Gilles Cambonie1

Chloé Desage1

Pénélope Thaller1

Anne Lemaitre1

Karine Bertran De Balanda1

Clémentine Combes1

Arthur Gavotto1

Gilles Cambonie
email: g-cambonie@chu-montpellier.fr

Context of a neonatal death affects parental perception of end-of-life care, anxiety and depression in the first year of bereavement

Keywords: Anxiety, Depression, End-of-life decisions, Mortality, Newborn, Parental grief, Withholding or withdrawing care HADS Hospital Anxiety and Depression Scale, NICU Neonatal intensive care unit, WWLST

Background

Neonatal death is often preceded by end-of-life medical decisions. This study aimed to determine whether the context of death -after a decision of withholding or withdrawing lifesustaining treatment (WWLST) or despite maximum carewas associated with subsequent risk of parental anxiety or depression. The secondary objective was to assess parents' perceptions of end-of-life care according to death context.

Methods

Prospective single center observational study of all neonatal deaths in a neonatal intensive care unit over a 5-year period. Data were collected during hospitalization and from face-toface interviews with parents 3 months after the infant's death. Anxiety and depression were assessed using Hospital Anxiety and Depression Scale (HADS) questionnaires, completed by parents 5 and 15 months after death.

Results

Of 179 deaths, 115 (64%) occurred after the WWLST decision and 64 (36%) despite maximum care. Parental satisfaction with newborn care and received support by professionals and relatives was higher in the first condition. Sixty-one percent of parents (109/179) attended the 3-month interview, with the distribution between groups very close to that of hospitalization. The completion rates of the HADS questionnaires by the parents who attended the 3-month interview were 75% (82/109) at 5 months and 65% (71/109) at 15 months. HADS scores at 5 months were consistent with anxiety in at least one parent in 73% (60/82) of cases and with depression in 50% (41/82). At 15 months, these rates were, respectively, 63% (45/71) and 28% (20/71). Risk of depression at 5 months was lower after a WWLST decision (OR 0.35 [0.14, 0.88], p = 0.02). Explicit parental agreement with the WWLST decision had an equivocal impact on the risk of anxiety at 5 months, being higher when expressed during hospitalization, but not at the 3-month interview.

Conclusions

Context of death has a significant impact on the emotional experience of parents after neonatal loss, which underlines the importance of systematic follow-up conversations with bereaved parents.

Background

The loss of a loved one is one of the most traumatic events in human life, and the intensity of grief is even higher for parents who have lost a child. Increased risk of anxiety, depression, somatic disease, and mortality have been reported among bereaved parents [START_REF] Li | Hospitalization for mental illness among parents after the death of a child[END_REF][START_REF] Youngblut | Parent health and functioning 13 months after infant or child NICU/PICU death[END_REF][START_REF] Li | Mortality in parents after death of a child in Denmark: a nationwide follow-up study[END_REF].

Neonatal death arouses feelings of profound sadness, shame, guilt and anger in parents [START_REF] Flenady | Meeting the needs of parents after a stillbirth or neonatal death[END_REF]. Compassionate, individualized, and skilled support from health professionals is currently part of the standard of care [START_REF] Koopmans | Support for mothers, fathers and families after perinatal death[END_REF]. Although testimonies underline the importance of this emotional sharing between parents and healthcare teams [START_REF] Gold | Navigating care after a baby dies: a systematic review of parent experiences with health providers[END_REF], investigations into the experiences and feelings of parents are still needed to achieve a deeper understanding of their emotions and needs and to enable more adequate care, information and support during hospitalization and after the infant's death.

Neonatal death in high-income countries is often preceded by end-of-life medical decisions [START_REF] Cuttini | End-of-life decisions in neonatal intensive care: physicians' self-reported practices in seven European countries[END_REF][START_REF] Barton | The contribution of withholding or withdrawing care to newborn mortality[END_REF]. A study conducted in the department of neonatal medicine of our institution showed that half the deaths occurred in this context [START_REF] Vidal | Limitation et arrêt des thérapeutiques actives en néonatologie [End-of-life decisions in neonatology[END_REF]. The review of our practices indicated that they were in most cases in line with the ethical and legal framework in our country [10], however it did not assess how parents and caregivers felt about the decision to limit or withdraw treatment. Few data are available on how the information given to parents and their contribution to the decision of withholding or withdrawing life sustaining treatment (WWLST) impact psychological well-being [START_REF] Caeymaex | Perceived role in end-of-life decision making in the NICU affects long-term parental grief response[END_REF][START_REF] Edmonds | The impact of decision quality on mental health following periviable delivery[END_REF].

The main objective of this study was to determine whether the context of a neonatal deathafter a WWLST decision or despite maximum carewas associated with the subsequent risk of parental anxiety or depression. The secondary objectives were to describe the opinions of caregivers, physicians and parents on end-of-life care and information.

Methods

This prospective observational study was performed in the department of neonatal medicine of the University Hospital of Montpellier (France). This department has a capacity of 47 beds, including 14 type 3 beds, corresponding to a neonatal intensive care unit (NICU), 18 type 2b beds, and 15 type 2a beds. The difference between bed types relates to patient's clinical severity, which establishes a ratio between the number of patients and the number of nurses for each bed type. The number of nurses per neonate is framed by the French perinatal decrees of 1998i.e., one nurse for two neonates for type 3 beds, one nurse for three neonates for type 2b beds, and one nurse for six neonates for type type 2a beds. The medical team is made up of 10 senior pediatricians and 3 fellows. The median (interquartile range) annual number of births in the center during the recruitment period was 3392 (3336-3560), including 14.7 (14.3-15.0) % preterm deliveries.

The physician regularly involved in the care of a particular infant is named the referent physician or practitioner. According to the French law [10], the referent physician triggers the organization of the multidisciplinary ethics meeting, if the patient's clinical situation requires it. The referent physician presents the case during the meeting and requests the committee's reflection on withholding or withdrawing life sustaining treatments. The referent physician records the decisions taken and the reasons for them in the child's medical file. This physician also receives the parents at the end of the meeting and engage with them a discussion on the decisions taken by the committee. In the context of the study, the referent physician collected parental agreement with these decisions after ethics debate.

Caregivers inform the parents that they can make an appointment with one of the psychologists working in the department, described as referent for the family. Two psychologists work in the department and distribute the families according to their availability. Thus, each family has a referent psychologist, whether or not the parents accept appointments during or after hospitalization. This referent psychologist is present at the multidisciplinary ethics meeting and the interview 3 months after infant death. In the context of the study, the referent psychologist collected and analyzed, with the principal investigator, information during the interview with parents 3 months after infant's death.

Population

Parents were included if they met the following conditions: (i) death of their newborn during the study period and (ii) signature of the study participation agreement. This study was not proposed to parents if (i) the deceased infant was > 28 days of age at admission to the department, if born full term; (ii) the deceased infant had a corrected gestational age > 41 weeks at admission to the department, if born preterm; and (iii) they could not read French.

Study period

The recruitment period included the deaths of newborns admitted to the department from January 2011 to December 2015. The study ended at the deadline for receiving the last parental questionnaires, i.e., 31 July 2017 for children who died during the first trimester of 2016.

Data collection

Data were collected in a case report form (Supplementaryfile) completed at various stages (see below) by (i) the referent physician and the referent psychologist after the multidisciplinary ethics meeting; (ii) the physician and the nurse present at the moment of the infant's death; (iii) the principal investigator and the referent psychologist after the interview with the parents 3 months after the death of their infant; and (iv) the principal investigator, upon receipt of the Hospital Anxiety and Depression Scale (HADS) questionnaires sent by the parents.

Multidisciplinary ethics meetings

These meetings were considered when providing care appeared as "unreasonable obstinacy" taking into account life expectancy or the expected quality of life. Unreasonable obstinacy is defined by the implementation or maintenance of treatments which appear useless and disproportionate or which have no other effect than the sole artificial maintenance of life [10]. Information was gathered on the reason for the meeting, the infant's main somatic features (perinatal characteristics, postnatal age, respiratory and hemodynamic support, and the main organ failures), the meeting participants, and the decision made at the conclusion of the meeting. The parents were informed beforehand of this meeting, and that feedback on the committee's opinion would be provided. They were received for an interview by the referent physician and the nurse immediately after the multidisciplinary ethics meeting. The limitations and/or withdrawal of care were clearly stated and their opinions were sought. The referent physician and the nurse then classified the parental opinions about the decision as explicit agreement, tacit agreement, ie, parents whose attitude or expression suggested that they did not oppose the decision, disagreement, or impossible/difficult to adjudicate.

Death

The information mainly focused on parental presence, the infant's pain or discomfort, and support provided to the family.

Interview 3 months after infant death

A face-to-face interview with the head of department, i.e., the principal investigator, and the referent psychologist was systematically offered. The interview was announced at the time of death, then a letter was sent to the parents 6-8 weeks after the death, providing the date and place of the meeting, located in the office of the referent psychologist, ie, 2 floors above from the department of neonatal medicine. The letter mentioned that the interview would focus on reviewing the medical history of their child, answering their questions, and providing a better understanding of the events that occurred during the hospitalization. It was also specified that particular attention would be paid to the family experience related to the loss of the infant.

