Erin Grinshteyn
email: egrinshteyn@usfca.edu

PhD Reid Whaley

MPH Marie-Claude Couture

Higher prevalence of fear of discrimination among racial, gender, and sexual minority university students

Background: Discrimination on college campuses is highly prevalent among racial/ethnic, gender, and sexual minority students. However very little is known about fear of discrimination.

The objectives of this paper are to (a) establish the prevalence of fear of hate crimes, fear of hate speech, and fear of microaggressions on college campuses, and (b) establish sociodemographic correlates of these fears among a diverse university sample.

Methods: This cross-sectional study was a convenience sample of undergraduate and graduate university students conducted at a diverse university in the United States. Data were collected using online surveys on sociodemographic correlates (i.e., age, gender, race/ethnicity, sexual orientation, citizenship, and religion), fear of hate crimes, fear of hate speech, and fear of microaggressions. To compare fear scores within each sociodemographic correlate, mean scores on each fear outcome were compared using Mann-Whitney (Wilcoxon rank sum tests) and Kruskal-Wallis tests for these non-normally distributed variables.

Conclusion:

Fear of discrimination is an important and understudied public health issue. Fear of hate crimes, fear of hate speech, and fear of microaggressions were all higher among racial, gender, and sexual minority university students. Universities must work to prevent and address these elevated fears and disparities among students.

Results: Race/ethnicity was significantly associated with fear of microaggressions (p<0.0001), fear of hate crimes (p<0.0001), and fear of hate speech (p<0.0001) with Black students having the highest mean scores for all three fears followed by Middle Eastern students. White students had the lowest mean scores for all three fears. Gender was significantly associated with fear of microaggressions (p<0.0001), fear of hate crimes (p<0.0001), and fear of hate speech (p<0.0001) with transgender and gender nonconforming students scoring highest followed by females for all three fears. Sexual orientation was also significantly associated with fear of microaggressions (p<0.0001), fear of hate crimes (p<0.0001), and fear of hate speech (p<0.0001) with lesbian students reporting the highest scores for fear of microaggressions and fear of hate speech, and gay students reporting the highest scores for fear of hate crimes.

Introduction

Discrimination is a significant public health issue. In universities, the prevalence varies across studies though is elevated among racial/ethnic, gender, and sexual minority students.

One study of Latino, Asian, Black, and multiracial college students found that the majority had experienced discrimination on campus [START_REF] Juang | Perceived Racial/Ethnic Discrimination and Adjustment Among Ethnically Diverse College Students: Family and Peer Support as Protective Factors[END_REF]. Multiple studies have shown Black students reporting higher perceived discrimination scores than other racial/ethnic groups [START_REF] Cokley | Impostor feelings as a moderator and mediator of the relationship between perceived discrimination and mental health among racial/ethnic minority college students[END_REF][START_REF] Prelow | Perceived Racial Discrimination, Social Support, and Psychological Adjustment Among African American College Students[END_REF] with one study showing that 98.5% of respondents experienced discrimination during the past year [START_REF] Prelow | Perceived Racial Discrimination, Social Support, and Psychological Adjustment Among African American College Students[END_REF]. Among college women, women of color report higher perceived discrimination than White women [START_REF] Daftary | Discrimination, depression, and anxiety among college women in the Trump era[END_REF].

Research comparing gender diverse college students with cisgender males/females found that not only did gender diverse students have significantly more discriminatory experiences, but they were also less likely to report these events to campus officials [START_REF] Thompson | Gender diverse college students' perceptions of climate and discriminatory experiences[END_REF].

Another study that assessed student perceptions of a nondiscriminatory climate on college campuses found that lesbian, gay, and bisexual students had lower scores (indicating worse perceptions) than cisgender, heterosexual students; transgender students scored lower even when compared with lesbian, gay, and bisexual students [START_REF] Dugan | Transgender College Students: An Exploratory Study of Perceptions, Engagement, and Educational Outcomes[END_REF].

More specifically, racial/ethnic, gender, and sexual minority college students experience hate crimes, hate speech, and microaggressions more often than White, cis-gender, male students. Microaggressions are commonplace and often subtle verbal, behavioral, or environmental offensive mechanisms, which can be intentional or unintentional, that communicate hostile, derogatory, or negative slights or insults [START_REF] Pierce | Offensive Mechanisms[END_REF][START_REF] Sue | Racial microaggressions in everyday life: Implications for clinical practice[END_REF].

A study of Black, female college students found that 96% experienced microaggressions at least a few times per year [START_REF] Donovan | Impact of Racial Macro-and Microaggressions in Black Women's Lives: A Preliminary Analysis[END_REF]. In Asian American college students, 78% of respondents reported experience of microaggressions during the two-week study period. A study of transgender college students found that 80% frequently or very frequently encountered gender binary microaggressions [START_REF] Woodford | A Mixed-Methods Inquiry Into Trans* Environmental Microaggressions on College Campuses: Experiences and Outcomes[END_REF]. Almost half of the gay, lesbian, bisexual, and queer college students (48%) experienced microaggressions in the past year [START_REF] Ylioja | Frequent Experience of LGBQ Microaggression on Campus Associated With Smoking Among Sexual Minority College Students[END_REF].

Hate speech is also prevalent on college campuses. While there is no internationally recognized definition of hate speech, one definition used by the United Nations describes hate speech as "any kind of communication in speech, writing or behaviour, that attacks or uses pejorative or discriminatory language with reference to a person or a group on the basis of who they are, in other words, based on their religion, ethnicity, nationality, race, colour, descent, gender or other identity factor" (United Nations, 2019). Much of the research on hate speech on college campuses examines legal issues [START_REF] Ceci | Who Decides What Is Acceptable Speech on Campus? Why Restricting Free Speech Is Not the Answer[END_REF][START_REF] Welshon | Hate Speech on Campus: What Public Universities Can and Should Do to Counter Weaponized Intolerance[END_REF] such as those related to free speech. Others examine hate speech in the context of online forum prevalence.

One study examining a popular online discussion forum found that approximately 25% of the discussion forums for college students had more hate speech than similar non-college forums on the same website [START_REF] Saha | Prevalence and Psychological Effects of Hateful Speech in Online College Communities[END_REF].

Hate crimes on college campuses are also more often targeted towards racial/ethnic and sexual minorities. According to the Federal Bureau of Investigation (FBI), hate crimes are those in which the perpetrators act predicated on a victim's race, color, religion, or national origin (FBI, n.d.). A total of 958 hate crimes, defined by the National Center for Education Statistics (NCES) as "a criminal offense which is motivated, in whole or in part, by an offender's bias(es) against a race, religion, disability, sexual orientation, ethnicity, gender, or gender identity", were reported on college campuses in 2017, a slight increase from 2010 (n=928) (National Center for Education Statistics, 2020). The vast majority (77%) of hate crimes on campus were associated with the victim's race/ethnicity, religion, or sexual orientation (National Center for Education Statistics, 2020). Destruction, damage, and vandalism accounted for the largest proportion of hate crimes followed by intimidation and simple assault (National Center for Education Statistics, 2020).

Fear of discrimination.

Far less is known about fear of discrimination than actual discrimination as the literature on fear of discrimination is limited. Some studies have explored fear of discrimination among racial/ethnic and sexual minority groups. Multiple studies of transgender individuals have explored whether respondents delayed or avoided healthcare due to fear of discrimination from their healthcare provider [START_REF] Casey | Discrimination in the United States: Experiences of lesbian, gay, bisexual, transgender, and queer Americans[END_REF][START_REF] Glick | The Role of Discrimination in Care Postponement Among Trans-Feminine Individuals in the U.S. National Transgender Discrimination Survey[END_REF][START_REF] Seelman | Transgender Noninclusive Healthcare and Delaying Care Because of Fear: Connections to General Health and Mental Health Among Transgender Adults[END_REF]. More than one in six LGBTQ respondents reported avoiding health care settings due to fear of discrimination [START_REF] Casey | Discrimination in the United States: Experiences of lesbian, gay, bisexual, transgender, and queer Americans[END_REF]. Another recent study found that Asian Americans avoided the doctor and also avoided calling the police due to fear of discrimination [START_REF] Mcmurtry | Discrimination in the United States: Experiences of Asian Americans[END_REF]. A similar paper comparing Black and White respondents found enormous differences in these groups with a significantly higher prevalence of Black respondents (22%) compared with White respondents (3%) reporting avoidance of health care due to fear of discrimination; similar statistically significant disparities existed between Black (31%) and White (2%) respondents with respect to avoidance of calling the police due to fear of discrimination [START_REF] Bleich | Discrimination in the United States: Experiences of black Americans[END_REF].

