Morgane Hamon
email: morgane@ullo.fr

Rémy Ramadour

Jérémy Frey
email: jfrey@ullo.fr

Exploring Biofeedback with a Tangible Interface Designed for Relaxation

Keywords: Biofeedback, Tangible Interface, Relaxation, Ambient Display, Interoception

Anxiety is a common health issue that can occur throughout one's existence. In this pilot study we explore an alternative technique to regulate it: biofeedback. The long-term objective is to offer an ecological device that could help people cope with anxiety, by exposing their inner state in a comprehensive manner. We propose a first iteration of this device, "Inner Flower", that uses heart rate to adapt a breathing guide to the user; and we investigate its efficiency and usability. Traditionally, such device requires user's full attention. We propose an ambient modality during which the device operates in the peripheral vision. Beside comparing "Ambient" and "Focus" conditions, we also compare the biofeedback with a sham feedback (fixed breathing guide). We found that the Focus group demonstrated higher relaxation and performance on a cognitive task (N-back). However, there was no noticeable effect of the Ambient feedback, and the biofeedback condition did not yield any significant difference when compared to the sham feedback. These results, while promising, highlight the pitfalls of any research related to biofeedback, where it is difficult to fully comprehend the underlying mechanisms of such technique.

Introduction

At times, to endure fear might be beneficial, when one is facing dangerous situations or unknown events. "Fight or flight" responses were proven important for survival. However if stress becomes chronic and is not treated, it can be a factor of sleep disorders or cardiovascular disease [START_REF] Kivimäki | Work stress and risk of cardiovascular mortality: prospective cohort study of industrial employees[END_REF]. It can also lead to a pathological state of anxiety when the anticipation of stressing stimuli is sufficient to trigger the same symptoms as with the actual appearance of stimuli. Finding effective and lasting solutions to reduce stress is necessary to alleviate this public health problem, which impedes the lives of many. Treatments exist against stress and anxiety, but they might require a strong and timely involvement (i.e. therapies) or provoke side effects (i.e. drugs). Studying anxiety and offering alternative solutions to drugs (sport, yoga, mindfulness) is a growing body of research, and nowadays tools exist to let people autonomously reflect on their states and better act upon themselves.

Biofeedback

Biofeedback is a method that enables users to learn to control autonomous bodily processes. Biofeedback is part of a larger notion known as "interoception" which is defined by [START_REF] Farb | Interoception, contemplative practice, and health[END_REF] as "the sense of signals originating within the body" or "the process of receiving, accessing and appraising internal bodily signals". Biofeedback relies on physiological measurements and is getting more and more popular thanks to the increasing availability of non-invasive sensors (Figure 1). Most of the time, signals orig-inate from respiration, electrodermal activity (EDA) or heart rate (HR) [START_REF] Mckee | Biofeedback: An overview in the context of heart-brain medicine[END_REF].

While these processes are mostly involuntary and with weak level of consciousness, through physiological sensors it becomes possible to visualize them in real-time. Users are then able to view effects of a particular behavior on their physiology . For example if a person wearing a HR sensor begins to run, HR is going to increase suddenly. Connected to a biofeedback display the increase of HR could be symbolized by a color change, a blinking light, or simply seen as a graph. This information can then be used to help users regulate their state, for example stay within a specific HR range in to prevent injuries or maximize the outcomes of the training. Biofeedback applications are diverse, from rehabilitation to stress management [START_REF] Mckee | Biofeedback: An overview in the context of heart-brain medicine[END_REF].

It is worth noting that despite the fact that biofeedback has been investigated and applied for decades, its effectiveness has not been systematically demonstrated. Notably, even though a review such as [START_REF] Yucha | Evidence-based practice in biofeedback and neurofeedback[END_REF] presents many studies across a variety of medical applications, there are hardly any comparisons between biofeedback and sham feedback, which is the only way to form a proper control group and pin-point the real efficacy of the technique.

Still, as a drug-free and a non-invasive approach, potential risks and side effects of Biofeedback are small. With a medical opinion it could be a compromise for people who can not or do not want to take drugs (e.g pregnant women).

Heart Rate Variability: a Marker of Anxiety

One of the most studied case of biofeedback for stress management is the cardiac activity. Heart Rate is under control of the autonomous nervous system (ANS) and is not constant at rest. Heart Rate Variability (HRV) -a marker of the evolution of HR over time -is a representative index of ANS activity. Among the variety of factors that could influence HR, a low HRV has been shown to be correlated with impaired parasympathic activity, higher anxiety, and a variety of disorders [START_REF] Vaschillo | Characteristics of Resonance in Heart Rate Variability Stimulated by Biofeedback[END_REF]. [START_REF] Tan | Heart rate variability (hrv) and posttraumatic stress disorder (ptsd): A pilot study[END_REF] showed that veterans with Post Traumatic Stress Disorder (PTSD) had a HRV significantly lower than subjects without PTSD. The HRV was compared between veterans with PTSD who received HRV biofeedback in addition to their regular treatment and veterans without the additional biofeedback treatment. The results indicated that the group with HRV biofeedback had significantly increased their HRV while reducing symptoms of PTSD compared to the other group.