In practice, this interview proceeded through four steps: (i) presentation of the objectives of the meeting; (ii) expression of the parents' feelings and answers to their questions; and (iii) a semi-structured interview on the family environment and the experience of the infant's hospitalization and death and the parents' current feelings and family reorganization. The last part of the interview was devoted to (iv) a detailed presentation of the study.

Family environment was assessed from hospitalization, during medico-psycho-social meetings -which gather each week the medical team, nurses, psychologists and social workers of the department-and appointments between the referent psychologist and the parents. In addition, some information was provided by the parents during the interview 3 months after infant death. The main environmental factors collected were understanding and expression of French, communication within the couple, support from relatives, social vulnerability (mainly assessed from the financial difficulties for the everyday life, including transport or the cost of accommodation close to hospital), family vulnerability (mainly assessed from the relationships and support from their own parents and siblings), psychological vulnerability (mainly assessed form a past-history of bereavement and the requirement of psychotropic medication for various causes). Considering the different sources of information for family environment, the assessment was based on the joint opinion of the principal investigator and the referent psychologist. For the purpose of standardization, this joint opinion was summarized on a 5-point scale. Satisfactory ratings (for French understanding and expression, communication within the couple, and support from relatives) and presence of a significant vulnerability (whether social, familial, or psychological) corresponded to scores from 4 to 5 on the 5-point scale.

Data on parental experience in relation to the loss of the infant provided from direct question asked during the interview 3 months after infant death. They focused on their relationship with the team (feeling of consideration, clarity and precision of medical information), their satisfaction with end-of-life care (involvement in infant's care, infant's pain control, support from their relatives and from the referent psychologist, spiritual support by the hospital chaplain). We also asked if persistent disturbances of appetite and sleep had occurred following infant's death, and whether they could return to their employment. We finally questioned them about their feelings of guilt and anger and about prospects of a future pregnancy. Answers to these direct questions to parents were scored as binary (yes/no).

A document holder was given to the parents, containing information about the study, consent document, and, for each parent, two HADS questionnaires to be completed 5 months and 15 months after death, with two stamped envelopes in the name of the principal investigator.

HADS questionnaire

This screening tool, developed Zigmond and Snaith [START_REF] Zigmond | The hospital anxiety and depression scale[END_REF] and validated in its French version [START_REF] Razavi | Validation de la version française du HADS dans une population de patients cancéreux hospitalisés [Validation of the French version of HADS in cancer in-patients[END_REF], includes 14 questions. Seven questions screen for anxiety (HADS-A) and seven screen for depression (HADS-D). Each question is rated from 0 to 3, giving sub-scores between 0 and 21, with cut-off value for each subscale > 8 to identify anxiety or depression [START_REF] Bjelland | The validity of the hospital anxiety and depression scale. An updated literature review[END_REF].

Statistical analysis

Comparisons were made using the Fisher, chi-squared, Student, and Wilcoxon-Mann-Whitney tests, as appropriate.

Based on a report from our department of an equivalent distribution of death rate occurring after a decision of WWLST or despite maximum care [START_REF] Vidal | Limitation et arrêt des thérapeutiques actives en néonatologie [End-of-life decisions in neonatology[END_REF], and under the assumption of a 50% rate of parental anxiety or depression 5 months after the loss of their infant, 50 parents per group were needed to demonstrate a 20% difference in the rate of anxiety or depression in at least one of the parents according to death condition, with a power of 80% and p < 0.05. Given that the annual number of deaths in the department is about 40 and that the parental participation rate in the interview 3 months after infant death is about 60%, the recruitment period was set at 5 years.

Statistical analysis was performed with SAS Version 9 software (SAS Institute, Cary, NC). Values are expressed as numbers (%) or medians (Q25, Q75). p < 0.05 was considered statistically significant.

Results

Population

One hundred and ninety infants died in the department of neonatal medicine during the study period. Among them, 179 were eligible, including 115 (64%) infants who died after a decision of WWLST and 64 (36%) despite maximum care (Fig. 1). Perinatal characteristics were comparable between groups (Table 1).

Multidisciplinary ethics meetings

The decision of WWLST was made following a collegial procedure in all cases. The reasons for the meeting, the composition and the decisions, as well as the opinions of the parents are provided in Table 2.

Death

The infant's postnatal age at the time of death was earlier in the event of death despite maximum care compared to death after a WWLST decision (Table 3). Severe brain lesions and congenital anomalies accounted for nearly three quarters of the deaths after the decision of WWLST, while death despite maximum care occurred mainly in the context of respiratory failure, infection or extreme prematurity.

One hundred and fifty-seven infants (88%) died in the presence of at least one of their parents, with no difference between groups. The endotracheal tube was removed in 52 (45%) infants of the group with a decision of WWLST. Death in human arms and in father's arms were more frequent after a decision of WWLST.

Caregivers present at the time of death felt that parents were better accompanied by relatives and were more often offered psychological and spiritual support in the event of WWLST (Table 3).

Interview 3 months after infant death

Of the 179 bereaved parents, 109 (61%) attended the 3-month interview. Among them, 68 (62%) had lost their infant after the decision of WWLST and 41 (38%) despite maximum care.

Data on family environment, collected since hospitalization, were comparable between the groups (Table 4).

Parents whose infants died after WWLST reported more frequently that they had received clear and detailed medical information, support from their relatives, and proposals of spiritual support by a hospital chaplain. In addition, they more often considered the prospect of a future pregnancy. Their involvement in care was higher, and their perception of their infant's pain control at the time of death was better. Appetite and sleep disturbances, feelings of guilt and anger, and return to work were comparable between groups (Table 4). In the cohort as a whole and compared to fathers, mothers had more frequent disturbances in appetite (16.5% vs. 2.7%, p < 0.001) and sleep (28% vs. 15%, p = 0.02). They also more often felt guilt (37% vs. 4.5%, p < 0.001).

Parental anxiety and depression 5 months and 15 months after infant death

Of the 109 couples interviewed 3 months after death, 140 HADS questionnaires were completed by 70 couples, 11 by mothers only and 1 by the father only, ie, in total 152 HADS questionnaires from 82 couples, including 81 completed by mothers, and 71 by fathers. At 15 months, 110 HADS questionnaires were completed by 55 couples, 15 by mothers only and 1 by the father only, ie, in total 126 HADS questionnaires from 71 couples, including 70 completed by mothers, and 56 by fathers.

Five months after death, HADS scores were consistent with anxiety in at least one parent in 73% of the cases and with depression in 50%. At 15 months, these rates were, respectively, 63% (p = 0.19 vs. 5 months) and 28% (p = 0.006 vs. 5 months) (Fig. 2).

Relationship to parental gender

Anxiety rates were higher in mothers than in fathers at 5 months (68% vs. 51%, p = 0.031) and 15 months (53% vs. 34%, p = 0.034). Between these two time-points, the change in anxiety rates was not significant in either mothers (p = 0.06) or fathers (p = 0.06) (Fig. 2).

Depression rates were comparable between mothers and fathers at 5 months (40% vs. 41%, p = 0.87) and 15 months (20% vs. 29%, p = 0.26). Between these two time-points, the change in depression rates was significant for mothers (p = 0.009) but not fathers (p = 0.15) (Fig. 2).

Relationship to the circumstance of death

No association was found between the circumstance of death and parental anxiety at 5 months and 15 months. The risk of depression at 5 months in at least one of the parents (OR 0.35, 95% CI 0.14-0.88, p = 0.02) and in the fathers (OR 0.32, 95% CI 0.12-0.86, p = 0.02) was lower in the event of death after WWLST (Table 5).

Relationship to parental agreement with the decision of WWLST

Explicit parental agreement after the multidisciplinary ethics meeting was associated with higher risks of anxiety at 5 months (OR 16.6, 95% CI 2.0-140.6, p = 0.005). No association was found with parental anxiety or depression at 5 months and 15 months in cases of explicit agreement with the decision of WWLST expressed 3 months after death (Table 6).

Discussion

This study showed that approximately 2/3 of neonatal deaths occurred in a context of WWLST, and 1/3 despite maximum care. Context of neonatal death influenced parental perception of end-of-life care and received support by professionals and relatives, as the risk of parental anxiety or depression in the first year of bereavement.

Our data are consistent with other single-center, regional and network studies, which found that a majority of newborn deaths occurred in context of WWLST [START_REF] Barton | The contribution of withholding or withdrawing care to newborn mortality[END_REF][START_REF] Wilkinson | Death in the neonatal intensive care unit: changing patterns of end of life care over two decades[END_REF][START_REF] Berger | Causes and circumstances of neonatal deaths in 108 consecutive cases over a 10-year period at the Children's Hospital of Lucerne Switzerland[END_REF][START_REF] Hellmann | Neonatal deaths: prospective exploration of the causes and process of end-of-life decisions[END_REF][START_REF] Boize | Neonatal end-oflife decision-making almost 20 years after the EURONIC study: a French survey[END_REF]. As noted, the two main causes in this context were severe brain damage and severe congenital malformations [START_REF] Hellmann | Neonatal deaths: prospective exploration of the causes and process of end-of-life decisions[END_REF][START_REF] Verhagen | Categorizing neonatal deaths: a cross-cultural study in the United States, Canada, and The Netherlands[END_REF]. As often reported in the neonatal period, decision-making mainly centered on quality of life considerations and, in much lower proportions, on the lack of further treatment benefit or ineffectiveness of care [START_REF] Berger | Causes and circumstances of neonatal deaths in 108 consecutive cases over a 10-year period at the Children's Hospital of Lucerne Switzerland[END_REF][START_REF] Hellmann | Neonatal deaths: prospective exploration of the causes and process of end-of-life decisions[END_REF][START_REF] Fontana | Modes of death in pediatrics: differences in the ethical approach in neonatal and pediatric patients[END_REF]. Death despite maximum care occurred in the context of acute respiratory failure or multi-organ failure, including sepsis and extreme prematurity [START_REF] Verhagen | Categorizing neonatal deaths: a cross-cultural study in the United States, Canada, and The Netherlands[END_REF]. The age of death was significantly earlier in this context, which highlights the somatic vulnerability of these infants.