There also have been studies of fear of discrimination among people with specific health conditions. One study of adults in New Zealand with mental health conditions reported that almost half of them reported fear of discrimination due to their mental health concern [START_REF] Peterson | Experiences of mental health discrimination in New Zealand[END_REF]. Another study of people living with HIV found that the majority of respondents experienced fear of discrimination [START_REF] Baros | Experiences of discrimination among people living with HIV in Serbia[END_REF]. In addition, there is a body of work discussing patients' and genetic counselors' fear of discrimination related to worry that insurance companies may discriminate against patients after learning of a genetic condition [START_REF] Rothenberg | Human genetics: Before It's Too Late--Addressing Fear of Genetic Information[END_REF].

Fear among university students. Fear of crime and victimization has been studied far more frequently than fear of discrimination among adolescent and college populations.

Determinants of fear of victimization include gender ( Grinshteyn et al., 2020;[START_REF] Grinshteyn | Individual-and neighborhood-level determinants of fear of violent crime among adolescents[END_REF][START_REF] Lee | The Role of Lifestyle and Personal Characteristics on Fear of Victimization among University Students[END_REF], race/ethnicity [START_REF] May | Predictors of fear of criminal victimization at school among adolescents[END_REF][START_REF] Grinshteyn | Minority Report: Prevalence of Fear of Violent and Property Crimes Among a Diverse College Sample[END_REF][START_REF] Grinshteyn | Individual-and neighborhood-level determinants of fear of violent crime among adolescents[END_REF], and sexual orientation [START_REF] Grinshteyn | Minority Report: Prevalence of Fear of Violent and Property Crimes Among a Diverse College Sample[END_REF][START_REF] Meyer | Sexual Orientation and Fear at Night: Gender Differences Among Sexual Minorities and Heterosexuals[END_REF]. Fear of victimization has been associated with adverse health outcomes among adolescents and college students including depression, anxiety, and substance use [START_REF] Couture | Effect of fear of victimization on hazardous alcohol drinking, tobacco, and marijuana use among university students: A tale of two sexes[END_REF][START_REF] Grinshteyn | Fear of violent crime and anxiety/depression among adolescents[END_REF]. However, little is known about fear of discriminatory violence (e.g., hate crimes, hate speech, microaggressions) in any population. To date, we are not aware of any other studies that have examined fear of hate crimes, hate speech, or microaggressions among university students and their predictors. However, given the common experience of discrimination among diverse groups on college campuses related to hate speech, hate crimes, and microaggressions, it is possible that the fear of these acts is even more widespread than their actual experience, which is already highly prevalent. Research shows that fear of violence is often more widespread than the experience of violence; while crime has decreased over time [START_REF] Gramlich | Voters' perceptions of crime continue to conflict with reality[END_REF], fear of crime has remained steady (Gallup, 2019). It is likely that fear of discrimination is also even more prevalent than the experience of discrimination among groups that experience discrimination at high rates. Thus, this is an important public health issue to understand and prevent.

Study objectives.

The objectives of this study are to i) determine the prevalence of fear of discriminatory violence as measured by fear of hate crimes, fear of hate speech, and fear of microaggressions in universities and ii) assess sociodemographic correlates of fear of hate crimes, fear of hate speech, and fear of microaggressions. Better understanding the determinants of fear of discriminatory violence among a diverse university sample is necessary in order to design interventions that can help reduce fear among these groups.

Methods

Sample. This study employed a cross-sectional convenience sample of undergraduate and graduate university students at an urban university that is considered one of the most diverse in the U.S. (U.S. News & World Report, n.d.). Eligibility criteria included being 18 years of age or older, being a current student at the university, and being able to give informed consent. Some students (n = 183) aged 16 and 17 years old responded to the survey and were included in the final sample after an addendum to the Institutional Review Board (IRB) was approved to allow these students to be included in the sample. Recruitment emails were sent to all university students inviting them to fill out this online, self-administered, standardized questionnaire. The questionnaire included questions about sociodemographic characteristics and fear outcomes. Participants who consented to participate could then be entered into a raffle to win participation prizes if they chose to provide their contact information in a separate form that was not linked to their survey data. Data were collected between October and November of 2017. This study was reviewed and approved by the IRB for the Protection of Human Subjects at the University of San Francisco.

Variables. The outcome of interest assessed fear of discriminatory violence using three questions about fear of hate crimes, hate speech, and microaggressions. Respondents were asked, "On a scale of 0 to 10 where 0 = no fear and 10 = maximum fear, how afraid are you about becoming a victim of any of these forms of victimization during the next year?" This question was asked separately for (a) hate crimes, (b) hate speech, and (c) microaggressions. These questions were adapted from previous fear of victimization measures that use similar 0 to 10 scales to ask about fear of or worry about a number of different forms of victimization [START_REF] Williams | Worry about victimization: An alternative and reliable measure for fear of crime[END_REF].

Sociodemographic correlate variables included age, which was categorized into those aged 16-20 years, 21-25 years, 26-30 years, and over 30 years. Race/ethnicity included a comprehensive set of categories including White, Black, Hispanic, American Indian or Alaskan Native, Asian, Native Hawaiian or Pacific Islander, and Middle Eastern. While Middle Eastern was not an originally assessed racial/ethnic category, a large number of students wrote this in and indicated "Race Not Included" thus, a category was created. Students were categorized as being one of these race/ethnicities or identified as multiracial if more than one was indicated.

Respondents self-identified as male, female, or transgender/gender nonconforming. Sexual orientation included categories for straight, gay, lesbian, bisexual, or not included. Respondents' citizenship was categorized as either being a US citizen or not being a US citizen. Religious affiliation included Catholic, Christian, Buddhist, Hindu, Jewish, Muslim, other faiths, or unaffiliated categories.

Statistical Analysis. Mean scores were calculated for fear of microaggressions, fear of hate crimes, and fear of hate speech. To compare fear scores within each sociodemographic correlate, mean scores for each fear outcome were compared using nonparametric tests as these were not normally distributed. Mann-Whitney (Wilcoxon rank sum tests) and Kruskal-Wallis tests were used to compare differences between groups in each of the three fear variables.

Results

Sociodemographics. The largest percentage (47.77) of respondents were 20 years of age or younger (Table 1). The sample was mostly female (71.8%) while 26.1% were male and 2.1% reported being transgender or gender nonconforming. This sample was 32.6% White, 28.5% Asian, 17.1% Hispanic, 14.2% multiracial, 5.5% Black, 1.5% Middle Eastern, and less than 1% Native Hawaiian/Pacific Islander. The majority of students reported their sexual orientation as straight (82.5%) while 4.4% reported being gay, 1.5% reported being lesbian, 7.7% reported being bisexual, and 3.6% reported a sexual orientation that was not included. US citizens accounted for 86.6% of this sample. While 38.9% of students reported being unaffiliated with a religion, 32.4% reported being Catholic, 15.8% reported being Christian, with the rest of the sample split between being other religions or faiths. Mean scores (Table 2) were highest for fear of microaggressions (mean: 3.40, SD: 3.37) followed by fear of hate speech (mean: 2.79, SD: 3.12) and fear of hate crimes (mean: 2.57, SD: 3.09).

Fear of microaggressions. Black students had the highest mean scores for fear of microaggressions (mean: 6.08, SD: 3.72) followed by Middle Eastern students (mean: 4.20, SD: 3.41) and Hispanic students (mean: 4.15, SD: 3.41) (Table 3). Asian (mean: 3.50, SD: 3.31), multiracial (mean: 3.42, SD: 3.42), and Native Hawaiian/Pacific Islander (mean: 3.25, SD: 3.81) students also had elevated fear of microaggressions with White students scoring lowest (mean: 2.40, SD: 2.88) (p<0.0001). Transgender and gender nonconforming students scored highest on fear of microaggressions (mean: 6.34, SD: 3.47) followed by females (mean: 3.73, SD: 3.35) with males having the lowest fear of microaggressions (mean: 2.27, SD: 3.04) (p<0.0001).

Lesbian students reported the highest scores (mean: 6.35, SD: 3.44) for fear of microaggressions followed by students whose sexual orientation was not included (mean: 5.56, SD: 3.43), bisexual (mean: 4.78, SD: 3.21), and gay (mean: 4.47, SD: 3.41) students compared with heterosexual students (p<0.0001). Citizenship status and religion were not significantly associated with fear of microaggressions.