Finding ways to assist people to learn to increase their own HRV and improve their health is one of the motivations of our study.

Increasing Heart Rate Variablity

Deep breathing is a well documented manner to increase the HRV. "Cardiac Coherence" is a notion according to which respiration and cardiovascular functions are synchronized. That means the HR increases during the inhalation and decreases during exhalation, and so periodically [START_REF] Mccraty | The coherent heart: Heart-brain interactions, psychophysiological coherence, and the emergence of system-wide order[END_REF]. Authors proposed that 6 breaths per minute is the respiratory frequency that allows one to reach cardiac coherence and the highest amplitude in heart rate oscillations (hence the highest HRV) [START_REF] Deboer | Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model[END_REF]. Cardiac Coherence is then a priori obtained when breathing at a 0.1Hz frequency which corresponds to six 10second breathes per minute.

Several studies have investigated a static breathing guidance at 6 breaths per minute to reduce stress. For example in [START_REF] Yu | Breathe with touch: a tactile interface for breathing assistance system[END_REF], where authors showed that HRV was higher after the breathing exercise, while subjective impressions -as measured by the State Trait Anxiety Index questionnaire, or STAI [START_REF] Spielberger | Manual for the state-trait anxiety inventory[END_REF] -were not different. In [START_REF] Dijk | Breathe with the ocean: a system for relaxation using audio, haptic and visual stimuli[END_REF] authors designed an immersive system which is composed of a blanket containing small vibrating motors (haptic stimulus) and headphones (audio stimulus). Haptic and audio stimuli are synchronized and generated at such a frequency that the user can follow as a breathing guidance. One of the studied frequency modality was 6 breaths/min. Some participants reported the frequency as too fast or too slow. The Authors highlighted that a poorly adapted frequency can potentially create hypo/hyperventilation. Even if a static guidance might, on average be optimal for the population, it is not the best way to maximize HRV for each individual. As a matter of fact, [START_REF] Vaschillo | Characteristics of Resonance in Heart Rate Variability Stimulated by Biofeedback[END_REF] found that resonant frequency (equivalent to the cardiac coherence) differs according to each person. By exposing a breathing guidance from 4.5 to 6.5 breaths per minute to their participants, they managed to define the best frequency for each subject.

As such, we opted for an adapted breathing guidance to create our biofeedback; in our current study we compare it with a fixed breathing feedback (i.e. "Dynamic" vs "Static" feedback) in order to have a better grasp on the effect of an adapted biofeedback.

1.4 Shaping the Best Biofeedback [START_REF] Muench | HRV: The manufacturers and vendors speak[END_REF] proposed a certain type of biofeedback to achieve higher HRV and reach a resonant frequency. In this study, a graph based on HR fluctuations was created, having users inhaling until the HR reaches a "peak" and exhaling until it reaches a "pit". Because of the improved HRV as compared to breathing exercises agnostic to HR, we also designed a biofeedback device that would use HR measurements to propose an adapted breathing guide.

However, the feedback modality used to convey the information back to the user is important, and graphs are not the only way to present a breathing guidance. Actually, such kind of feedback might even impede acceptability because it could appear as being too judgmental due to its close relationship to a metric. In order to craft a more "organic" and yet informative biofeedback, we decided instead to rely on a physical object to present the feedback.

Indeed, thanks to recent advances in humancomputer interaction, is is now possible to directly integrate digital information within users' surroundings, for example through the use of tangible interfaces. These interfaces have been proven effective to help people learn about bodily processes -see e.g. [START_REF] Fleck | Teegi's so Cute!": Assessing the Pedagogical Potential of an Interactive Tangible Interface for Schoolchildren[END_REF]. Through tangible interfaces, biofeedback can then be more easily integrated in the natural settings of users, and become part of a specific scenario.

Ambient feedback

Ambient computing contrasts with disrupting notifications. In this context "ambient" refers to information that is being presented in the peripheral attention of users [START_REF] Maclean | Putting haptics into the ambience[END_REF]. Ambient devices do not mobilize attention. They require minimal efforts from the user and yet they provide informative feedback; rather than "pushing" a notification it is up to users to "pull" information when they require it.

Along those lines, [START_REF] Moraveji | Peripheral Paced Respiration: Influencing User Physiology during Information Work[END_REF] highlights two ways to train respiration: consciously thinking about it or learning to follow an external stimulus such as a pacing light or an auditory guide. While the former method implies focus of attention, the latter, if proven effective, could alleviate the required amount of cognitive resources [START_REF] Hazlewood | Issues in evaluating ambient displays in the wild: two case studies[END_REF].