Parental satisfaction with NICU staff is underpinned by the accuracy of the information provided, as well as calm, confident and controlled communication [START_REF] Sawyer | Parents' experiences and satisfaction with care during the birth of their very preterm baby: a qualitative study[END_REF]. In the context of a death in the NICU, parents also stress the importance of healthcare providers' guidance for bonding with their infant and creating memories [START_REF] Kilcullen | Palliative care in the neonatal unit: neonatal nursing staff perceptions of facilitators and barriers in a regional tertiary nursery[END_REF]. The most frequently expressed regret is not to have spent enough time with their baby [START_REF] Shelkowitz | Counseling for personal care options at neonatal end of life: a quantitative and qualitative parent survey[END_REF]. These observations provide insight into some of the differences between the two groups related to the parents' relationship with the team and their satisfaction with their infant's care. More parents in the context of WWLST reported satisfactory control of their infant's pain, but rates were low in both groups and significantly lower than the caregivers' estimates [START_REF] Williams | Supporting bereaved parents: practical steps in providing compassionate perinatal and neonatal end-of-life care. A North American perspective[END_REF][START_REF] Cortezzo | End-of-life care in the neonatal intensive care unit: experiences of staff and parents[END_REF]. Among bereaved parents, the perception of infant suffering at the end of life in the NICU has been associated with the decision to have another child [START_REF] Keim | Parent distress and the decision to have another child after an infant's death in the NICU[END_REF]. We observed that prospect of a future pregnancy was indeed more frequent in the event of WWLST.

The physician and nurse present at the time of death also perceived a more optimal environment for the parents in the context of WWLST. Caregivers generally encouraged physical contact with the infant at the time of death. Nevertheless, about 15% of the deaths occurred in the incubator. For personal or cultural reasons, some parents or family members may feel discomfort with physical and emotional closeness to the infant at this time [START_REF] Williams | Supporting bereaved parents: practical steps in providing compassionate perinatal and neonatal end-of-life care. A North American perspective[END_REF]. Context also plays a role since death in the incubator was two times less frequent in the event of WWLST. Removal of the endotracheal tube, practiced in nearly half the patients in this group, may favor the infant's placement in the arms of parents for the last moments. As highlighted by Wilkinson et al., in infants going to die despite treatment, transition to palliative care is now the standard of care [START_REF] Wilkinson | Death in the neonatal intensive care unit: changing patterns of end of life care over two decades[END_REF].

The high rates of anxiety and depression observed in bereaved parents during the first 15 months after the infant's death is consistent with the literature, and about two-three times the rates among community parents [START_REF] Dyregrov | Anxiety and vulnerability in parents following the death of an infant[END_REF][START_REF] Vance | Psychological changes in parents eight months after the loss of an infant from stillbirth, neonatal death, or sudden infant death syndrome-a longitudinal study[END_REF][START_REF] Lykke | Anxiety and depression in bereaved parents after losing a child due to life-limiting diagnoses: a Danish nationwide questionnaire survey[END_REF][START_REF] Vance | Couple distress after sudden infant or perinatal death: a 30-month follow up[END_REF][START_REF] Vance | Gender differences in parental psychological distress following perinatal death or sudden infant death syndrome[END_REF][START_REF] Adeyemi | Depressive symptoms in a sample of women following perinatal loss[END_REF]. Less intense grief reactions in fathers have generally been reported and were explained partly by their expected role of "supportive partner" [START_REF] Dyregrov | Anxiety and vulnerability in parents following the death of an infant[END_REF][START_REF] Vance | Psychological changes in parents eight months after the loss of an infant from stillbirth, neonatal death, or sudden infant death syndrome-a longitudinal study[END_REF][START_REF] Vance | Gender differences in parental psychological distress following perinatal death or sudden infant death syndrome[END_REF][START_REF] Jones | New understandings of fathers' experiences of grief and loss following stillbirth and neonatal death: A scoping review[END_REF][START_REF] Leemann | Differing needs of mothers and fathers during their child's end-of-life care: secondary analysis of the "Paediatric end-oflife care needs" (PELICAN) study[END_REF]. Our results did not fully confirm these gender differences in mental health: rates were indeed higher for anxiety in mothers, but comparable for depression, and the lower rate of depression over time was mainly driven by the mothers. Several recent reviews have pointed out that the psychological and emotional impact of neonatal death in men, which has been under-explored compared to women, varied considerably between studies [START_REF] Jones | New understandings of fathers' experiences of grief and loss following stillbirth and neonatal death: A scoping review[END_REF][START_REF] Obst | Men's grief following pregnancy loss and neonatal loss: a systematic review and emerging theoretical model[END_REF].

In this cohort, death after a decision of WWLST was not associated with an increased risk of parental anger, guilt, anxiety or depression. Indeed, most parents with an infant hospitalized in an intensive care unit can imagine situations in which they would consider withdrawing LST, notably suffering, ineffective therapies, and quality of life considerations [START_REF] Michelson | Parental views on withdrawing life-sustaining therapies in critically ill children[END_REF]. The differences observed for parental mental health indicators according to the context of the death mainly raise questions about family well-being after infant death despite maximum care. An infant's rapid deterioration and the ineffectiveness of the medical acts performed can generate the feeling, among caregivers and parents, of a total lack of control in the clinical history, including the final moment of the infant's death. Previous studies have pointed to the psychological benefits of taking control and self-efficacy and the risk of parental depression following rapid or sudden child loss [START_REF] Bandura | Social cognitive theory: an agentic perspective[END_REF][START_REF] Ito | The link between response styles and major depression and anxiety disorders after child-loss[END_REF].

The French law specifies that parents' opinion of the medical decision of WWLST for their child must be obtained [10]. In practice, few data accurately address parental involvement in the decision-making process, in NICUs [START_REF] Shaw | Initiating end-oflife decisions with parents of infants receiving neonatal intensive care[END_REF] as in pediatric intensive care units [START_REF] De Vos | Talking with parents about end-of-life decisions for their children[END_REF]. These studies highlight the gap between the literature, which emphasizes that parents generally prefer to be involved in the decision, and the difficulty of reaching a genuinely shared decision in daily practice [START_REF] Gillam | Ethics at the end of life: who should make decisions about treatment limitation for young children with life-threatening or life-limiting conditions?[END_REF][START_REF] Zimmermann | When parents face the death of their child: a nationwide cross-sectional survey of parental perspectives on their child's end-of life care[END_REF]. The question we asked the parents, namely their degree of approval of a decision already made by the medical team, reflects the preferential choice of our team that parents participate in the decision without being directly responsible for it, which appears as intermediate between a paternalistic approach and a shared decision [START_REF] Shaw | Initiating end-oflife decisions with parents of infants receiving neonatal intensive care[END_REF]. In reality, however, some parents during the 3-month interview reported having been the main actors in the decision-making process, using the words "we were asked to decide." A recent qualitative study underlined that most parents could "well live" with the decision they made for their child [START_REF] Sullivan | After an end-of-life decision: parents' reflections on living with an end-of-life decision for their child[END_REF]. The results of our work also suggest that the parental perception of having explicitly agreed to the decision, or even of having been an actor in the decision, can change over time. This dynamic is illustrated in the variable association with parental anxiety at 5 months, higher when expressed during hospitalization but not when expressed 3 months later.

The results of this single-center study may be difficult to extrapolate to other centers. Death after a decision of WWLST depended on the essential condition that provision of care appeared as "unreasonable obstinacy". However, this condition was not sufficient in itself, as we definitely classified a death in this group if, in this condition, a multidisciplinary ethics meeting was also held. Death despite maximum care sometimes occurred too early to allow for the organization of the meeting, and it cannot be excluded that, if longer survival had been possible, some of these situations would have led to decisions of WWLST. Maximum care for a patient may also be defined differently, depending on the center. For example, in the case of congenital diaphragmatic hernia, death without recourse to extracorporeal membrane oxygenation may indicate that maximum care has been given for one center and yet be defined as withholding care for another [START_REF] Kays | ECMO in CDH: Is there a role?[END_REF].