Fear of hate crimes. Fear of hate crimes scores were highest among Black (mean: 4.75, SD: 3.73), Middle Eastern (mean: 4.65, SD: 4.32), Native Hawaiian/Pacific Islander students (mean: 3.38, SD: 4.03), Hispanic (mean: 3.36, SD: 3.21), and Asian (mean: 3.10, SD: 3.21) students compared with White students (p<0.0001). Gender was significantly associated with fear of hate crime (p<0.0001) with transgender and gender nonconforming students having the highest scores (mean: 4.93, SD: 3.89) followed by female students (mean: 2.71, SD: 3.13) compared with males. Sexual orientation was also associated with fear of hate crimes with gay students reporting the highest scores (mean: 4.69, SD: 3.27) compared to heterosexual students (p<0.0001). Scores were also elevated among lesbian (mean: 4.21, SD: 3.59), those with a sexual orientation not included (mean: 3.63, SD: 3.21), and bisexual students (mean: 3.19, SD: 3.04). Citizenship status was associated with fear of hate crimes (p=0.02) with students who were not US citizens (mean: 3.15, SD: 3.43) reporting more fear of hate crimes than those who were US citizens (mean: 2.48, SD: 3.03). Age and religion were not significantly associated with fear of hate crimes.

Fear of hate speech. Race/ethnicity was also associated with fear of hate speech (Table 3) among university students (p<0.0001) with Black students scoring highest (mean: 5.06, SD: 3.61) followed by Middle Eastern (mean: 4.10, SD: 3.63), Hispanic (mean: 3.64, SD: 3.28), Asian (mean: 3.11, SD: 3.13), multiracial (mean: 2.60, SD: 3.03), and Native Hawaiian/Pacific Islander students (mean: 2.38, SD: 2.88) compared with White students.

Gender was also significantly associated with fear of hate speech (p<0.0001) with transgender and gender nonconforming students experiencing the highest scores (mean: 5.82, SD: 3.59) followed by female (mean: 2.97, SD: 3.16) students with male students experiencing the lowest mean score (mean: 2.08, SD: 2.76). Sexual orientation was significantly associated with fear of hate speech (p<0.0001) with lesbian students experiencing the highest score (mean: 5.05, SD: 3.22) followed by those with a sexual orientation not included (mean: 4.68, SD: 3.38), gay students (mean: 4.53, SD: 3.31), and bisexual students (mean: 3.81, SD: 3.23) compared to heterosexual students. Age, citizenship, and religion were not significantly associated with fear of hate speech among university students.

Discussion

This research is the first study that we are aware of that assesses multiple forms of fear of discriminatory violence and its correlates among a diverse university sample. Our results show that racial, gender, and sexual minorities are more likely to experience all three forms of fear of discrimination, highlighting the disparities in experience of fear. Race/ethnicity was significantly associated with fear of microaggressions, fear of hate crimes, and fear of hate speech with Black students having the highest scores for all three followed by Middle Eastern students. Fear of microaggressions, fear of hate crimes, and fear of hate speech scores were higher among transgender and gender nonconforming students followed by females. Sexual orientation was also significantly associated with fear of microaggressions, fear of hate crimes, and fear of hate speech with lesbian students reporting the highest scores for fear of microaggressions and fear of hate speech and gay students reporting the highest scores for fear of hate crimes. It is important to understand fear of these specific forms of discriminatory violence and their higher prevalence in minority groups. A better understanding of fear of discriminatory violence and the disparities in the experience of these fears is necessary in order to ultimately prevent it.

While these specific fears are not often studied in this population or other populations, our results support findings from previous research showing that fear is higher in minority populations. Fear of violence among transgender and gender nonconforming students is significantly higher than among males or females [START_REF] Grinshteyn | Minority Report: Prevalence of Fear of Violent and Property Crimes Among a Diverse College Sample[END_REF]. Fear of violence among students of a variety of race/ethnicities is much higher than among white students [START_REF] Grinshteyn | Minority Report: Prevalence of Fear of Violent and Property Crimes Among a Diverse College Sample[END_REF]. This research finds similar patterns for fear of hate speech, fear of hate crimes, and fear of microaggressions. In addition, while the literature is scant of fear of discrimination, there is quite a bit of literature showing the high prevalence of experiencing discrimination among racial/ethnic, gender, and sexual minorities [START_REF] Cokley | Impostor feelings as a moderator and mediator of the relationship between perceived discrimination and mental health among racial/ethnic minority college students[END_REF][START_REF] Daftary | Discrimination, depression, and anxiety among college women in the Trump era[END_REF][START_REF] Dugan | Transgender College Students: An Exploratory Study of Perceptions, Engagement, and Educational Outcomes[END_REF][START_REF] Juang | Perceived Racial/Ethnic Discrimination and Adjustment Among Ethnically Diverse College Students: Family and Peer Support as Protective Factors[END_REF][START_REF] Prelow | Perceived Racial Discrimination, Social Support, and Psychological Adjustment Among African American College Students[END_REF][START_REF] Thompson | Gender diverse college students' perceptions of climate and discriminatory experiences[END_REF].

The findings presented in this paper suggest that similarly, the fear of hate crimes, fear of hate speech, and fear of microaggressions are also higher among these same groups, which fits with the existing literature on the experience of these acts.

Limitations. This study was a convenience sample. Those who responded to the survey may not be representative of the general population of university students. In addition, Asian, Hispanic, and multiracial students were overrepresented in our sample. While these analyses are more representative of fear of discriminatory violence among minority populations, which was the intent of this research, it may not be representative of all university students. These data are cross-sectional; sociodemographic correlates and fear of discriminatory violence were only assessed at one point in time. Thus, causality cannot be established. In addition, these are new measures. While these were adapted from a number of existing measures of fear of crime that measure these variables on a scale from zero to ten, they are new measures that have not been validated. Thus, measurement error may occur using these novel assessments.

Implications. More research needs to be done to better understand fear of discriminatory violence. Compared to fear of crime and violence, these are newer concepts that have been researched less within the literature that examines fear. Yet, it is clear that these are concerns that need to be better understood especially among racial/ethnic, gender, and sexual minority populations who experienced fear of discriminatory violence at higher levels. Research should continue to understand the determinants and consequences of these fears among high-risk university students using longitudinal study design to better assess the temporality of the relationships. Previous research has established that fear of violent victimization has been associated with depression and anxiety [START_REF] Grinshteyn | Fear of violent crime and anxiety/depression among adolescents[END_REF][START_REF] Lee | The Role of Lifestyle and Personal Characteristics on Fear of Victimization among University Students[END_REF] among adolescents and substance use among college students [START_REF] Couture | Effect of fear of victimization on hazardous alcohol drinking, tobacco, and marijuana use among university students: A tale of two sexes[END_REF]. Future research should examine whether fear of discriminatory violence is also associated with these deleterious mental health outcomes. Finally, research should also determine whether the experience of discrimination is associated with fear of discrimination.

Universities must consider the prevalent experience of fear of discrimination, especially among minority students and plan to address them using the existing university infrastructure (e.g., mental health services, health services, and offices of diversity, student services, student life, and housing). Leveraging these stakeholders and the existing university infrastructure to address fear of hate crimes, hate speech, and microaggressions would be imperative in orchestrating a multilevel response to address fear of discriminatory violence among university students.

While previous work has not been done, to our knowledge, to understand how to reduce fear of discriminatory violence, there are many interventions that have been tested to reduce actual discrimination among adolescents and college students. Gay-straight alliances and antihomophobic bullying policies have been associated with reduced discrimination among LGB adolescents [START_REF] Saewyc | School-Based Strategies to Reduce Suicidal Ideation, Suicide Attempts, and Discrimination among Sexual Minority and Heterosexual Adolescents in Western Canada[END_REF]. Research shows that talking about race may reduce prejudice among students [START_REF] Aboud | Exploring and Evaluating School-Based Interventions to Reduce Prejudice[END_REF] while other work that trained participants on stereotype replacement, counter-stereotypic imaging, individuation, perspective talking, and increasing opportunities for contact saw increases in concern about discrimination and awareness of bias [START_REF] Devine | Long-term reduction in implicit race bias: A prejudice habit-breaking intervention[END_REF]. While these interventions were aimed at reducing discrimination, perhaps a positive externality of these types of programs would be that they may also reduce fear of discriminatory violence, though that would need to be formally tested.

In conclusion, universities must take seriously the prevalence of fear of hate crimes, fear of hate speech, and fear of microaggressions among diverse students, especially racial/ethnic, gender, sexual minorities. Using the existing university infrastructure to address this fear could result in effective reductions in fear of discriminatory violence among university students. This is a novel area of research, and more must be done to better understand this emerging public health issue.