In [START_REF] Moraveji | Peripheral Paced Respiration: Influencing User Physiology during Information Work[END_REF], authors investigated whether a breathing guidance at the periphery of the screen during work had a influence on breath rate. As this type of guide does not require full attention they called it Peripheral Paced Respiration (PPR). This ambient guide can be very useful by allowing the user to fully commit to another task. The guide rate setting was 20% below the user baseline. They showed significant difference on breath rate depending on the activation of the PPR. The same thinking led [START_REF] Azevedo | The calming effect of a new wearable device during the anticipation of public speech[END_REF] to develop a wearable device that delivers tiny vibrations on the wrist with a frequency 20% slower than the participant resting HR. Users didn't know the function of the device and were preparing an oral presentation (to induce stress). Results showed that the control group had significantly higher anxiety according to questionnaires (STAI) and physiological data (EDA). [START_REF] Schein | Treating hypertension with a device that slows and regularises breathing: a randomised, double-blind controlled study[END_REF] investigated in a longitudinal study if a device called BIM (for Breathe with Interactive Music) had a positive influence on Blood Pressure (BP). The BIM device creates a musical pattern which is related to the user breathing rate. A 10 minutes long quiet synthesized music recording was used as an active control. Results showed BP reduction was greater in the experimental group compared to the control, and seem to have a long-term effect (significantly different 6 months after).

Based on these various findings, we decided to investigate not only a "Focus" but an "Ambient" utilization of a tangible biofeedback device as well. In order to better frame our experimental design, we turned to previous work from psychology and physiological computing that aimed at investigating various dimensions of stress.

Evaluating and inducing stress

Inducing stress to evaluate short-term effects of biofeedback devices is common in the literature. To artificially put participants in a more stressed state increases the range of measurements and help to reduce variability between subjects. Different type of stress can be induced, physical (e.g. extreme heat or cold), psychological (e.g. increase in mental workload) or psychosocial (e.g. public speaking) [START_REF] Mühl | Eeg-based workload estimation across affective contexts[END_REF]. Psychosocial stress can be induced by faking an interview -Trier Social Stress Test [START_REF] Kirschbaum | The "Trier Social Stress Test" -A Tool for Investigating Psychobiological Stress Responses in a Laboratory Setting[END_REF] -or simply asking participants to prepare a speech, as in [START_REF] Azevedo | The calming effect of a new wearable device during the anticipation of public speech[END_REF].

In [START_REF] Yu | Breathe with touch: a tactile interface for breathing assistance system[END_REF] authors induced psychological stress with a mathematical task for a ten-minutes period. Several manners exists to check if the stress inducing task had an effect. First, it can be detected by recording physiological data, for example with HRV as a marker of anxiety. EDA is also a common recorded measure -e.g. [START_REF] Roseway | BioCrystal : An Ambient Tool for Emotion and Communication[END_REF] -to detect arousal. Because physiological signals might have poor specificity, those indicators do not repre-sent how participants are feeling, what is their state of mind. Questionnaires can compensate for this situation. To measure anxiety the most frequently used questionnaire is the STAI as in [START_REF] Yu | Breathe with touch: a tactile interface for breathing assistance system[END_REF], [START_REF] Azevedo | The calming effect of a new wearable device during the anticipation of public speech[END_REF], or [START_REF] Mühl | Eeg-based workload estimation across affective contexts[END_REF]. In the latter work authors compared the robustness of various physiological signals to detect stress. They crossed psychosocial stress (TSS) with psychological stress, by manipulating the amount of cognitive workload endured by participants. To do so, they employed the N-back task, which leverage on memory load [START_REF] Owen | N-back working memory paradigm: A meta-analysis of normative functional neuroimaging studies[END_REF]. We chose to use the N-back task as well to induce stress in our study since it is effective in doing so and since we can easily compute a performance metric to sense how participants might be affected by the exposition to a tangible biofeedback.

Objectives

In the present study, our first objective is to investigate if an ambient modality could have positive effects on stress. To explore this issue we compared two modalities: Ambient vs Focus. "Ambient" stands for the presence of the device during the whole experiment (30min) in the peripheral visual field of the participant. "Focus" refers to a short (6 min) utilization in the middle of the experiment requiring full-attention.

Our second objective is to check the relevance of breathing guidance based on HR . Indeed, as we propose a new device it is important to consider that any observable effect might be due to a "novelty effect". Moreover, we wanted to assess the usefulness of actually measuring physiological activity. Hence we compare a true biofeedback ("Dynamic" condition, where the breathing guide is adapted using HR) with a sham biofeedback, or "pseudofeedback" ("Static" condition, where the breathing guide is set to a fixed rate). As explained by [START_REF] Health | Controlled Group Designs in Biofeedback Research: Ask, "What Does the Control Group Control For?[END_REF], a "pseudofeedback is defined as a non contingent stimulus presented in exactly the same manner as the true biofeedback and with the intention of having subjects believe that it is true biofeedback".

Study

This study possesses a 2 (Attention: Ambient vs Focus) × 2 (Biofeedback: Dynamic vs Static) between-subject experimental plan. As a result we split our participants into four distinct groups: Ambient-Dynamic, Ambient-Static, Focus-Dynamic and Focus-Static.

Because in the Focus group the device is used only mid-experiment, the first part of the experiment in Focus serves as a control group (no device) for the investigation of attention.

Our hypotheses are: H1. Exposition to an Ambient feedback (H1a) or to a Focus feedback (H1b) reduces psychological stress.

H2. An adapted breathing guidance with a biofeedback device (Dynamic) will reduce stress as compared to a pseudofeeback (Static).