Another weakness is our limited number of patients. Our calculation of the number of subjects needed was based on an equivalent distribution of patients according to the context of death from a study carried out in the department in the 2000s [START_REF] Vidal | Limitation et arrêt des thérapeutiques actives en néonatologie [End-of-life decisions in neonatology[END_REF]. However, as observed in other centers, death in a context of WWLST has now become the majority condition [START_REF] Berger | Causes and circumstances of neonatal deaths in 108 consecutive cases over a 10-year period at the Children's Hospital of Lucerne Switzerland[END_REF][START_REF] Hellmann | Neonatal deaths: prospective exploration of the causes and process of end-of-life decisions[END_REF][START_REF] Boize | Neonatal end-oflife decision-making almost 20 years after the EURONIC study: a French survey[END_REF][START_REF] Verhagen | Categorizing neonatal deaths: a cross-cultural study in the United States, Canada, and The Netherlands[END_REF][START_REF] Fontana | Modes of death in pediatrics: differences in the ethical approach in neonatal and pediatric patients[END_REF][START_REF] Sorin | Formal procedure to facilitate the decision to withhold or withdraw life-sustaining interventions in a neonatal intensive care unit: a seven-year retrospective study[END_REF]. The participation rate in the interview 3 months after infant death was consistent with our prevision and with the rates usually reported in studies on this topic [START_REF] Mchaffie | Follow up care of bereaved parents after treatment withdrawal from newborns[END_REF][START_REF] Schulz-Baldes | Neonatal end-oflife practice in a German perinatal centre[END_REF][START_REF] Banerjee | Factors influencing the uptake of neonatal bereavement support services -findings from two tertiary neonatal centres in the UK[END_REF]. In addition, context of death had no influence on attendance of the meeting, with the distribution between the two groups at 3 months being very close to that observed during hospitalization. Our sample size was sufficient to observe a significant difference between the groups for the primary endpoint, i.e., the rate of anxiety or depression in at least one of the parents at 5 months. In this respect, it is also important to note that rates of parental anxiety and depression were probably affected by the consultation carried out 3 months after infant death, which allowed them to obtain information, particularly on the cause of the death, to receive emotional support, and to express their experiences with their infant and the caregivers. A recent review showed that these conversations are beneficial for a large majority of parents [START_REF] Van Kempen | Insight into the content of and experiences with follow-up conversations with bereaved parents in paediatrics: a systematic review[END_REF].

Conclusions

This study shows that the context of death has a significant and prolonged impact on the emotional experience of bereaved parents. It highlights the need for training of healthcare professionals to provide effective support to bereaved parents [START_REF] Vig | Parental bereavementimpact of death of neonates and children under 12 years on personhood of parents: a systematic scoping review[END_REF]. Notably, a medicopsychological appointment should be systematically offered to parents to discuss all events surrounding their infant's death, and to welcome their feedback on the care given. This can facilitate meaning-making processes and, potentially, the acceptance of death [START_REF] Meert | Meaning making during parent-physician bereavement meetings after a child's death[END_REF].

Acknowledgements

We are very indebted to all the bereaved parents who shared their experiences and insights and for sending us so courageously HADS questionnaires. We extend our warmest thanks to the physicians and nurses for their contribution to this study.

Funding

No financial support was received.

Availability of data and materials

The datasets used and /or analysed during the current study are available from the corresponding author on reasonable request.

Authors' contributions

GC conceptualized and designed the study, collected the data, prepared the manuscript and is the corresponding author. CD and PT reviewed the literature, participated to data analysis, and prepared the manuscript. AL and KBdB reviewed the literature, collected the data, and reviewed the manuscript. CC carried out the statistical analyses, and reviewed the manuscript. AG participated to data analysis and prepared the manuscript. All authors reviewed the manuscript. The author(s) read and approved the final manuscript.

Declarations

Ethics approval and consent to participate

The research was carried out in compliance with French regulations, particularly the provisions related to biomedical research, Public Health Law 2004-806 of 9 August 2004, the Data Protection Act, and the study was carried out in accordance with Declaration of Helsinki. Ethics approval was granted by the ethics committee Sud Méditerranée IV (number 2011-A00136-35). Written informed consent was obtained from all participants.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.


Daniel Wilhelm

Luciana Arantes

Pierre Sens

DCS : A logical clock composed of a dynamic set of probabilistic clocks

Keywords: Logical clock, Causal Broadcast, probabilistic clock, distributed algorithms

) ont été proposées dans la littérature. Ces horloges capturent la causalité avec une grande probabilité mais ne la caractérisent pas. L'efficacité d'une horloge de taille constante pour ordonner correctement les messages est négativement impactée par la charge de messages du système. Néanmoins, cet impact peut être géré en variant la taille de l'horloge en fonction de la charge de messages. Cependant, la taille des horloges de taille constante existantes est fixée à l'initialization et ne peut pas changer durant l'exécution. Ce papier présente les Dynamic Clock Set(DCS), qui sont constitués d'un ensemble d'horloges probabilistes. La taille de l'ensemble peut changer dynamiquement durant l'exécution et peut notamment s'adapter à la charge de messages.

Introduction

Distributed and parallel applications are composed of an ever increasing number of processes that cooperate by exchanging messages. Many of them also require that events, i.e., sending and reception of messages as well as local events, are causally ordered as defined by Lamport's happened before relationship [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF].

Logical clocks have been used in the literature [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF][2] [START_REF] Mattern | Virtual time and global states of distributed systems[END_REF] to track the causality of events in distributed systems. Events are timestamped with logical clock values, which are appended on application messages and are updated through rules. However, Charon-Bost [START_REF] Charron-Bost | Concerning the size of logical clocks in distributed systems[END_REF] proved that, in order to precisely capture the causality of events, i.e., to characterize their causality, logical vector clocks must have one entry per process in the system. Thus, in a distributed system with N processes, causality can only be characterized with a structure in O(N ), inducing scalability issues, especially in large systems, since the size of vector clocks grows linearly with the number of processes.

Constant size clocks (e.g., Probabilistic [START_REF] Mostéfaoui | Probabilistic causal message ordering[END_REF], Plausible [START_REF] Torres-Rojas | Plausible clocks : Constant size logical clocks for distributed systems[END_REF], etc.) circumvent such scalability issues by having a size that is much smaller and independent to than the number of processes. On the other hand, even though they provide a high level of ordering accuracy, they do not characterize causality. Such clocks are useful in systems where ordering concurrent events impacts only performance and not correctness [START_REF] Torres-Rojas | Plausible clocks : Constant size logical clocks for distributed systems[END_REF].

The size of existing constant size clocks is fixed at initialization and does not vary during execution. However, the system's message load negatively impacts the accuracy of constant size clocks. Therefore, the clock size should ideally vary with the current message load [START_REF] Mostéfaoui | Probabilistic causal message ordering[END_REF], increasing (resp., decreasing) whenever the message load is above (resp., below) a given bound value. A wrong choice can result in an oversized clock or in a clock that is less effective in ordering messages.

This paper presents a new clock, denoted Dynamic Clock Set (DCS), which consists of a set of probabilistic clocks. The size of the set can dynamically vary during application execution. Operations required to modify the size of the clock as well as to compare them are defined. DCS clocks can, for example, be used to implement causal broadcast such as in the algorithm proposed in [START_REF] Mostéfaoui | Probabilistic causal message ordering[END_REF] that uses Probabilistic clocks.

Background

Causal order ensures that two causally related messages are delivered to applications respecting that order. The causal order relation between events is based on the well-known Lamport's happened before relation between events in distributed systems [START_REF] Lamport | Time, clocks, and the ordering of events in a distributed system[END_REF] : Happened before relationship : Considering two events e 1 and e 2 , e 1 causally precedes e 2 (e 1 → e 2 ) iff : (a) e 1 and e 2 occur on the same process and e 1 precedes e 2 or (b) for a message m e 1 =send(m) and e 2 =deliver(m) or (c) there exists an event e 3 such that e 1 → e 3 and e 3 → e 2 . Causal order : Processes deliver messages while respecting the causal relation between them. For any message m and m , if m causally precedes m , denoted m → m , then all processes deliver m before m : send(m) → send(m ) ⇒ deliver(m) → deliver(m ).

A constant size clock V [START_REF] Torres-Rojas | Plausible clocks : Constant size logical clocks for distributed systems[END_REF][5] has M entries, 1 ≤ M ≤ N, where N corresponds to the number of processes of the system. M is usually much smaller than N. Probabilistic clocks have the best performances among constant size clocks [START_REF] Mostéfaoui | Probabilistic causal message ordering[END_REF]. Therefore, we use them to build the clock proposed in this article.

In a system using probabilistic clocks, each process p i keeps a local clock V i of size M, whose entries are initialized to 0. A hash function f (p i ) returns the set of k clock entries assigned to p i , with 1 ≤ k ≤ M, i.e. one to several entries of the probabilistic clock are respectively associated to each process. Process p i uses the following two rules R1 and R2 to update its local probabilistic clock : -R1 : Before executing an event, p i updates its local clock as follows :

∀x ∈ f (p i ), V i [x] = V i [x] + 1 -R2 :
Each message m carries with it the vector clock of its sender process at sending time. On the receipt of a message m, process p i :

-Updates its local clock as follows : ∀x,

V i [x] = max(V i [x], m.V[x]) -Executes R1, Deliver(m) Comparison of two probabilistic clocks Considering V 1 and V 2 : V 1 < V 2 , iff ∀x, 1 ≤ x ≤ M, V 1 [x] ≤ V 2 [x] ∧ ∃i, V 1 [i] < V 2 [x] Note that probabilistic clocks ensures that : send(m 1 ) → send(m 2 ) ⇒ m 1 .V < m 2 .V.
Using probabilistic clocks to implement a causal broadcast algorithm, the authors of [START_REF] Mostéfaoui | Probabilistic causal message ordering[END_REF] showed that the probability that a process delivers a message m out of causal order is equal to

(1 -(1 -1 M ) X * k ) k
, where M is the size of the clock attached on m, k is the number of entries associated to each process, and X the number of messages concurrent to m. We do two observations out of this equation. First, increasing the size of the clock attached to m decreases the probability that a process delivers m out of causal order. Second, increasing the number of concurrent messages increases the probability that m is delivered out of causal order. In fact, a concurrent message might increment the same clock entries as dependencies of m. Therefore, the higher the number of concurrent messages to m that p i delivers, the higher the probability that such deliveries increment the same clock entries as dependencies of m, and p i will then wrongly conclude that it has delivered all dependencies of m upon receiving m, thus delivering m out of causal order.