Table 1 .

 1 Sociodemographic characteristics of university students (n=1,415).

	Characteristic

a Native Hawaiian/Pacific Islander b Gender non-conforming

Table 2 .

 2 Mean fear of discriminatory violence scores among university students (n=1,415).

	Fear Outcome

Table 3 .

 3 Correlates of fear of discriminatory violence among university students (n=1,415).

		F
		e
		ar
		o
		f
		m
		ic
		r
		o
		a
		g
		g		Fear of hate crimes		Fear of hate speech
	Characteristic	re
		ss	p-value	Mean (SD)	p-value	Mean (SD)	p-value
		io
		n
		s
		M
		e
		a
		n
		(
		S
		D
		)
	Age		0.002		0.41		0.09
	16-20	3.		2.57 (3.08)		2.67 (3.05)
		1
		6
		(
		3.
		1
		9


Stefania Carapezzi

Corentin Delacour
email: corentin.delacour@lirmm.fr

Gabriele Boschetto

Elisabetta Corti

Madeleine Abernot
email: madeleine.abernot@lirmm.fr

Thierry Gil
email: thierry.gil@lirmm.fr

Siegfried Karg

Aida Todri-Sanial

Multi-Scale Modeling and Simulation Flow for Oscillatory Neural Networks for Edge Computing 1 st

Keywords: Oscillatory neural networks (ONN), density functional theory (DFT), technology computer aided

An oscillatory neural network (ONN) is a neuromorphic computing paradigm based on encoding of information into the phases of oscillators. In this paper we present an ONN whose elemental unit, the "neuron", is implemented through a beyond-CMOS device based on vanadium dioxide (VO2). Such ONN technology provides ultra-low power solutions for performing pattern recognition tasks, and it is ideally suited for edge computing applications. However, exploring the groundwork of the beyond-CMOS ONN paradigm is mandatory premise for its industry-level exploitation. Such foundation entails the building of a holistic simulation flow from materials and devices to circuits, to allow assessment of ONN performance. In this work we report results of this advanced designing approach with special focus over the VO2 oscillator. This establishes the ground to scale up to evaluate beyond-CMOS ONN functionalities for pattern recognition.

I. INTRODUCTION

Systems of biological neurons can be mimicked by neural networks, with the neurons emulated after the McCulloch-Pitts [START_REF] Hopfield | Neural networks and physical systems with emergent collective computational abilities[END_REF] or "integrate and fire" [START_REF] Kandel | Principles of Neural Science[END_REF] models. However, neural systems can be modeled also as periodic oscillators. For instance, features of the visual system are reproduced via nonlinear oscillatory network. In last years, a novel neuromorphic architecture has been suggested [START_REF] Hoppensteadt | Oscillatory neurocomputers with dynamic connectivity[END_REF] based on an ensemble This work was supported by the European Union's Horizon 2020 research and innovation programme, EU H2020 NEURONN (www.neuronn.eu) project under Grant 871501. of coupled oscillators. In such oscillatory neural networks (ONNs) the information is hold by the phases of the oscillators. The coupling laws among the oscillators determine the phase relations among them. It has been demonstrated that the ONNs work as Hopfield neural networks with limit cycles as attractors [START_REF] Hoppensteadt | Oscillatory neurocomputers with dynamic connectivity[END_REF]. Thus, the phase-locked synchronized states yield the outcome of the ONN computation.

A Hopfield neural network realizes a "memory" that can be addressed by content, similarly to the biological associative memory. In this respect, it can perform pattern recognition, which is pivotal for edge artificial intelligence (AI)'s applications, such as surveillance or autonomous driving. By edge AI is meant the evolution of AI of bringing data processing the closest to the location where data are collected, that is our smart devices at the edge of the Internet-of-Things (IoT). The goal is to perform the data analysis at the user's level, differently to what happens in cloud computing where data have to be sent across Internet. Applications of edge AI pose a serious constrain over power consumption, given that edge devices possess reduced power resources. ONN presents an alternative paradigm that is suitable for computing at the edge due to its low power computing capability. For instance, the embedding of information into oscillator's phase is a power-saving solution compared to its encoding into oscillator's amplitude. Also, ONNs have demonstrated fast operation speed that makes them ideally suited for real-time data processing.

In this work we present an innovative implementation of the ONN paradigm to target ultra-low power neuromorphic computing at the edge. We explore beyond-CMOS devices based on vanadium dioxide (VO 2 ) for the realization of the fundamental block of the ONN architecture, the oscillator emulating the neuron. The capability of optimizing an ONN architecture with respect to its functionalities is a mandatory step towards the industrial exploitation of this technology. In this context, the assessment of the ONN dynamics and phaselocking synchronization is a necessary premise. In literature, the ONN concept is mainly discussed in terms of mathematically abstract models [START_REF] Maffezzoni | Oscillator array models for associative memory and pattern recognition[END_REF]. Here, we provide an exploratory design flow from materials and devices to circuit-level to enable ONN performance and power assessment. Then, the setting-up of an advanced design toolbox dedicated to beyond-CMOS ONN is an important first step toward achieving technological maturity. This advanced simulation toolchain will encompass all the aspects of interest of the beyond-CMOS ONN, from materials (through atomistic simulations) to devices (by means of technology-computer-aided-design, TCAD) up to circuits (simulations performed through mixedmode approach and compact models). In this paper, we report the results obtained from such simulation flow with the focus on investigating the beyond-CMOS oscillator (Fig. 1). The simulation flow serves as the exploratory toolbox to scale up ONN circuit level description and evaluate its performance on the pattern recognition task.

II. VO 2 NEURON

A. Material

Among the transition metal oxides (TMOs), VO 2 has attracted interest because its phase transition occurs near room temperature (∼340 K). It causes a remarkable change in its physical properties, and in particular the material's resistivity varies up to 5 orders of magnitude within a temperature window of 0.1 K for pristine VO 2 . Furthermore, the phase transition is reversible, and often shows hysteretic behavior. Such low-temperature, ultrafast, and reversible switching is a technological advantage over "traditional" TMOs, and enables the use of VO 2 for ultrafast memory switches and memory devices.

From a structural perspective, above 340 K VO 2 has a tetragonal rutile-like (R) crystal structure where the distance between V atoms along the c axis is constant throughout the lattice, and is 2.96 Å. Notably, R-VO 2 shows metallic behavior with zero band gap. However, when VO 2 undergoes its phase transition a distortion in the lattice occurs, and V atoms dimerize with long (3.12 Å) and short (2.65 Å) distances. This breaks the crystal symmetry, and causes a shift to the monoclinic (M1) structure with non-vanishing band gap. This is commonly referred to as metal-to-insulator transition (MIT).

The vast majority of theoretical studies on VO 2 is about the mechanism leading to the MIT that is now believed to be a cooperative Mott-Peierls [START_REF] Chen | Calculation evidence of staged Mott and Peierls transitions in VO2 revealed by mapping reduced-dimension potential energy surface[END_REF]. However, significantly less studied is the interaction between VO 2 and the metal electrode in a typical device architecture, which can provide useful insights into device-level properties. Atomistic simulations of this kind are challenging, as one has to explicitly construct the VO 2 /metal interface geometry, and thus investigating the different possible surface terminations of VO 2 becomes pivotal. Furthermore, an in-depth understanding of VO 2 surfaces is also relevant in order to explore grain boundaries, as it has been observed that the strain caused by the lattice mismatch is able to affect the properties of the MIT, such as the transition temperature and the hysteresis window [START_REF] Yang | Suppression of structural phase transition in VO2 by epitaxial strain in vicinity of metal-insulator transition[END_REF].

In this regard, a limited number of density functional theory (DFT) studies are available in the literature: for instance, focusing on the insulating phase, DFT simulations were carried out on the monoclinic VO 2 (011) surface in order to compute its electronic properties for catalytic applications [START_REF] Haras | Electronic properties of the VO2 (011) surface: density functional cluster calculations[END_REF]. The effect of doping on VO 2 surfaces has also been explored [START_REF] Yang | Suppression of structural phase transition in VO2 by epitaxial strain in vicinity of metal-insulator transition[END_REF], and results suggest that tuning the material's work function by doping could correlate with a change in the transition temperature.

Ultimately, the aim of our atomistic simulations is to bridge the gap between material's and device properties by constructing VO 2 /metal interface models that will enable the prediction of relevant material-(band gap, work function) and device-level parameters (e.g., type of contact, interface thermal resistance) that will be fed in subsequent TCAD simulations.