H3. The usability resulting from the use of a biofeedback device is improved as compared to a pseudofeedback (Focus-Dynamic vs Focus-Static). In order to test our hypothesis, we iterated over various form factors to craft a tangible biofeedback that could both act as an ambient feedback and as a breathing guide. Among the biofeedback modalities that are traditionally employed -visual, audio or haptics - [START_REF] Frey | Breeze: Sharing Biofeedback Through Wearable Technologies[END_REF] suggests that there is little difference regarding the effectiveness of conveying a breathing feedback. We chose to rely on visuals with color LEDs since they offered many degrees of freedom to work with (e.g. location of the lights, intensity, color, speed of the animation) and since it was easy to implement.

Inner Flower

We employed laser cutting, Arduino-based microcontollers (Arduino mini), and Adafruit1 Neopixel LEDs to prototype several artifacts (Figure 2). It quickly became apparent that frosted plastic was the best material to work with in order to improve the LEDs' diffusion, smooth the light and prevent an impression of a pixelated display, which would be too much reminiscence of a desktop display. Regarding the actual appearance of the object, after having explored more abstract shapes, we decided to create a somewhat stereotypical flower in order to convey a sense of well-being. Additionally, as one might want to smell the scent of a flower, it is in a way a valid proxy for breathing.

Then we had to design the feedback that would guide the breathing. While it was straightforward to pick movements as a guidance, several adjustments were required in order to smooth the animation of the LEDs that were disposed on the "petals" of the flower. In the final version (Figure 2, right), the user would breathe in when the lights from of the Inner Flower move outwards and breathe out when the lights move inward. In the Static condition this animation is set to 6 breaths/min. In the Dynamic condition, the breathing rate (BR) is coupled with the heart rate of the participant. We start our investigation with a simple coupling: BR = HR/∆. The divider ∆ has a default value of 15. It can be set to adapt the breathing guidance to each user during a calibration phase. During the Dynamic condition, the breathing guidance varies in real-time according to the HR of the user so as to reach cardiac coherence. For example with a HR at 90 beats per minute and a divider set to 12, the resulting breathing guide pulses 7.5 times per minute.

There is no direct representation of the HR (e.g. no light blinking at the pace of the heart rate) so as not to overwhelm users with information not related to current usage scenario.

Measures

During the study we were interested in collecting two types of data: the (psychological) stress level of participants, and a usability index related to the tangible biofeedback. Stress was assessed along three dimensions: physiological activity (HR), behavioral measures (performance in a N-back task) and questionnaires (STAI). Usability was assessed through a questionnaire (USE) administrated at the end of the experiment for those groups that explicitly used the device (i.e. Focus groups).

Heart rate

Each participant was equipped with a smartwatch measuring heart rate ("Link" from Mio 2 ), placed on their non-dominant hand. Mio smartwatchs employ photoplethysmography (PPG) to compute heart-2 https://www.mioglobal.com/ rate, a technique which basically detects variations in skin's color to assess heartbeats. This solution was preferred over electrocardiography (ECG) to improve comfort and acceptance of the system, which is meant to be used in ecological settings, outside the laboratory. Even though PPG is less robust than ECG, being that the participants are steady and seated, i.e. without the risk of creating motion artifacts throughout this study, PPG is a sufficiently good sensor. During pilot studies, we validated that the instantaneous HR measured by this particular smartwatch was accurate enough to detect changes in HRV associated with deep relaxation.

Data was collected over Bluetooth, processed in real-time in the Dynamic condition and stored for further analysis. From HR measurements we focused our investigation on one index of HRV: RMSSDroot mean sum of the squared differences. RMSSD takes as input the inter-beat interval (the inverse of the instantaneous HR measured by the smartwatch). It is one of the best indicator of cognitive workload [START_REF] Mehler | A comparison of heart rate and heart rate variability indices in distinguishing single task driving and driving under secondary cognitive workload[END_REF], a specific type of psychological stress induced during the experiment. The N-back task served both to induce psychological (cognitive) stress, and to evaluate the cognitive load of participants. The latter is revealed by calculating participants' performances. During this task, as in [START_REF] Mühl | Eeg-based workload estimation across affective contexts[END_REF], each letter appears on the screen for 0.5 second every 2 seconds. Participants have to determine whether the current letter is the same as the one they saw N steps before (left click on a mouse) or not (right click). We employed a 2-back task (Figure 3), which showed to induce a high workload level [START_REF] Mühl | Eeg-based workload estimation across affective contexts[END_REF]. Typically, when workload increases the performance during the task decreases.

N-back

An immediate feedback is provided to inform participants whether their answers are correct or not.

Two N-back tasks were presented to each participant, denoted as "N-back1" and "N-back2". Each task is comprised out of three sequences of one minute (30 letters). The first task (N-back1) includes an additional sequence at the beginning that acts as a training session. Over each N-back task we measured participants' performance (percentage of correct answers).