Dynamic Clock Set

A Dynamic Clock Set (DCS) is composed of a set of probabilistic clocks, denoted components, which all have the same number of entries (M). Figure 1 gives a representation of a DCS clock. The number of components of a DCS can dynamically vary during execution. A component C k is uniquely identified by its index k. It is either active or inactive. A DCS clock D is composed of one or several active components, followed by no or several inactive components, as shown in Figure 1, i.e. C 1 is always active, followed by no or several active components C i with 1 < i < |D| followed by no or several inactive components C j with i < j ≤ |D|. A process only attaches the active components of its DCS clock on messages. A process increments one or several active components of its DCS clock to keep track of events. The set C incr,i contains the index of the components that process p i increments to track events. p i applies the hash function f (p i ) to all components whose index is contained in C incr,i .

The size of DCS clocks is adaptable to the message load. As shown in the Background, the efficiency of constant size clocks to causally order messages decreases when the message load increases. Nevertheless, increasing the size of a constant size clock also increases its resillience to the message load. The size of DCS clocks is dynamically adjustable during execution. DCS clocks can therefore ensure a desired accuracy of causal message ordering by varying their size according to the message load.

DCS : A logical clock composed of a dynamic set of probabilistic clocks

Active components

Inactive components Process p i uses the following two rules R1 and R2 to update its local DCS clock : -R1 : Before executing an event, it updates its local clock as follows :

x 0 x 1 ... x M x 0 x 1 ... x M ...... x 0 x 1 ... x M x 0 x 1 ... x M C 1 of M entries C 2 of M entries C k-1 of M entries C k of M entries
∀x ∈ f (p i ), ∀k ∈ C incr , V i .C k [x] = V i .C k [x] + d (d > 0) -R2
: Each message m carries with it the vector clock of its sender process at sending time. On the receipt of a message (m, V m ), process p i :

-Updates its local clock as follows :

(1)

If |D i | < |D|, p i calls Add(), defined below, till |D i | = |D|. (2) ∀k ∈ [1, |D|], ∀x ∈ [1, M], D i .C k [x] = max(D i .C k [x], D.C k [x]) -Executes R1, Deliver(m)
Comparison of two DCS clocks The comparison operator < of DCS clocks is based on the comparison operator of probabilistic clocks. Each component of a DCS clock is an independent probabilistic clock. As a reminder, the comparison operator < of two probabilistic clocks C 1 and C 2 is defined as follows : A process p j updates its DCS clock D j when delivering a message m : p j adds components to D j in order to ensure that D j has at least as many components than m.D. Therefore, we have Activate() / Deactivate() A process calls the operation Activate() (resp., Deactivate()) to activate (resp. deactivate) an inactive (resp., active) component of its DCS clock.

C 1 < C 2 iff ∀x, C 1 [x] ≤ C 2 [x] ∧ ∃k, C 1 [k] < C 2 [k] For two DCS clocks D 1 and D 2 , we have D 1 < D 2 provided that : (1) |D 1 | ≤ |D 2 | (2) Each component C k of D
|D j | > |m.D|. Second p j updates D j : ∀x, ∀k, D j .C k [x] = max(D j .C k [x], m.D.C k [x]). Therefore, we have ∀x, ∀k, D j .C k [x] ≥ m.D.C k [x].
We remind that DCS clock requires that the component of lowest index, namely C 1 , to be always active. Thus, the call to Activate() (resp., Deactivate()) immediately returns f alse if p i 's DCS clock has no inactive (resp., only one active) component ; otherwise, the component of p i 's DCS clock with the lowest (resp., highest) index among its inactive (resp., active) components will be activated (resp., deactivated).

For example, let's consider a process p i whose DCS clock D has four components : D = {C 1 , C 2 , C 3 , C 4 }. If p i wants to deactivate one or more components, such a deactivation will be done in decreasing order, i.e, first C 4 , then C 3 , and finally C 2 . On the other hand, if p i wants to re-activate them, first C 2 will be activated, then C 3 , and finally C 4 . Furthermore, p i locally keeps deactivated components C d , since p i can receive a message from another process p j that contains C d , i.e. C d has not been deactivated by p j yet. By locally keeping C d , p i ensures that the delivery conditions of C d will be satisfied locally.

Add() / Remove() A process decides locally to add a new component to its DCS clock, i.e., without communicating with other processes. When p i calls the Add() operation, it first creates a new component C in active state, sets its entries to 0, and appends C to the end of its DCS clock. Therefore, C will be the component of p i 's DCS clock with the highest index.

Having called the Add() operation, p i should also call the Activate() operation for all the inactive components C k of its DCS clock. Indeed, by definition, a DCS clock is composed of active and inactive components and the index of the latter are strictly higher than the former. Consequently, adding an active component at the end of a DCS clock implies that all components of that DCS clock must be active.

Process p i calls Remove() to remove the component of its DCS clock with the highest index.

Conclusion

This paper presents the Dynamic Clock Set (DCS), a new logical clock built with probabilistic clocks. The size of DCS clocks is modifiable during execution, contrary to the size of constant size clocks. This is particularly important since the optimal size of DCS and constant size clocks depends on the system's message load, and knowing the system's message load beforehand is difficult or even impossible.

We implemented a causal broadcast algorithm using DCS clocks and compared it to the causal broadcast algorithm using probabilistic clocks proposed in [START_REF] Mostéfaoui | Probabilistic causal message ordering[END_REF]. Experimental results confirm that DCS clocks adapt well to the message load and can reduce the size of causal information as well as the number of messages delivered out of causal order. The causal broadcast algorithm and experimental results could not be included due to lack of space and can be found in [START_REF] Wilhelm | A probabilistic Dynamic Clock Set to capture message causality[END_REF].

FIGURE 1 :

 1 FIGURE 1: Representation of a Dynamic Clock Set

1 Theorem 1 .

 11 is smaller or equal to the corresponding component C k of D 2 , and at least one component C j of D 1 is strictly smaller than the componentC j of D 2 : ∀k ∈ [1, |D 1 |], D 1 .C k ≤ D 2 .C k ∧ ∃C j , D 1 .C j < D2 .C j . We claim that two causally related messages m 1 and m 2 with respective DCS clocks m 1 .D and m 2 .D verify the following condition : send(m 1 ) → send(m 2 ) ⇒ m 1 .D < m 2 .D. Note that two messages m 1 and m 2 whose DCS clock comparison does not satisfy the above two conditions are said to be concurrent, denoted as m 1 ||m 2 . Formally : m 1 .D m 2 .D ∧ m 2 .D m 1 .D ⇒ m 1 ||m 2 . For any two messages m and m of respective DCS clocks m.D and m .D, if m → m then we have : send(m) → send(m ) ⇒ m.D < m .D Proof. Consider that process p i of DCS clock D i sends a message m of causal dependencies Dep m . We prove that ∀m ∈ Dep m , m .D < m.D, by showing that when p i sends m, we have ∀m ∈ Dep m , m .D < D i .

  Therefore, after p j delivered m, we have m.D ≤ D j . For all messages m ∈ Dep m , either p i delivered m , or another process p j delivered m and broadcasted a message m" such that m → m" → m and that p i delivered m". If p i delivered m , then m .D ≤ D i as showed above. Otherwise, (1) a process p j has delivered m and therefore m .D ≤ m".D (2) p i has delivered m" and therefore m".D ≤ D i . Therefore, m .D ≤ D i . Hence, we have ∀m ∈ Dep m , m .D ≤ D i . When p i sends m, it first updates its DCS clock by incrementing at least one entry x of at least one component C k before appending D i on m. Therefore, ∃k, ∃x, ∀m ∈ Dep m , m.D.C k [x] > m .D.C k [x]. Therefore, ∀m ∈ Dep m , m .D < m.D.


Francesco Cabiddu
email: cabidduf@cardiff.ac.uk

Mitja Nikolaus
email: mitja.nikolaus@univ-amu.fr

Comparing Children and Large Language Models in Word Sense Disambiguation: Insights and Challenges

Keywords:

Understanding how children process ambiguous words is a challenge because sense disambiguation depends on sentence context bottom-up and top-down aspects. Here, we seek insight into this phenomenon by investigating how such a competence might arise in large distributional learners (Transformers) that purport to acquire sense representations from language input in a largely unsupervised fashion. We investigated how sense disambiguation might be achieved using model representations derived from naturalistic child-directed speech. We tested a large pool of Transformer models, varying in their pretraining input size/nature as well as the size of their parameter space. Tested across three behavioral experiments from the developmental literature, we found that these models capture some essential properties of child sense disambiguation, although most still struggle in the more challenging tasks with contrastive cues. We discuss implications for both theories of word learning and for using Transformers to capture child language processing.