B. TCAD simulation of Two-Terminal Device

TCAD has been a powerful propellant for the pathway to success of the silicon semiconductor technology. Nonetheless, the mainstream trends of device development (extreme miniaturization, beyond-Si materials) are currently defying the traditional TCAD models. In particular, in case of VO 2 , its temperature-induced phase change lies outside the standard semiconductor physics commonly provided by TCAD tools. For this reason, the electrical transport in VO 2 is usually emulated by modeling it as a resistor network [START_REF] Dai | Modeling of temperaturedependent resistance in micro-and nanopolycrystalline VO 2 thin films with random resistor networks[END_REF], and results on TCAD simulations of VO 2 devices are essentially missing as yet.

We present a TCAD approach suitable to cope with the resistive switching of VO 2 . To this aim, we customize the Phase Change Material (PCM) model available in Silvaco Victory Device TCAD tool [12]. This model is developed for phase change (PC) materials that pass from crystalline (low resistivity ρ) to amorphous state (high ρ) depending on T . PC materials are stable in crystalline/amorphous phase for T lower/higher than the critical temperatures T C,cryst / T C,am , thus therein ρ = ρ cryst /ρ = ρ am . In Silvaco TCAD tools PC materials are modeled as conductors whose local ρ is made dependent from local T through the PCM model. The hysteresis of experimental ρ vs T curves is accounted for through the Johnson-Mehl-Avrami model.

PC materials and VO 2 show similar behavior of ρ with T . However, the PCM model has to be adapted to simulate VO 2 , because ρ depends on T also when VO 2 is in semiconducting phase (T < T C,IMT,L ). We use a dedicated c-function to customize the PCM model and implement such behavior. We also introduce a T -dependence of the ρ for T > T C,IMT,H when VO 2 is in metallic phase, in agreement with experimental findings.

We use the customized PCM model to simulate experimental current vs voltage (I -V ) characteristics of a VO 2 device. This device consists of a VO 2 layer on top of a silicon dioxide substrate (Fig. 2d). The external heater which heats the device at 315.7 K is emulated as thermal boundary condition at the bottom part of the insulator. In VO 2 devices the resistive switching occurs while the current flows across the device. We use the PCM model for VO 2 and we perform electrothermal simulation to investigate the role of self-heating over the resistive change of VO 2 . Fig. 2a shows the good match achieved between simulated (blue line) and experimental (cyan symbols) data. This is a validation of our customized PCM approach to simulate a VO 2 device. Also, it supports that selfheating is triggering the resistive change of VO 2 , as it has been conjectured [START_REF] Li | Joule Heating-Induced Metal-Insulator Transition in Epitaxial VO2/TiO2 Devices[END_REF]. self-heating and 2) T -dependence of ρ. This results to be in agreement also with experimental findings [START_REF] Zimmers | Role of Thermal Heating on the Voltage Induced Insulator-Metal Transition in VO 2[END_REF]. Fig. 2e and f are 2D maps of lattice temperature and resistivity, respectively, as extracted in β point of I -V of Fig. 2a. As it can be seen, the temperature varies across the VO 2 due to Joule heating effect, and this mirrors in a consequent change of the local resistivity (see also Fig. 2c).

The next step is to embed the device physics as provided by the TCAD I -V into the circuit level simulation of the oscillator at room temperature. To this aim, we simulate I -V at 303 K (Fig. 2b, red line). It can be observed the impact of the ambient temperature over the I -V s, especially the voltage and current values at which the IMT occurs. Then, we feed this TCAD I -V into a Matlab circuit solver tool used to perform the simulation of the oscillator circuit, as it is described in the next section. Our aim is to join up the device level description inside the circuit level simulation (Fig. 1).

C. Oscillator Circuit Simulation

In our beyond-CMOS ONN, the neuron is modeled as a compact relaxation-oscillator made of a VO 2 device in series with a resistor. This highly scalable architecture is shown in Fig. 3a and has been validated experimentally [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF], [START_REF] Corti | Resistive Coupled VO2 Oscillators for Image Recognition[END_REF]. It yields output oscillations at the node V out for a certain range of supply voltage V DD and biasing resistor R S . The voltage V applied to the VO 2 device is driven by V DD and V out across the output capacitor C P . A hysteresis window is defined by the two threshold voltages, V L and V H , corresponding to the occurrence of MIT and IMT respectively (Fig. 3b). To obtain oscillations, the bias current line I L = (V DD -V )/R S must intercept the current I of the VO 2 device in its hysteresis window. Indeed, it is in this region that a Negative Differential Resistance (NDR) takes place -visible in the I -V curve when the VO 2 is driven by a current source (Fig. 2b) -from which we can form an unstable fixed point to get oscillations.

To simulate the VO 2 -oscillator dynamics, we solve the circuit equation expressed by Kirchhoff's law:

C P dV dt = I L -I (1)
This first-order differential equation can have oscillatory solutions thanks to the hysteresis relationship between I and V . One way to model it at circuit-level is to use a comparator with a positive feedback as in [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF]. In this compact model, the comparator continuously stores the time-dependent VO 2 state and switches abruptly when the device voltage V reaches one of the two thresholds V L or V H . Hence, it is only near MIT or IMT that the VO 2 resistance varies significantly. Otherwise, the VO 2 resistance is rather constant and is either R met or R ins . The dynamics can then be interpreted as simple cycles of RC-charges and discharges. However, TCAD simulations that fit experimental data show a non-linear resistance while VO 2 is in insulator state (right-hand side of Fig. 3b). R ins decreases when V grows in the hysteresis window, due to the combined effect of 1) self-heating and 2) temperaturedependence of resistivity (Fig. 2c).

( V DD = 3V. The dashed line is obtained with the compact model [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF] and parameters:

VO2 R S C P V DD V out V I L I C p dV dt = I L -I V L V H Metallic NDR region Insulator I L (c) (d) VDD = 3.5 V VDD = 3 V ΔI I L TCAD lookup table VO2 compact model TCAD lookup table VO2 compact model a) (b)
Rmet = 3.822 kΩ, R ins = 246.2 kΩ, V H = 2.818V,V L = 2.
424V, α = 200 and τ 0 = 10 ns. Solid lines are TCAD results: I -V relationship in insulator state is non-linear. (c) and (d): comparison between oscillatory behavior as generated by the model [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF] and through our TCAD approach for V DD = 3.5V and 3V, respectively. The simulation time-step is 1 ns. In the last example, our method gives different results as C P 's discharge slows down before IMT. To take into account this non-linearity during circuit simulations, we build a Matlab circuit solver that takes as inputs the VO 2 I -V data from TCAD simulations and the ONN architecture description -number of oscillators, circuit parameters, coupling elements and input signals -(Fig. 1). More precisely, we numerically solve (1) by using Euler's method and by keeping track of the VO 2 state. We extract the VO 2 resistance at every time step by interpolating TCAD data stored in a lookup table.

Comparison between our TCAD-based circuit solver and the model [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF] are presented for V DD = 3.5 V and V DD = 3 V in Fig. 3c andd, respectively. In the first case -yellow load line -, we observe almost no variation between the two approaches. Indeed, if we label ∆I the difference between the current extracted with TCAD and the one with the model [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF], we have I L >> ∆I so (1) does not change significantly and there is small discrepancy between the two circuit-solving methods. However, in the second example -magenta load line -I L (V H ) ≈ 2 ∆I(V H ) thus dV /dt is more affected before IMT. This situation is likely to occur as I L is generally set as low as possible by increasing R S or by decreasing V DD to minimize the ONN energy consumption. Using our TCAD approach, we predict that the output oscillation slows down because of the gradual decrease of R ins in the hysteresis window. Consequently, the ONN computation time -given by multiple oscillation periods -increases along with the energy. Therefore, we believe that the non-linearity in the VO 2 insulator state should be considered for accurate ONN simulation and energy assessment.

To further illustrate the impact of non-linearity in the VO 2 insulator state, we simulate two oscillators coupled by R C = 10 kΩ (Fig. 4). The second oscillator is turned-on 300 ns after the first one which is 10% of the oscillation period based on the compact model [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF]. For a pattern recognition application [START_REF] Corti | Resistive Coupled VO2 Oscillators for Image Recognition[END_REF], the two coupled oscillators correspond to a first white pixel and a second light-gray pixel of an input image. Intuitively, we would expect the two oscillators to converge to an in-phase relationship as the compact model [START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF] predicts (Fig. 4a), because the oscillators are initialized with a small delay with respect to the oscillation period. However, by using our TCAD approach we observe the opposite outcome (Fig. 4b), i.e the two oscillators converge to an out-of-phase relationship. Hence, considering non-linearity in VO 2 insulator state is key for precise ONN circuit simulation. Finally, we believe our TCAD-based circuit solver is a step toward more robust ONN design and training, as we can also analyze the influence of various factors such as material parameters or ambient temperature.