STAI

The State Trait Anxiety Index (STAI) enables the measurement of self-reported anxiety levels [START_REF] Spielberger | Manual for the state-trait anxiety inventory[END_REF]. The STAI Y-A version of the questionnaire measures anxiety as a state (about one's current endeavor). The classical version is composed of 20 items (e.g. "I am tense"; "I feel content") that participants rate on a 4-point Likert scale. A higher score reflects a higher anxiety state. Because we administrated multiple times the STAI during the experiment, we favored a six-item short-form [START_REF] Marteau | The development of a six-item short-form of the state scale of the Spielberger State-Trait Anxiety Inventory (STAI)[END_REF]. It was faster to fill by participants and still produced similar scores to those obtained with the full-form.

Usability

In order to assess the usability of the device, we adapted the USE questionnaire [START_REF] Lund | Measuring usability with the use questionnaire12[END_REF]. We removed the "Usefulness" subscale because it was not relevant to our study -participants did not use the device long enough. Questions were translated to French. The resulting questionnaire comprises three subscales: "Ease of use", "Ease of learning" and "Satisfaction". Each is composed of three items (e.g. "I easily remember how to use it", "It is simple to use"). Participants had to state their agreement to each sentence on a 4-point Likert scale ("Not at all" ... "Very much"). Since such usability questionnaire is poorly suited to assess an ambient device, with which users merely interact directly and/or consciously, the USE was only administrated to participants of the Focus groups.

Participants

A total of 36 volunteers (18 females) took part in the study. Overall the mean age was 23.80 years old (SD = 4.82). The demographics per group is depicted in Figure 4.

Procedure

The timeline of the experiment is presented Figure 5. The experiment took place in a quiet room, deprived of distractions, and we detail it step by step as follows. Upon entering the room and sitting at a table, participants signed a consent form. Afterwards we proceeded to explain briefly how the experiment would take place and equipped participants with the smartwatch. The Inner Flower was then switched on and its core functionalities were explained to participants. In the Focus-Dynamic group, a calibration phase occurred in order to determine a pace that would suit users (i.e. obtaining a breathing guide that would not appear too fast nor too slow). After the calibration, the device was switched off. On the other hand, the Focus-Static group had no calibration, hence the device was simply switched off. Lastly in the Ambient groups the device was left active on the side of the table, in the peripheral vision of participants.

Afterwards, to induce psychological stress and control for the effect of the N-back task participants fulfilled a first STAI (STAI-1), performed a first Nback task (N-back1) and finally fulfilled a second STAI (STAI-2). At this point of the experiment, by comparing Ambient groups (active device on the side) with Focus groups (devices turned off) we are able to investigate the effect of an ambient breathing guide.

In order to assess how much the Inner Flower would affect HRV while employed as an explicit breathing guide, further in the experiment we switched-on the device in the Focus groups and participants carried out the breathing exercise. In the Ambient groups participants performed a substitute task instead; they read the short story "The Oval Portrait" by Edgar Allan Poe. Both tasks lasted 6 minutes and were designed to equally involve users' attention. At the end of the task, the device was switched-off in the Focus groups.

Then, all participants performed a second N-back task (N-back2). Their performance, during this test would enable us to assess the efficacy of the Inner Flower as a tool to reduce psychological stress and improve cognitive availability.

Finally, participants filled out a third STAI (STAI-3). Additionally, in the Focus groups, participants answered the USE questionnaire.

Results

Due to the nature of the data and the modest number of participants per group, we used non-parametric statistical tests to analyze the data. For studying HRV, N-back and STAI, we performed resampling (permutation) statistics using the Minque3 package from R. Answers to the USE questionnaire were analyzed with a Wilcoxon rank sum test. When applicable, we tested for the effect of each main factor (Attention, Biofeedback and moment of measurement) as well as for the interaction of thereof.

HRV

HRV was computed during both N-back tasks (time1 and time3) and during the breathing exercise (time2). There was a significant interaction between the Attention factor and time, with a difference between Focus during the breathing task (M=1.47×10 -2 , SD=0.67×10 -2 ) and the rest of the conditions (M=1.07×10 -2 , SD=0.48×10 -2 , p < 0.05, Figure 6). Across other factors and interactions there were no significant differences in HRV.

Note that due to technical issues the HR data is incomplete for 5 participants (out of 36).

N-back

We investigated the evolution of the percentage of accuracy during the N-back between the first and the second test (i.e. N-back2 -N-back1). Overall performance increased between those two tests; with a significant effect of the Attention factor. Performance increased more sharply in Focus groups (M=+11.23pp, SD= 8.36) as compared to Ambient groups (M=+4.21pp, SD= 7.03, p<0.01, Figure 7). Across other factors and interactions there was no significant differences in the evolution of N-back performance.

STAI

There was a significant effect of time. STAI-2 scores (after the first N-back task) were higher (M=42.4, SD=9.08, p < 0.01) when compared to the other scores (M=34.8,SD=8.57,Figure 8,top). There was a significant interaction between Attention and time, with lower scores in the Focus groups in STAI-3 at the end of the experiment (M=30.8, SD=5.92), when compared to the rest of the conditions. (M, 38.5,

USE Questionnaire

As mentioned earlier the USE questionnaires were fulfilled only in Focus groups. There was no significant difference between Static (M=32.8, SD= 2.92) and Dynamic (M=28.9, SD=6.79, p=0.26) groups.