Introduction

Large language models are deep artificial neural networks pretrained on large unlabeled datasets via self-supervised learning. These models have had a great impact in the field of Natural Language Processing for their performance in language understanding and generation tasks (e.g., [START_REF] Bommasani | On the Opportunities and Risks of Foundation Models[END_REF]. Here, we examined the plausibility of these models as distributional learners posited by usage-based approaches of language acquisition (e.g., [START_REF] Ambridge | Abstractions made of exemplars or 'You're all right, and I've changed my mind': Response to commentators[END_REF][START_REF] Bybee | Language, Usage and Cognition[END_REF]). We focused on child word sense disambiguation (e.g., [START_REF] Cabiddu | The Role of Verb-Event Structure in Children's Lexical Ambiguity Resolution[END_REF][START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF]. That is, how children use sense-specific representations (e.g., band = music band, elastic band).

We tested models based on the Transformer architecture [START_REF] Vaswani | Attention Is All You Need[END_REF] that perform sense disambiguation using sentence context to form contextualized representations. Transformers are sensitive to syntactic and semantic sentence structures (e.g., [START_REF] Jawahar | What Does BERT Learn about the Structure of Language?[END_REF][START_REF] Tenney | BERT Rediscovers the Classical NLP Pipeline[END_REF] on which sense disambiguation depends. Here, we refer to these high-level structures as topdown cues that a usage-based learner might acquire through language experience [START_REF] Alishahi | Gradual Acquisition of Verb Selectional Preferences in a Bayesian Model[END_REF][START_REF] Bybee | Language, Usage and Cognition[END_REF]. Transformers' inherent sensitivity to these cues allowed us to apply these models to raw naturalistic language, without having to enrich the input with external resources to provide sensitivity to such structures (e.g., [START_REF] Alishahi | Gradual Acquisition of Verb Selectional Preferences in a Bayesian Model[END_REF].

Transformers form adult-like sense representations in natural language classification tasks, where annotators select a fitting target sense given the sentence context [START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF]. However, these tasks may not suitably assess model developmental plausibility as they use coherent test sentences (i.e., all cues in the context unambiguously point toward one target sense). Relying on these tasks makes it difficult to differentiate adultlike from child-like performance, as both adults and children perform well at disambiguating coherent sentences (e.g., [START_REF] Khanna | Children's use of language context in lexical ambiguity resolution[END_REF][START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF]. Thus, we tested models on contrastive tasks alongside coherent ones. Contrastive tasks put bottom-up (i.e., word associations) and top-down sentence cues in competition. They represent a more suitable test of developmental plausibility because differences exist in how children and adults behave in such tasks. In fact, in sense disambiguation children rely more on bottom-up aspects of sentence context (e.g., word associations) than adults, with less reliance on top-down cues likely due to differences in language experience or slow cognitive maturation [START_REF] Khanna | Children's use of language context in lexical ambiguity resolution[END_REF][START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF].

Previous studies have computed models' representations based on adult language [START_REF] Loureiro | LMMS Reloaded: Transformer-based Sense Embeddings for Disambiguation and Beyond[END_REF][START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF]. Here, we evaluated how properties of child sense processing could be captured using model representations formed from naturalistic childdirected speech. This choice is motivated by differences in how senses are assigned to words in children and adults, likely due to differences in word use in child and adult environments [START_REF] Meylan | Quantifying Lexical Ambiguity in Speech To and From English-Learning Children[END_REF].

We examined Transformers using datasets from behavioral studies that tested 4-year-old children's abilities to use bottom-up (word associations) and top-down (sentence global plausibility, verb-event structure) cues to sense disambiguation [START_REF] Cabiddu | The Role of Verb-Event Structure in Children's Lexical Ambiguity Resolution[END_REF][START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF]. We tested a large pool of models (N=45) from 14 different families. This integrative approach [START_REF] Schrimpf | The neural architecture of language: Integrative modeling converges on predictive processing[END_REF] allowed us to examine consistent dimensions across models, instead of relying on single models which might be influenced by specific peculiarities (architecture, pretraining objectives, amount/type of pretraining input, etc.). Specifically, we ex-plored how scalability in models' size (number of parameters) and pretraining data size related to sense disambiguation. These dimensions have been explored separately and not specifically in child sense disambiguation. Based on findings about word age of acquisition norms [START_REF] Laverghetta | Modeling Age of Acquisition Norms Using Transformer Networks[END_REF], we expected models with a higher number of parameters to better fit child data. We also expected a null effect of pretraining size, in line with evidence of small (i.e., more realistic) pretraining input being enough to align models to adult neural data and reading comprehension scores [START_REF] Hosseini | Artificial neural network language models align neurally and behaviorally with humans even after a developmentally realistic amount of training[END_REF].

We first introduce evidence of child sense disambiguation. Secondly, we discuss the theoretical significance of Transformers and introduce a recent framework for evaluating models in sense disambiguation.

Child Word Sense Disambiguation

Sentence context plays a significant role in sense disambiguation (e.g., Sophia [played in / twisted] a band). Children master word ambiguities in naturalistic conversations [START_REF] Meylan | Quantifying Lexical Ambiguity in Speech To and From English-Learning Children[END_REF], which raises a question about which sentence properties facilitate child word disambiguation [START_REF] Cabiddu | The Role of Verb-Event Structure in Children's Lexical Ambiguity Resolution[END_REF][START_REF] Hahn | Rapid Linguistic Ambiguity Resolution in Young Children with Autism Spectrum Disorder: Eye Tracking Evidence for the Limits of Weak Central Coherence[END_REF][START_REF] Khanna | Children's use of language context in lexical ambiguity resolution[END_REF][START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF]. Children should access cues at different linguistic levels to successfully disambiguate senses. Here, we focused on key studies that showed that 4-year-old children could use both bottom-up and topdown disambiguation cues, although to different degrees depending on the specific cue. Table 1 shows an overview of the three experiments considered. A general goal across experiments was to test children's sensitivity to sentence context for sense disambiguation. Further, they tested if top-down cues (global plausibility, verb-event structures) played a role beyond bottom-up word associations (when the two types of cues are in direct competition). Similarly, we investigated if Transformers could use sentence context for word sense disambiguation like children, and if they would demonstrate comparable sensitivity to top-down cues in contrastive conditions.

In all studies, children heard short stories ending with a target word and saw four pictures. Two depicted the target word's alternative senses: One frequent in child-directed speech (dominant = elastic band) and one less frequent (subordinate = music band), with a 3:1 frequency ratio. The other two pictures depicted semantic distractors (e.g., sock, sport team). After the story, children chose the picture that best matched the story's final word.

In a first experiment, [START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF] tested if children could use sentence context to disambiguate dominant and subordinate senses. Disambiguation cues were presented in a previous sentence (Prior context), or in the same sentence as the target (Current context). Example stimuli are shown in Table 1. Children showed successful disambiguation across conditions, selecting more dominant senses (above 50% chance) in dominant-plausible conditions, and more subordinate senses in subordinate-plausible conditions (i.e., less than 50% dominant selections).

However, in this experiment, children could have relied solely on bottom-up associations. For example, in Dora was in her room. She stretched the band, one could track the association between stretching and elastic band in naturalistic conversations without processing sentence structures (i.e., using verb-event knowledge to infer that stretchable entities are usually objects). In the second experiment from [START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF] and in [START_REF] Cabiddu | The Role of Verb-Event Structure in Children's Lexical Ambiguity Resolution[END_REF], bottom-up and topdown cues were in competition. Stories always began with a prior context containing word associates of the target subordinate sense. As shown in Table 1, prior contexts contain the words music or songs pointing toward the subordinate music band. Further, in experimental conditions, stories ended with top-down cues pointing toward the opposite dominant sense elastic band (see underlined cues in Table 1).

In [START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF] experiment 2, experimental stories shifted global semantic plausibility toward the dominant sense. Children struggled to use global plausibility and relied heavily on word associations (39% dominant selections, below chance). However, a significant difference from a control condition emerged (21% dominant selections when the story 1). This result indicated residual sensitivity to top-down global plausibility in 4-year-old children. [START_REF] Cabiddu | The Role of Verb-Event Structure in Children's Lexical Ambiguity Resolution[END_REF] focused on verbs. As shown in Table 1, in a Verb-Event condition, stories ended with verbs that never co-occurred with dominant senses in naturalistic conversations (i.e., children never or rarely hear twisting a band, which controls for verb-object associations). However, the verbs' event structure only accepted the dominant senses (i.e., one can only twist an elastic band, not a music band), making it the only available cue.

Further, the researchers examined the effect of verb-object associations (see Verb-Lexical condition in Table 1): Verbs had a neutral verb-event structure (e.g., one could get an elastic or music band), but often co-occurred with dominant senses in naturalistic conversations (i.e., children frequently hear getting an elastic band). Given the role of verb-object associations in children's word processing [START_REF] Mani | Proactive" in many ways: Developmental evidence for a dynamic pluralistic approach to prediction[END_REF], this condition tested if children would weigh more word associations coming from a verb than the rest of the context.

Children successfully resolved dominant senses using both verb-event structures and verb-object associations, beyond bottom-up word associations from prior contexts.