III. CONCLUSION

In this work we present an innovative ONN architecture whose basic element, the "neuron", is realized as an oscillator based on vanadium dioxide (VO 2 ). Such ONN promises to provide ultra-low power technology for pattern recognition tasks in IoT applications. However, to guide its physical realization a robust design procedure is required. This entails the building of an advanced simulation toolchain (Fig. 1) to cover from materials to devices up to circuits, for the assessment of ONN functionality. We show the development of this advanced designing approach with special focus over the VO 2 oscillator. We succesfully perform electrothermal simulation of experimental VO 2 devices by customizing the Silvaco TCAD PCM model. In particular, we account the non Ohmic behavior of the I -V below IMT with the interplay between 1) selfheating and 2) T -dependence of ρ. Also, our results support the role of self-heating in driving the phase transition in VO 2 . Then, we feed the TCAD I -V into a Matlab circuit solver tool to simulate the dynamics of the VO 2 compact relaxation-oscillator. Our simulation approach is able to link the device physics to the circuit level description. Especially, we assess the impact of the non-linearity of resistance in the VO 2 insulator state in the oscillatory behavior, and, in turn, over a proof-of-concept pattern recognition task. Thus, our TCAD-based circuit solver is a first step toward more robust ONN design and training. As future work, we plan to analyze the influence of various factors such as material parameters or ambient temperature over VO 2 oscillator behavior.

Figure 1 .

 1 Figure 1. Advanced design toolbox for the simulation workflow of the VO 2 oscillator.

  Fig. 2c plots the local ρ, probed inside VO 2 , vs the local T . It should be noticed that the non Ohmic behavior of I -V below IMT is fully explained with the interplay between 1)

Figure 2 .

 2 Figure 2. (a) Simulated (blue line) and experimental (cyan symbols) I -V of VO 2 device. The device has been heated up to 315.7 K by an external heater. (b) Simulated I -V s at the external temperature T of 315.7 k (blue line) and of 303 k (magenta line). (c) Local resistivity probed within VO 2 . The IMT switching is highlighted as α point of I -V in panel (a) and of resistivity vs temperature in panel (c). (d) Structure of the 2D simulated device. A 53-nm thick VO 2 layer sits on top of an insulator layer. The VO 2 channel length is of 0.4 µm, the channel width is 1 µm. The thermal conductivity of 0.06 W / (cm K) [13] is used in electrothermal simulations. The temperature of the lower boundary of the insulator substrate is set at 315.7 K. (e) Temperature and (f) resistivity 2D plots across the VO 2 layer as extracted in β point of I -V of panel (a).

Figure 3 .

 3 Figure 3. (a) VO 2 -based oscillator with R S = 4 kΩ and C P = 500 pF. (b) VO 2 I-V curve at 303 K and load lines -yellow: V DD = 3.5V and magenta:V DD = 3V. The dashed line is obtained with the compact model[START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF] and parameters:Rmet = 3.822 kΩ, R ins = 246.2 kΩ, V H = 2.818V,V L = 2.424V, α = 200 and τ 0 = 10 ns. Solid lines are TCAD results: I -V relationship in insulator state is non-linear. (c) and (d): comparison between oscillatory behavior as generated by the model[START_REF] Maffezzoni | Modeling and Simulation of Vanadium Dioxide Relaxation Oscillators[END_REF] and through our TCAD approach for V DD = 3.5V and 3V, respectively. The simulation time-step is 1 ns. In the last example, our method gives different results as C P 's discharge slows down before IMT.

Figure 4 .

 4 Figure 4. Two oscillators coupled by R C = 10kΩ. Oscillator 2 is turnedon 300 ns after Oscillator 1. They represent pixels for pattern recognition applications -white=in-phase and black=out-of-phase -. a) Simulation using the compact model [15]. b) Using our TCAD method.


Madeleine Abernot

Gabriele Boschetto

Stefania Carapezzi

Corentin Delacour

Thierry Gil

Aida Todri-Sanial

FPGA Implementation of Oscillatory Neural Networks for Artificial Intelligence Edge Computing

published or not. The documents may come   L'archive ouverte pluridisciplinaire

▪Oscillatory Neural Networks with phase computation for energy-efficient analog circuit design [START_REF] Todri-Sanial | NEURONN: Two-Dimensional Oscillatory Neural Networks for Energy Efficient Neuromorphic Computing[END_REF] ▪Learning to define weights with patterns using unsupervized Hebbian Learning rule [START_REF] Morris | The Organization of Behavior[END_REF]. ▪Inference to retrieve a learnt pattern from a noisy one.

CONCLUSION

▪Development of a proof of concept of the ONN computing paradigm with a digital design implemented on FPGA. ▪Use of the digital ONN for image recognition from a camera stream respecting real-time constraints. ▪Combination of two digital ONNs in-a-row to perform obstacle avoidance on an arduino robot using 8 proximity sensors.

FPGA

  implementation of Oscillatory Neural Networks for Artificial Intelligence edge computing Madeleine Abernot, Gabriele Boschetto, Stefania Carapezzi, Corentin Delacour, Thierry Gil, Aida Todri-Sanial Microelectronics Department, LIRMM, University of Montpellier, CNRS, Montpellier, France MOMO MOTIVATION AND GOALS ARTIFICIAL INTELLIGENCE AT THE EDGE ▪Support online learning ▪Excellent inference engine ▪Low power consumption ▪Scalable/low cost ▪Bandwidth (inference/second) ▪Latency (frames/second) ▪Privacy concerns ▪Power consumption The NeurONN project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 871501. ACKNOWLEDGEMENTS AND FUNDING www.neuronn.eu Project page Project Channel Project Channel ▪ Energy-efficient Analog ONN Architecture Design ▪ ONN Dynamics Control ▪Obstacle avoidance with an Arduino robot and 8 proximity sensors (5x8 ONN) ▪Digits recognition from a camera stream to an HDMI screen (10x6 ONN)

ONN size Synapses FPGA resources LUTs Flip-Flops Initialization time (us) Computation time (us)

								NEUROMORPHIC COMPUTING
									M patterns
										𝑊 𝑖𝑗 =	1 𝑀	𝑘	𝜉 𝑘𝑖 𝜉 𝑘𝑗 =	𝑊 11 ⋯ 𝑊 1𝑖 ⋮ ⋱ ⋮ 𝑊 𝑖1 ⋯ 𝑊 𝑖𝑖
							FPS	Results and Performances		ONNs			ONN 5x8	ONN 1x8
								Frequency	37,5 MHz	#Training Patterns		256	16
	5x3	225	1,8%	0,68%	2	5,2	141000	ONN Computation time	5 µs -10 µs	Frequency			12 MHz	12 MHz
	10x6	3600	12%	2,6%	7,8	5,4	75000	Accuracy (test set = 25	76 %	ONN computation time	24 us	17 us
								corrupted digits)		Accuracy			100 %	74 %
										Full system
										FPS			40
										8-s measure time		18 ms

Battery, Current Cons., Robot life time 6V/2850 mAh, 700 mA, 4h

Table 1 :

 1 Results and performances of the digital ONN design for multiple ONN sizes -a 5x3 ONN with 15 neurons and a 10x6 ONN with 60 neurons

Table 2 :

 2 Results and performances of the digit recognition application using images from a camera stream

Table 3 :

 3 Results and performances of obstacle avoidance application using 8 proximity sensors


Djamaleddine Djeldjli
email: djamaleddine.djeldjli@univ-lorraine.fr

Frédéric Bousefsaf
email: frederic.bousefsaf@univ-lorraine.fr

Choubeila Maaoui
email: choubeila.maaoui@univ-lorraine.fr

Fethi Bereksi-Reguig

Imaging Photoplethysmography: Signal Waveform Analysis

Keywords: photoplethysmography, pulse waveform, signal processing, camera, facial video processing

Imaging photoplethysmography (iPPG) is used to remotely measure the blood volume pulse using a camera. Traditionally, it has been employed to estimate heart and respiratory rates, and recently blood pressure and oxygen saturation. Biomedical engineering researchers have become increasingly interested in iPPG because of its several advantages as comfort, non-invasive, simple, nonstressful and inexpensive characteristics. Moreover, the results of the waveform signal analysis obtained by the conducted studies on contact PPG sensors made the use of iPPG a more promising technique for early screening of various atherosclerotic and cardiovascular pathologies. iPPG waveform has not been studied before. In this paper we process the iPPG signal obtained using a camera to extract its waveform features such as areas and time parameters. These features will make possible a non-contact estimation of arterial stiffness and early diagnosis of many cardiovascular pathologies. The obtained results show a high correlation with those obtained by an approved contact PPG sensor.