Discussion

The N-back task had a significant effect on the perceived anxiety, as the STAI-2 was higher than the STAI-1. This replicates the validity of such task to induce stress.

As opposed to previous work -e.g. [START_REF] Yu | Breathe with touch: a tactile interface for breathing assistance system[END_REF], which employed arithmetic tasks between breathing exercises -we did not measure a noticeable effect of the Ambient condition and could not validate H1a. There was no significant difference within any marker of stress (HRV, N-back performance, STAI) between participants with an active ambient device and participants with no device (beginning of the study). We would need longer experiments, or even longitudinal studies, to better grasp the influence and the dynamic of an ambient (and subtle) biofeedback. Interestingly, when asked after the experiment during informal interviews, participants in the Ambient groups reported that they did not pay attention to the device -an indicator that at the very least it was not disruptive. Still, it is possible that such an ambient biofeedback might reduce stress even more than a short explicit breathing exercise when users are exposed for a couple hours, or over the course of several days.

In contrast, over the 6-minute breathing exercise participants of the Focus group demonstrated a lower level of stress on all three markers -H1b is validated. Not only did the breathing exercise increased HRV and helped participants to feel less anxious, but it also induced a higher performance during the N-back task. This scenario mirrors the (negative) effects that might arise when a psychological test is administrated to a sensitive population in a stressful environment (e.g. elderly in a hospital). In similar situations, the use of a device alike the Inner Flower might increase patients' cognitive availability before a test and prevent biases during a psychological evaluation.

Since there was no effect of the Feedback modality over the course of the experiment, we cannot validate H2. An actual biofeedback did not perform better (or worse) than a simple breathing exercise based on a fixed breathing rate. There are however multiple factors that could explain this outcome and that would need further investigations.

First, by trying to give more freedom to users and finely adapt the breathing guide (i.e. calibration phase in Focus-Dynamic group) we might have introduced a higher between-subject variability, as we observed more variability in the Focus-Dynamic group.

Second, the N-back task might have resulted in a ceiling effect with some participants. While overall participants tended to improve their scores between N-back1 and N-back2, those who already had a good score (i.e. >80%, n=17) had difficulties to improve afterward. This plateau is among the confounding factors that we would need to control more finely during recruitment for future work, alongside personality traits.

Third, and maybe most importantly, our choice of biofeedback might not have been perceived as an actual manifestation of user's physiology. While we did not want to overwhelm users with too many stimuli, the absence of a dedicated HR biofeedback might have impeded their sense of agency, i.e. users did not realize that they were actually "connected" with the device.

This latter interpretation would be on par with the fact that there was no significant difference in the usability questionnaire. With current results we cannot validate H3, since Focus-Dynamic and Focus-Static groups rated equally high the device, between 80% and 90%. We would expect a higher sense of agency (i.e. in Focus-Dynamic) to be reflected on "Ease of use" and "Ease of learning" subscales of USE.

Despite the encouraging effect on relaxation and cognitive availability of the Focus groups, when users are presented with an explicit breathing guide, the absence of results between a coupled (Dynamic) and a fixed (Static) breathing guidance highlights once again how much rigor is needed when assessing the effect of physiological measures and the resulting benefit of biofeedback.

Limitations and Future Work

As shown by [START_REF] Hazlewood | Issues in evaluating ambient displays in the wild: two case studies[END_REF] it is difficult to evaluate ambient technology on a one-time basis because it has to be by definition blended into the environment. In the present study, conditions were maybe not ecological enough in the sense that experiments took place in a small and impersonal room. To solve these issues we are working with a designer to better script the overall interaction and bring the study to a home studio replica. Our next experimental design will include as well a control group without any device, for a better control of the confounding variables. While it is harder to bring the technology outside the laboratory, longitudinal studies, over several days or weeks, would inform us about the required amount of time for an ambient biofeedback to become effective.

Concerning the form factor, we conducted informal interviews at the end of the experiment. Some of the participants showed interest in multi-modal feedback, for example an audio feedback to let them continue the breathing exercise while closing their eyes. In order to enable such usage we will complement existing feedback, for example with audio waves as in [START_REF] Dijk | Breathe with the ocean: a system for relaxation using audio, haptic and visual stimuli[END_REF].

To determine the importance of physiological measurements, we hypothesize that a social usage of the device might be a way to reinforce the association with an actual biofeedback. [START_REF] Roseway | BioCrystal : An Ambient Tool for Emotion and Communication[END_REF] designed an ambient device embedded in the workplace that informs those around about one's state. Thanks to that colleagues were more sensitive to emo-tional states of others. Similar examples inspired us to create a collaborative scenario where users would try to synchronize their heart rate through the device, with a color-based HR feedback. We envision such exercise as a way to establish trust between people. The Inner Flower could then become both a tool to manage stress and a proxy for communication, for example in situations involving care takers and care givers, or when people suffer from communicative disorders.