Word Sense Disambiguation in Transformers

Testing a usage-based learner requires an architecture that forms top-down abstractions while accounting for effects of bottom-up statistical cues in language development (e.g., [START_REF] Ambridge | The ubiquity of frequency effects in first language acquisition[END_REF][START_REF] Mccauley | Language learning as language use: A cross-linguistic model of child language development[END_REF][START_REF] Saffran | Statistical Learning by 8-Month-Old Infants[END_REF]. Consider the meaning of table in [START_REF] Ambridge | Against stored abstractions: A radical exemplar model of language acquisition[END_REF]. A fixed topdown rule defining a table category (e.g., has legs; used for eating; made of wood, metal, or plastic; waist height) becomes falsifiable by counterexamples (e.g., an empty barrel used as a table at a bar). A solution is to embed specific contexts in the table representation [START_REF] Ambridge | Abstractions made of exemplars or 'You're all right, and I've changed my mind': Response to commentators[END_REF]Srinivasan & Rabagliati, 2021). Bottom-up context-dependent information allows the child to estimate the similarity between a new instance barrel table and previously encountered tables. This recursive process of estimation facilitates the emergence of a context-independent, fuzzy, and probabilistic category of table (i.e., a prototype). In sense disambiguation, context-dependent and context-independent representations could gradually lead to multiple sense categories for a single word (Srinivasan & Rabagliati, 2021), with clusters of instances sufficiently separated in the semantic space (e.g., an object band prototype, a music band prototype).

The idea of context-dependent representations aligns with Transformers' core self-attention mechanism. For each token, these models construct distinct representations that dynamically integrate sentence context. Although children have access to referential and social cues beyond sentence context, using Transformers is useful to answer the question: How far can a distributional learner that uniquely processes naturalistic sentence context go?

After training, Transformers encode generalized (contextindependent) knowledge. Tokens from different senses organize into separate clusters within model layers, reflecting the organization of senses in dictionaries and adult representations [START_REF] Loureiro | LMMS Reloaded: Transformer-based Sense Embeddings for Disambiguation and Beyond[END_REF][START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF]. In [START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF], Transformers were evaluated using a nearest neighbor approach (e.g., [START_REF] Melamud | context2vec: Learning Generic Context Embedding with Bidirectional LSTM[END_REF][START_REF] Peters | Deep Contextualized Word Representations[END_REF]. This uses sense-annotated corpora to create model sense prototypes by averaging the representations of a collection of tokens belonging to a specific sense (see Method). Sense prototypes are then used to evaluate the model disambiguation at test. Using this method led to a Pearson's correlation of .9 between the best model and adult annotators. This method is useful because it investigates knowledge of models that are not pretrained on disambiguation, but only on predicting a word given its context (which should be more in line with what children do). Further, compared to previous studies [START_REF] Haber | Word Sense Distance in Human Similarity Judgements and Contextualised Word Embeddings[END_REF], [START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF] showed that models' performance better aligned with adults' when a reference sense-annotated corpus reflected the coarse-grained knowledge that adults have (e.g., collapsing senses that adults likely do not distinguish, but that are differentiated in a dictionary). This suggests that it is possible to tailor the models' sense prototypes to a specific population. In our work, reference sentences were transcribed child-directed utterances, reflecting children's naturalistic input and containing senses known to 4-year-olds based on behavioral evidence.

Method Models

We used 13 Transformer-based model families with varying training tasks and input encoding mechanisms. We also included a bidirectional recurrent neural network (ELMo, [START_REF] Peters | Deep Contextualized Word Representations[END_REF], which achieved state-of-the-art results in sense disambiguation before the introduction of Transformers (e.g., [START_REF] Wiedemann | Does BERT Make Any Sense? Interpretable Word Sense Disambiguation with Contextualized Embeddings[END_REF]. Model descriptions can be found on our OSF page, where we also share materials and code to reproduce the study results (https://doi.org/10.17605/OSF.IO/A2BZQ).

In various configurations within families, we varied model size (number of million parameters, M = 287, range = 8 -1,630) and pretraining size in gigabytes of text (M = 103, range = .005 -806). On our OSF, we also include results from models with randomly initialized weights, showing that performance differences were not due to architectural differences in connection patterns among units.

Model Evaluation via Nearest Neighbor

Following [START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF], we extracted sense prototypes using annotated sentences (see Corpora for details) in which a word occurred in a specific sense (e.g., elastic band). We extracted a model's contextualized vector for each sense occurrence, summing the last four layers. For models that work at the subword level, we first averaged representations of subword tokens for the target word. Finally, we averaged the word vectors to obtain a centroid representing the elastic band prototype. We repeated the process for the alternative music band.

To evaluate model performance, we extracted a contextualized vector for each test sentence's target word. We compared each vector to the two sense prototypes using cosine similarity. The most similar prototype determined the assigned sense for the test word. We then transformed this binary measure (Dominant = 1, Subordinate = 0) into a continuous measure by computing the percentage of dominant senses assigned in a specific condition (matching the child outcome measure in Table 1).

Corpora

We took sentences for computing prototypes from ChiSense-12 (Cabiddu, Bott, Jones, & Gambi, 2022a), which contains speech directed to children up to age 4 from the English section of the CHILDES database [START_REF] Macwhinney | The CHILDES project: Tools for analyzing talk: Transcription format and programs[END_REF]. Each sentence was tagged for occurrences of 12 ambiguous words in dominant or subordinate senses (e.g., chicken animal, chicken food). We used 9 words, excluding homophones with different spelling (e.g., son, sun) for which no ambiguity exists as the models process orthographic input. We also tagged 4 new words to cover more items from children's experiments. Details about items and annotation process are on our OSF. The final corpus had 15,901 sentences for 13 target words, with dominant senses appearing 69% of the time on average (3:1 dominant/subordinate ratio).

Comparing Child to Model Performance

We computed an optimal outcome measure comparing child and model performance. We examined if the models exhibited a dominant sense bias reflecting the dominant/subordinate ratio in the input. For experiment 1 in [START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF] with non-contrastive cues, we fitted a linear mixed-effects model using the percentage of dominant senses selected by each model as the outcome, and model size and pretraining size as the predictors. Model family was used as random effect intercept. Only pretraining size negatively predicted dominant selection (β = -1.53, 95% CI = [-2.30, -.75], p <.001), but not model size (β = -1.47, 95% CI = [-3.01, .08], p = .062). As shown in Figure 1, the models better approximated the 69% dominant sense bias as pretraining size decreased.

Differences in dominant sense bias pose a confound: A model pretrained on a small corpus might select a similar percentage of dominant senses to children not only due to context cue sensitivity, but also because it prefers dominant senses more than a model pretrained on a large corpus. We controlled for this confound by examining the relative difference in dominant sense selections between dominant-plausible and subordinate-plausible conditions.

For example, in the first experiment, children selected dominant senses (e.g., elastic band) in 81% of trials in the dominant-plausible condition (She streched the band) and 38% in the subordinate-plausible (She listened to the band). For a relative difference of 81% -38% = 43% in children, a model with 60% -17% difference and one with 80% -37% were considered equally similar to children. Essentially, the relative difference focused on a model's sensitivity to shifts in sentence context and compared it to children's sensitivity. The final outcome measure estimated the distance between model and children (e.g., [60% -17%]) -[81% -38%]), with values of 0 indicating equal sensitivity in the model and children, and values lower and higher than 0 indicating lower and higher sensitivity, respectively.

Results

Rabagliati et al. (2013) -Experiment 1

Figure 2 shows models' performance by model size (2a) and pretraining size (2b). Some models reached child baseline (y = 0), while others performed worse (y < 0) or better (y > 0). The best nested linear mixed-effects model indicated higher context sensitivity as model size increased (β = 5.36, 95% CI = [2.07, 8.64], p = .002) and pretraining size increased (β = 3.81, 95% CI = [2.16, 5.47], p <.001). A main effect of condition (β = -9.98, 95% CI = [-16.18, -3.78], p = .002) showed models performing better in the current-context condition, which may not align with child performance. Although the main effect of condition was not tested in the child experiment, children's average scores might suggest similar sensitivity to prior and current context (see Table 1).

Rabagliati et al. (2013) -Experiment 2

This task used contrastive bottom-up and top-down cues, which most models seemed to struggle with: Figure 3 shows a floor effect, which led to null effects of model size (β = 3.37, 95% CI = [-.35, 7.09], p = .075) and pretraining size (β = 0.12, 95% CI = [-1.74, 1.98], p = .895). As confirmed in Appendix S4, the floor effect led to only few models showing a difference in dominant selection between conditions. This aligns with children's residual sensitivity to top-down cues, as they displayed a difference between conditions despite low selection rates. Nevertheless, most models performed worse than children, suggesting an overall difficulty in managing contrastive cues.

Cabiddu et al. (2022b)

The models better handled contrastive bottom-up and topdown cues in this task, resembling the strong role of verbs in child processing. The models showed higher sensitivity to verbs with a strong event structure (Figure 4a; e.g., She twisted a band), with model size being positively related to models' sensitivity to verb-event cues (β = 7.57, 95% CI = [3.48, 11.67], p = .001), but not pretraining size (β = -.30, 95% CI = [-2.35, 1.74], p = .765). Instead, sensitivity was lower to verbs that were only lexically associated with the dominant sense (Figure 4b; e.g., She got a band), with no significant effects of model size (β = 1.73, 95% CI = [-0.87, 4.34], p = .186) or pretraining size (β = 0.16, 95% CI = [-1.14, 1.45], p = .809).