INTRODUCTION

Photoplethysmography (PPG) is an optical noninvasive technique used to determine blood volume changes in the microvascular bed of tissue [START_REF] Challoner | Photoelectric plethysmography for estimating cutaneous blood flow[END_REF]. The PPG technology has been used in wide range of commercialized medical devices for the assessment of heart rate, oxygen saturation, blood pressure and cardiac output, autonomic function and also detection of peripheral vascular pathologies [START_REF] Allen | Photoplethysmography and its application in clinical physiological measurement[END_REF]- [START_REF] Miyai | Noninvasive assessment of arterial distensibility in adolescents using the second derivative of photoplethysmogram waveform[END_REF]. However, in some critical cases, such as burns, traumas, contagious diseases and severe infections, the use of contact PPG sensor is not always possible. Also contact sensors interfere with the subject by producing a psychological stress which can affect the measurement. These various limitations of contact PPG make the use of contactless photoplethysmography more attractive for the measurement and the monitoring of cardiovascular data.

Imaging photoplethysmography allows to determine physiological data such as blood volume pulse remotely, without any skin contact. This is achieved by the analysis of facial video based on subtle momentary changes in the subject's skin color which are not noticeable to the human eye. iPPG has recently attracted increasing interest especially in cardiac activity [START_REF] Bousefsaf | Peripheral vasomotor activity assessment using a continuous wavelet analysis on webcam photoplethysmographic signals[END_REF], [START_REF] Poh | Non-contact, automated cardiac pulse measurements using video imaging and blind source separation[END_REF] and respiratory monitoring [START_REF] Bousefsaf | Continuous wavelet filtering on webcam photoplethysmographic signals to remotely assess the instantaneous heart rate[END_REF], [START_REF] Poh | Advancements in Noncontact, Multiparameter Physiological Measurements Using a Webcam[END_REF] driven by the demand for low cost, simple, portable, comfortable and non-stressful technology. It was also used for the assessment of mental stress [START_REF] Bousefsaf | Remote detection of mental workload changes using cardiac parameters assessed with a low-cost webcam[END_REF], oxygen saturation [START_REF] Shao | Noncontact monitoring of blood oxygen saturation using camera and dual-wavelength imaging system[END_REF]- [START_REF]Non-contact estimation of heart rate and oxygen saturation using ambient light[END_REF] and blood pressure measurements [START_REF] Jeong | Introducing contactless blood pressure assessment using a high speed video camera[END_REF]- [START_REF] Fan | Robust blood pressure estimation using an RGB camera[END_REF].

In this paper we present a particular pulse waveform analysis based on the detection of iPPG from videos recorded by a camera. The paper is organized as follow: a first background section which describes the basics of PPG and iPPG, their applications, limits and clinical significances. In the second section we present the proposed approach which is focused on the measurement of iPPG signal using a camera, its processing and the relevant waveform features extraction. Finally, results are presented and discussed before the last section, where we present conclusion and perspectives about this work.

II. BACKGROUND

Currently, to our knowledge, no systematic study has been carried out in existing literature on iPPG signal waveform analysis. For this reason, we review the existing works on contact PPG waveform features and their applications.

PPG waveform is affected by heartbeat, hemodynamic properties and physiological conditions caused by the change in the properties of arterioles. Such effect can be noticed as distortion in the wave profiles [START_REF] Elgendi | On the analysis of fingertip photoplethysmogram signals[END_REF]. Its analysis is very interesting especially in blood circulation assessment [START_REF] Reisner | Utility of the photoplethysmogram in circulatory monitoring[END_REF] and respiratory monitoring [START_REF] Nilsson | Respiration can be monitored by photoplethysmography with high sensitivity and specificity regardless of anaesthesia and ventilatory mode[END_REF]. Fig. 1. represents a PPG signal wave of a healthy subject. It was analyzed to extract several features by its second derivative. Initially, Ozawa [START_REF] Takazawa | Assessment of vasoactive agents and vascular aging by the second derivative of photoplethysmogram waveform[END_REF] introduced the use of first and second derivatives to facilitate the interpretation of the original PPG waves. The PPG parameters shown in Fig. 1 can be listed as follows: 1. Crest time (CT) is the time from the foot of the PPG wave to the systolic peak [START_REF] Alty | Predicting arterial stiffness from the digital volume pulse waveform[END_REF]- [START_REF] Wu | Novel application of parameters in waveform contour analysis for assessing arterial stiffness in aged and atherosclerotic subjects[END_REF]. Alty et al proved the CT can be an useful variable for cardiovascular disease classification [START_REF] Alty | Predicting arterial stiffness from the digital volume pulse waveform[END_REF]. It details the early systolic phase, which is due to the fast injection of blood during systole. CT increases when vascular blood flow resistance increases [START_REF] Sugita | Contactless Technique for Measuring Blood-Pressure Variability from One Region in Video Plethysmography[END_REF] . 2. Pulse interval (PI) is the time from the starting to the ending points of PPG waveform. It can be used for heart pulse rate measurement instead of the peak to peak interval [START_REF] Elgendi | On the analysis of fingertip photoplethysmogram signals[END_REF]. The ratio between pulse interval and pulse amplitude provide an understanding of cardiovascular system properties [START_REF] Poon | Changes in the photoplethysmogram waveform after exercise[END_REF]. It is strongly correlated to the assessment of heart rate variability compared to R-R interval of ECG [START_REF] Lu | Can Photoplethysmography Variability Serve as an Alternative Approach to Obtain Heart Rate Variability Information?[END_REF]. 3. Diastolic time (DT) corresponds to the time from the PPG waveform peak to its end. 4. Pulse area (PA) is calculated as the total area under the waveform curve [START_REF] Elgendi | On the analysis of fingertip photoplethysmogram signals[END_REF], [START_REF] Wang | Quantification of radial arterial pulse characteristics change during exercise and recovery[END_REF], [START_REF] Tanveer | Cuffless blood pressure estimation from electrocardiogram and photoplethysmogram using waveform based ANN-LSTM network[END_REF]. The blood vessel elasticity, peripheral resistance and physiological changes in ejection function modify the total pulse area [START_REF] Wang | Quantification of radial arterial pulse characteristics change during exercise and recovery[END_REF]. It also decreases with exercise [START_REF] Zhang | Dynamic analysis for blood flow parameters of cardiovascular system on work load[END_REF]. Seitsonen et al. [START_REF] Seitsonen | EEG spectral entropy, heart rate, photoplethysmography and motor responses to skin incision during sevoflurane anaesthesia[END_REF] found the PPG total area response to skin incision to differ between movers and non-movers. 5. Area 1 (A1) is the area measured under the curve from the starting point to the dicrotic notch [START_REF] Wang | Quantification of radial arterial pulse characteristics change during exercise and recovery[END_REF], [START_REF] Tanveer | Cuffless blood pressure estimation from electrocardiogram and photoplethysmogram using waveform based ANN-LSTM network[END_REF]. It mainly reflects the systolic pulse wave characteristics, which are influenced by cardiac ejection function [START_REF] Salvi | Left ventricular ejection time, not heart rate, is an independent correlate of aortic pulse wave velocity[END_REF]. 6. Area 2 (A2) is the area measured under the curve from the dicrotic notch to the end of the waveform [START_REF] Wang | Quantification of radial arterial pulse characteristics change during exercise and recovery[END_REF], [START_REF] Tanveer | Cuffless blood pressure estimation from electrocardiogram and photoplethysmogram using waveform based ANN-LSTM network[END_REF]. It reflects the diastolic pulse characteristics which are affected by peripheral resistance and arterial compliance [START_REF] Huang | Radial Pressure Pulse Heart Rate Variability in Heat-and Cold-Stressed Humans[END_REF].