Over the course of the study we demonstrated how a tangible device could help reduce perceived anxiety (measured with STAI) and alleviate a physiological symptom of stress (increase in HRV). Moreover, it enabled participants to improve performance in a cognitive task. Increasing cognitive availability before a psychological test is one of the most promising applications of this technology. With a usability score between 80% and 90% we can state that the device was appealing to users. In the future we will further investigate the influence of both attention and type of biofeedback.

Figure 1 :

 1 Figure 1: In this example heart-rate is measured through a smartwatch; tangible interfaces serve both as breathing guides for the user and as biofeedback devices (image c Inria, photograph C. Morel).

Figure 2 :

 2 Figure 2: Left: Examples of prototypes toward an tangible biofeedback. Right: Design of the Inner Flower used in the study

Figure 3

 3 Figure 3: 2-back task. Participants have to click left when the displayed letter is the same as two steps before.

Figure 4 :

 4 Figure 4: Demographics of our groups.

Figure 5 :

 5 Figure 5: Timeline of the experiment.

Figure 6 :

 6 Figure 6: HRV across Attention factor and time (i.e. during N-back1, exercise, N-back2). "*": p-value < 0.05.

Figure 7 :

 7 Figure 7: Evolution of the performance between the first and the second N-back task. Performance increased further in the Focus groups. "**": p-value < 0.01.

Figure 8 :

 8 Figure 8: Top: STAI scores across time (lower score: less anxiety). Bottom: STAI scores across Attention factor and time. "**": p-value < 0.01.

https://www.adafruit.com/

https://cran.r-project.org/web/packages/ minque/minque.pdf


Jérémy Frey
email: jfrey@ullo.fr

Jessica R Cauchard
email: jcauchard@acm.org

Remote Biofeedback Sharing, Opportunities and Challenges

Keywords: Biofeedback, Tangible interface, Remote Communication ACM Classification H.5.2 [User Interfaces]: Interaction styles; H.1.2 [User/Machine Systems]: Human information processing

Biofeedback is commonly used to regulate one's state, for example to manage stress. The underlying idea is that by perceiving a feedback about their physiological activity, a user can act upon it. In this paper we describe through two recent projects how biofeedback could be leveraged to share one's state at distance. Such extension of biofeedback could answer to the need of belonging, further widening the applications of the technology in terms of well-being.

Introduction

Maslow describes in [START_REF] Maslow | A theory of human motivation[END_REF] a hierarchy of needs, a model of states and goals that one would strive to reach throughout their life. While this model was debated and refined over the years, it is still a strong framework to describe a trajectory that could lead to healthiness and well-being. For instance, in the current paper, we use this framework to describe how and why biofeedback could be employed to increase wellbeing. Moreover, we argue that biofeedback could be used to leverage higher levels of Maslow's hierarchy.

Biofeedback is a method that enables users to learn to control autonomous bodily processes. It relies on physiological measurements; most of the time, signals originate from respiration, electrodermal activity or heart rate [START_REF] Michael | Biofeedback: An overview in the context of heart-brain medicine[END_REF]. These measures are then be translated to an output that the user is able to perceive, for example a visual or an audio cue. While this physiological activity is mostly involuntary and is associated with a low level of awareness, through biofeedback it becomes possible to visualize, reflect and eventually act on it in real-time.

Biofeedback applications are diverse, from rehabilitation to stress management [START_REF] Michael | Biofeedback: An overview in the context of heart-brain medicine[END_REF]. For instance, someone could use a combination of breathing guidance and breathing biofeedback to reach a specific respiration and breathe "correctly". That situation could be associated with the first "level" in the hierarchy of needs, Physiologycal needs. However this situation is also closely associated to the second level, Safety needs. Indeed, when a stressful stimuli arise, basic physiological responses will occur -i.e. "fight or flight" responses -and, in case of a pathological state of anxiety, the sole anticipation of those stimuli is sufficient to trigger stress, without their actual appearance. Therefore, by being aware at the earliest of those changes, one could regulate themselves their state and alleviate the suffering.

In the following sections, we demonstrate ways to put biofeedback into practice through two recent projects. Dišimo and Breeze are two tangible devices drawing from ubiquitous computing in order to propose an "ecological" biofeedback that could be integrated in the environment of the users. Specifically, they were designed to enable different levels of connectedness. By sharing signals among devices, it becomes possible to supplement and positively influence the third need in the Maslow pyramid: Belonging.

Dišimo

Dišimo [START_REF] Mladenović | Dišimo: Anchoring Our Breath[END_REF] acts as a gentle and ambient feedback of one's state (Figure 1). It provides a multi-modal feedback through light, sounds, and the actuation of physical particles. When used in conjunction with a smartwatch measuring heart rate, it will sense a decrease in heart rate variability (HRV)a sign of stress or cognitive workload [START_REF] Stephen | A metabolic measure of mental effort[END_REF] -and play a sound as a reminder to breathe. If the user chooses to ignore the device, it will automatically stop playing the sound. Otherwise, if they decide to take a break and grasp Dišimo, the device lights up. Then, upon increase in HRV, physical particles embedded inside Dišimo will start to flutter and produce harmonious tones when hitting the enclosure. The device itself can be equipped with sensors to monitor HRV by the mean of electrocardiography when users grasp its edges, where conductive thread is positioned.