Discussion

We examined the capabilities of large Transformer models in capturing child word sense disambiguation. Our results support the idea that children, like these models, might be usagebased learners who bootstrap word knowledge from the naturalistic environment [START_REF] Bybee | Language, Usage and Cognition[END_REF], and that sense knowledge can, in principle, arise from probabilistic representations embedding context-dependent and context-independent information [START_REF] Ambridge | Abstractions made of exemplars or 'You're all right, and I've changed my mind': Response to commentators[END_REF]Srinivasan & Rabagliati, 2021).

In line with Laverghetta Jr and Licato (2021), larger models were more sensitive to both coherent (Figure 2) and contrastive cues (Figure 4a), likely because they form more precise representations based on both bottom-up and topdown aspects of sentence structure [START_REF] Devlin | BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding[END_REF][START_REF] Hewitt | A Structural Probe for Finding Syntax in Word Representations[END_REF][START_REF] Radford | Language Models are Unsupervised Multitask Learners[END_REF].

Contrary to our prediction, models trained on larger corpora were more sensitive to coherent cues (Figure 2), while we found the predicted null effect of pretraining for contrastive cues (Figure 3 and4). In coherent sentences, a model can rely on both word associations and top-down cues, with more pretraining likely increasing sensitivity to both. However, more pretraining might not always be as valuable for resolving contradicting bottom-up and top-down cues in the other conditions. Larger models might instead have an advantage in this regard. Further, a visual inspection of models' performance at contrastive tasks (see raw plots of sense selection for each model in OSF, Appendix S4) showed a stronger overall preference for subordinate senses across conditions compared to children, which might indicate models' higher sensitivity to prior context word associations (an analysis of relative differences could not highlight this, as it specifically controls for absolute differences in sense selection). In a follow-up analysis (see OSF, Appendix S5), we found evidence for this interpretation. We used an alternative outcome measure (Euclidean distance) which, compared to the relative difference, additionally looked at how close models got to y = 0 (Figure 2, 3, and 4), and at the exact match between models and children (i.e., difference in absolute scores): Given 81% -38% as the children's response difference, a model performing 80% -37% would be now closer to children than one that performs 60% -17%. This measure might suffer from dominant sense bias (Figure 1), which we included as covariate in the statistical models to control for its effect. We replicated the positive effect of pretraining size in experiment 1 (Figure 2b), and found a negative effect of pretraining size in the verbevent structure condition of the third experiment (Figure 4a). This result might indicate that smaller pretraining prevented an extreme sensitivity to word associations, allowing models to find the right balance between bottom-up and top-down cues. Interestingly, the best models in this condition received pretraining that was judged as psychologically plausible in previous studies (100 million tokens, [START_REF] Hosseini | Artificial neural network language models align neurally and behaviorally with humans even after a developmentally realistic amount of training[END_REF], although for an older population than ours (10-year-olds). To gain deeper insights into word association sensitivity, future work will examine by-item performance across models. This will help us assess how prior context associations for each target word impact models' performance, and whether this relation aligns with that observed in children.

Basing sense prototypes on child input partially tuned models' representations to children's. Only models with small pretraining approximated the dominant sense bias in the child input (Figure 1), and only few models (Figure 4b) showed sensitivity to verb-sense associations (e.g., getelastic band), which are idiosyncrasies of the child input, likely not present in the adult language used for pretraining (e.g., Wikipedia). One way to align models with the child environment would be pretraining directly on child input [START_REF] Hosseini | Artificial neural network language models align neurally and behaviorally with humans even after a developmentally realistic amount of training[END_REF][START_REF] Warstadt | What Artificial Neural Networks Can Tell Us About Human Language Acquisition[END_REF]. However, this task is limited by the lack of sufficiently large corpora. For example, in our study we included BabyBERTa (Huebner, Sulem, Cynthia, & Roth, 2021), which despite being pretrained on child input showed no sensitivity to sentence context, likely due to its small pretraining (5 million tokens).

Models' performance was impaired in tasks that introduced contrastive cues (Figure 3 and4). This suggests that previous results showing that Transformers can even approximate adult performance [START_REF] Loureiro | Analysis and Evaluation of Language Models for Word Sense Disambiguation[END_REF] still require further investigation. Sense prototypes based on child input might have contributed to the low performance of the models in our study. In upcoming work, we will examine the role of reference sentences by additionally using adult-directed sensetagged sentences (from the spoken part of the British National Corpus; BNC Consortium, 2007). Given that previous studies have not used contrastive tasks, another possibility is that such tasks might be difficult for models. Few models were sensitive to contrastive cues (Figure 3 and 4), indicating that at least some information about top-down structures might be captured from sentence context via distributional learning. However, overall models' performance was lower than children's. Difficulties in approximating child knowledge could be due to the fact that children's representations of top-down structures are not only based on sentence context but also include real-world knowledge, which would need to be integrated into neural systems. For example, when modelling word acquisition trajectories, Transformers are not influenced by grounded sensorimotor, social, and cognitive factors (e.g., noun concreteness), but rely on surface features (e.g., word frequency) to a greater extent than children [START_REF] Chang | Word Acquisition in Neural Language Models[END_REF]. We speculate that this lack of grounded knowledge might also explain the fact that the models performed worse at disambiguating prior contexts than current contexts (Figure 2). Current contexts contained words that might appear closer to target words in naturalistic language, becoming easier to track by a distributional learner. This difficulty might not exist for children who can use their real-world knowledge for semantically-related (but distant) words (e.g., in "Dora looked in her drawer. The band was cool", a child can infer that entities stored in a drawer are usually objects). Indeed, word acquisition trajectories can probably be better captured by neural models that process a richer multimodal signal comprising auditory features, communicative intentions, and perceptual information about word referents (e.g., [START_REF] Frank | Using speakers' referential intentions to model early cross-situational word learning[END_REF][START_REF] Nikolaus | Evaluating the Acquisition of Semantic Knowledge from Crosssituational Learning in Artificial Neural Networks[END_REF][START_REF] Nyamapfene | A Multimodal Model of Child Language Acquisition at the One-Word Stage[END_REF]. Future work should focus on modelling child multimodal processing, currently limited by the scarcity of naturalistic multimodal corpora (e.g., [START_REF] Nikolaus | Learning English with Peppa Pig[END_REF]. Finally, enriching models' input would allow researchers to test if acquiring multimodal knowledge suffices to capture sensitivity to top-down structures, or whether one would need to integrate domain-specific constraints in line with nativist approaches (e.g., [START_REF] Pinker | Learnability and Cognition[END_REF][START_REF] Thornton | Studies at the interface of child language and models of language acquisition[END_REF] or more domain-general innate biases (e.g., [START_REF] Perfors | The learnability of abstract syntactic principles[END_REF].

We began to examine the capabilities and limitations of Transformer models for studying early word sense disambiguation. We showed that an evaluation approach that leverages sense-annotated corpora can sensibly be used to examine the developmental plausibility of sense representations in large language models. We emphasized the importance of filling the gap between children and models by integrating multimodal knowledge in neural systems.

Figure 1 :

 1 Figure 1: Percentage of dominant senses selected by each model in Rabagliati et al. (2013) experiment 1, by pretraining size in log GB. The dashed horizontal line indicates dominant sense prevalence in ChiSense-12.

Figure 2 :

 2 Figure 2: Models' distance from children by model size (a) and pretraining size (b), in current and prior context conditions. Model families are shown in the legend. The black horizontal line indicates child performance. The dashed regression line with 95% confidence interval shows performance across models. Colored regression lines are also shown for each model family, although only when examining model size as there is almost null variation in pretraining size within family. Points in panel b are jittered by 2 points in the y axis to facilitate visualization of overlapping points.

Figure 3 :

 3 Figure 3: Models' distance from children by model size and pretraining size, in Rabagliati et al. (2013) experiment 2.

Figure 4 :

 4 Figure 4: Models' distance from children by model size and pretraining size, when comparing verb-event vs. control (a) and verb-lexical vs. control conditions (b).

Table 1 :

 1 Behavioral experiments. Target words are shown in bold. Underlined text indicates cues to the dominant sense elastic band, while italicized text refers to cues to subordinate music band. The Dominant selection column indicates average dominant sense selections in children, for dominant-plausible (underlined) and subordinate-plausible conditions (italicized).

	Study	Cue type	Example	Dominant selection
	(Rabagliati et al., 2013) Prior Context	Dora [looked in her drawer / heard some music]. The	79% / 33%
	Exp 1, Coherent cues		band was cool.
		Current Context	Dora was in her room. She [stretched / listened to] the	81% / 38%
			band, which was cool.

[START_REF] Rabagliati | Topdown influence in young children's linguistic ambiguity resolution[END_REF]

Global Plausibility Elmo and his class were singing songs. The teacher Exp 2, Contrastive cues could play music with [anything / anyone], even a band. 39% / 21% (Cabiddu et al., 2022b) Verb-Event Structure Sophia listened to some music. Then she [twisted / 62% / 26% Contrastive cues played in] a band. Verb-Lexical association Sophia listened to some music. Then she [got / played in] 60% / 26% a band. fully supported the subordinate; see italicized cue in Table

Acknowledgments

We would like to express our gratitude to Alex Warstadt for his valuable comments during the initial stages of this project, and to Abhishek Agrawal for offering helpful suggestions on the manuscript. We also extend our thanks to the anonymous reviewers for their insightful feedback. The research presented in this article has been generously supported by a Study Visit Grant from the Experimental Psychology Society (UK).