches a knowledge base to find relevant documents for the generation of a summary. These documents are integrated in the generation by means of a copy mechanism. A reduced version of the model was evaluated on the MultiXScience dataset. The preliminary results are already com-petitive with the state of the art however we expect to improve our results further by: 1) properly fixing the cold start problem, and 2) training the full model. In the future, we also plan to increase the size of the knowledge base with new data and apply our method to other MDS benchmark datasets.

Table 1 :

 1 on the MultiXScience dataset are reported in table 1.

	Method	R-1 R-2 R-L
	Ours	30.6 6.5 17.7
	Bart (Our run)	32.4 7.2 17.3
	T5 (Our run)	29.6 6.3 17.0
	Primera*	31.9 7.4 18.0
	PointerGenerator* 33.9 6.8 18.2

https://github.com/florianbaud/retrieval-augmented-mds (visited on 11/08/2023)

https://huggingface.co/allenai (visited on 11/08/2023)

Acknowledgments

We gratefully acknowledge support from the CNRS/IN2P3 Computing Center (Lyon -France) for providing computing and data-processing resources needed for this work. In addition, This work was granted access to the HPC resources of IDRIS under the allocation 2022-AD011013300 made by GENCI. Finally, we would like to thank Roch Auburtin from Visiativ for his advice.