III. MATERIALS AND METHODS

A. Materials

In this study, a fast color Camera (Edmund Optics EO-2223C) is used to record images at nominally 125 frames per second (fps) with 640 × 480 pixels resolution. The three RGB channels are encoded with 8 bits per pixel. Also, the illumination is controlled through two LEDs panels (Neewer NL480). Light intensity is fixed at 80% from a maximum of 3360 lux/m and color temperature at 3750 K. It is important to note that exposure and white balance have been fixed in these experiments. White balance locally regulates colors and generates non-desired artifacts in webcam PPG signals [START_REF] Bousefsaf | Continuous wavelet filtering on webcam photoplethysmographic signals to remotely assess the instantaneous heart rate[END_REF]. For results validation, an approved contact PPG sensor (BVP-Flex/Pro by Thought Technologies Ltd.) was used to record the earlobe PPG signal at a sampling rate of 256 Hz.

B. iPPG signal extraction

The overall system is composed with both image and signal processing. The fast camera parameters such as zoom, brightness, contrast and color saturation are controlled by the developed algorithm to save a sequence of subject facial images for 60 seconds. Then image processing operations are applied to isolate the forehead pixels used as region of interest (ROI) for the extraction of iPPG signals. The forehead and cheeks areas are rarely covered by clothing or facial hair and correspond to ROI with significant signal to noise ratio [START_REF] Bousefsaf | Automatic Selection of Webcam Photoplethysmographic Pixels Based on Lightness Criteria[END_REF], [START_REF] Lempe | ROI Selection for Remote Photoplethysmography[END_REF]. Only the green channel of the RGB forehead images is used for signal extraction. Oxy-and deoxyhemoglobin have a better wavelengths absorption coefficient between 540 and 577 nm, which correspond to yellow/green colors wavelengths [START_REF] Horecker | The absorption spectra of hemoglobin and its derivatives in the visible and near infra-red regions[END_REF]. The raw iPPG signal is extracted using a spatial average which transforms a set of pixels into a scalar on green channel forehead image [START_REF] Bousefsaf | Continuous wavelet filtering on webcam photoplethysmographic signals to remotely assess the instantaneous heart rate[END_REF]. This operation is applied on a set of n frames to generate n scalar points succession which correspond to the raw iPPG signal, as given in Fig. 2. Raw traces are firstly detrended using a technique based on a smoothness priors approach [START_REF] Tarvainen | An advanced detrending method with application to HRV analysis[END_REF] then interpolated to 256 Hz to get regular sampling rate. The resulting iPPG signal was denoised by the use of a Butterworth pass band filter. The cutoff frequencies range is comprised between 0.5 and 3 Hz in order to facilitate the feet and peaks detection (see Fig. 3). We note that the PPG module delivers a filtered PPG signal.

C. Waveform features extraction

Both the filtered iPPG and the contact PPG (ground truth) signals undergo the same processing. We compute, for each pulse wave, several features (see section II). The waves were cut according to the valleys (signal feet) detection as shown in Fig. 3. A wave corresponds to the curve located between two successive signal feet. Their amplitudes were normalized between 0 and 1 because of the amplitude of contact PPG is greater than iPPG and this leads to a large differences in areas calculation. In addition, and to improve features stability, we average every 10 successive pulse waves (moving window of 10 waves for a step of one wave). The dicrotic notch has been localized by a detection of the central maximum in the second derivative of each pulse wave [START_REF] Takazawa | Assessment of vasoactive agents and vascular aging by the second derivative of photoplethysmogram waveform[END_REF], as shown in Fig. 4 for iPPG and in Fig. 5 for PPG waveforms. The extraction method of each features has been detailed in section II.

D. Experimental setup

The experimental setup is illustrated on Fig. 6. During the measurement, the participants were asked to sit and stay still in front of the camera at a distance of approximately 1 m. An RGB images sequence of 60 second length was recorded. Images were saved directly as bmp format without any compression. These experiments were performed indoor and using LED light sources (Neewer NL480). For the validation of our results, an approved contact PPG measurement module was employed (see section III.A for details). PPG signal was recorded from the earlobe at a sampling rate of 256 Hz. IV. RESULTS AND DISCUSSION Fig. 7 shows the evolution of the extracted features (see section II) for each pulse wave. Red dashed lines correspond to the reference PPG, measured from earlobe with contact sensor, while blue solid lines to iPPG, measured on the forehead with the fast camera. The resulting traces were normalized by subtracting the mean and dividing by the standard deviation. iPPG waveform analysis results are shown in Fig. 7 where a complete 60 seconds signal was processed without removing any distortion. The signal includes 47 successive waves that were analyzed and averaged to obtain the 37 presented values for each feature.

The obtained results exhibit high correlation with those obtained by an approved contact PPG sensor. We

Dicrotic Notch

Dicrotic Notch

notice that time features are more correlated than areas. Pulse interval and diastolic time showed a very high correlation coefficient as given in Table I. This can allow an accurate contactless measurement of heart rate and good understanding of cardiovascular system properties as mentioned in [START_REF] Poon | Changes in the photoplethysmogram waveform after exercise[END_REF]. Crest time has also shown a great stability (see Fig. 7) and high correlation coefficient. In Table I. CT values differs between both measurements. We assume that this deviation is due to the pulse wave shape and in particular to its curvature because the measurements are made on two different sites, the contact sensor being placed on earlobe while the camera measures the iPPG in the forehead area. This parameter can be used for remote evaluation and diagnosis of cardiac diseases [START_REF] Alty | Predicting arterial stiffness from the digital volume pulse waveform[END_REF]. In addition, the presented correlation results of areas are strongly acceptable. They correspond to the most important features that can be used for several vascular diseases diagnosis, which can allow arterial stiffness and atherosclerosis assessment [START_REF] Salvi | Left ventricular ejection time, not heart rate, is an independent correlate of aortic pulse wave velocity[END_REF], [START_REF] Huang | Radial Pressure Pulse Heart Rate Variability in Heat-and Cold-Stressed Humans[END_REF] without any skin contact. Area 2 correlation equals 0.64 for subject 2 (see Table I). This drop in correlationcan be due to motion artifact.

Despite that the two waveforms are not extracted from the same ROI, they also exhibit strong correlation. These results open up prospects to use iPPG for the assessment of several cardiovascular diseases.

V. CONCLUSION

In this study we have developed an approach to analysis imaging photoplethysmography signal waveform. We found that the extracted waveform features such as crest time, pulse interval, diastolic time and areas are strongly correlated to those extracted from contact photoplethysmography signal. We have also quoted their potential diagnostic applications. Therefore, this made the use of iPPG more promising as contactless technonology for early screening of various atherosclerotic and cardiovascular pathologies. A non-contact diagnosis of certain vascular diseases will be the subject of our future work.

Figure 1 .

 1 Figure 1. Original PPG waveform features, CT: Crest time, PI: Pulse interval, DT: Diastolic time, TA: Total area, A1: dotted area and A2: Area with blue lines.

Figure 2 .

 2 Figure 2. Forehead raw iPPG signal obtained using camera

Figure 3 .

 3 Figure 3. Raw PPG signal (orange) and filtered PPGi (blue), the black markers correspond to the detected valleys

Figure 4 .

 4 Figure 4. iPPG dicrotic notch detection, blue trace is the iPPG waveform and yellow trace its second derivative.

Figure 5 .

 5 Figure 5. Contact PPG dicrotic notch detection, blue trace is the PPG waveform and the yellow trace its second derivative.

Figure 6 .

 6 Figure 6.Experimental setup

Figure 7 .

 7 Figure 7. extracted features evolution (presented in order CT, PI, DT, TA, A1, A2), the red features traces are computed from the contact PPG and the blue traces from contactless iPPG.

TABLE I

 I

	.	STATISTICAL ANALYSIS OF THE OBTAINED FEATURES
			RESULTS
			SUBJECT 1			SUBJECT 2
	FEATURE
	S	PPG	IPPG	CORR	PPG	IPPG	CORR
		mean	mean		mean	mean
		± std	± std		± std	± std
	CT (S)	0.09	0.30	0.87	0.10	0.31	0.83
		±0.005	±0.01		±0.004	±0.01
	PI (S)	1.32	1.32	0.96	1.07	1.07	0.95
		±0.07	±0.08		±0.04	±0.05
	DT (S)	1.22	1.08	0.95	0.97	0.75	0.94
		±0.07	±0.06		±0.04	±0.03
	PA	0.65	0.78	0.89	0.51	0.59	0.87
		±0.03	±0.04		±0.02	±0.02
	A1	0.26	0.37	0.86	0.24	0.38	0.87
		±0.01	±0.25		±0.01	±0.01
	A2	0.38	0.40	0.84	0.26	0.21	0.64
		±0.02	±0.02		±0.01	±0.01