Not only one Dišimo can be used for self-regulation over the course of the day with breathing exercises, but several of them can be connected remotely among a cluster of users. This way, a relaxation session can be experienced between close ones. In this scenario, the global brightness of the light is mapped to the ratio of active users who increased their HRV. In order to be as non-judgmental as possible, we purposely avoided to give information about who specifically reached a higher HRV. Dišimo is not meant to foster competition, that would defeat the purpose of improving well-being, instead it is an aid and a mediator. Knowing that relatives or friends are using Dišimo could be an incentive to use the device, through emulation. Moreover, joining a relaxation session could create an alternate way to connect and empathize with the others, even without physical contact or explicit communication. While this specific project enables a group to occasionally communicate their relaxation, the next project enables a direct and real-time sharing of biofeedback throughout the day.

Breeze

Breeze [START_REF] Frey | Breeze: Sharing Biofeeback Through Wearable Technologies[END_REF] was developed as a wearable device to communicate breathing biofeedback (Figure 2). Breeze functions bidirectionally, by collecting a person's breathing and providing in real time an ambient biofeedback to a paired pendant. Three biofeedback modalities are embedded in the device: visual, audio and haptic. Each one maps the entire range of breathing to one degree of freedom (i.e. light brightness, pink noise amplitude, vibration motor intensity), thus supporting a more natural and intuitive interface. The wearable relies on an inertial measurement unit to measure breathing, a technology both portable and non-invasive. Breeze is worn as a pendant; this location reduces motion artifacts and increases comfort, while each feedback modality can still be perceived.

Compared to other physiological signals, breathing can be easily modulated. It also conveys a variety of information; for instance many features could be associated to different emotions. During a lab study, we demonstrated how users wearing Breeze were able to perceive and discriminate di-mensions of emotions from various breathing patterns, even when they were conveyed through a rather simple biofeedback. Interestingly, almost all participants were mimicking the breathing pattern in order to understand it. We were surprised by how empathetic participants became toward unimodal cues. This is an encouraging finding; it might indicate that when exposed to such a shared biofeedback, users have a tendency to naturally -and physically -engage with it. That could help to create a "meta biofeedback loop" between users, with emerging properties to be expected from such interaction.

Results gathered from the study reinforce the hypothesis that by sharing biofeedback it could be possible to increase the feeling of belonging. In fact, participants described how they would use Breeze in long distance relationships with people close to them, such as a partner or family member. It should be noted that in general participants would only use such device with loved ones, probably since feeling someone else's breathing pertains to strong intimacy. We envision that making physiological signals more visible could promote empathy, enforcing a bond between people. However, no matter how grand, this opportunity to extend on existing biofeedback applications comes with its challenges, among which are privacy and acceptability.

Challenges

Physiological sensors are constantly being refined, up to the point that it is now possible to remotely measure physiological states without the awareness of the person being monitored. For example one could use wireless signals in the Wifi range to detect breathing, even when the person is behind a wall (e.g. [START_REF] Ravichandran | WiBreathe: Estimating respiration rate using wireless signals in natural settings in the home[END_REF]). Besides its convenience, such technology questions users' consent and privacy. One of the core design principle of our projects is that users have ownership of their physiological activity. It is up to them to mea-sure and stream their signals to others. On the other hand, when users perceive the biofeedback of someone else, for example with Breeze, it is because their partner chose to activate the device. We stumbled upon another aspect of privacy while we were developing our prototypes. In a scenario where one would be willing to share a biofeedback with a relative throughout the day, the question of the feedback modality arises. Depending on the social contextfamily, friends, co-workers, strangers -users might not want outsiders to be aware of this particular bond. This is where ownership and customization are important. In Breeze there are three different output modalities that users can freely choose from (visual, audio, haptic). Each possesses a specific "radius" and can be perceived to a different extend by self and others depending on the choice of the user, so as not to impede social acceptance.

Within the two projects hereby presented, users have a symmetric and bidirectional relationship; all devices are equals and they present incentives to share with our peers. This use case brings new challenges. In particular, some expectations might arise when people are "connected" like so; one sending a biofeedback might expect to receive a feedback in return, or one might be tempted to listen to a biofeedback without sharing. These (mis)use of the technology can be alleviated, though; as for example with Dišimo where by design it is not possible to know exactly who in a cluster participates to a relaxation session. We will argue that freedom and reciprocity are important to empower people and ensure a balanced interaction, and that these considerations should be embedded in the design of a shared biofeedback so as not to be detrimental to well-being.

Conclusion

Over the course of this paper we presented two examples of shared biofeedback that were designed not only to in-crease awareness and help users to regulate their inner states, but that can as well foster a feeling of connectedness. Using Maslow's hierarchy of needs, it is straightforward to articulate the underlying mechanisms and understand how such devices can positively impact well-being. While there are challenges associated to the technologyboth in terms of practical aspects and users' empowerment -a careful design can mitigate the appearance of unforeseen negative effects. Our next step is to deploy this technology outside the laboratory during longitudinal studies, in order to asses how such artifacts will be employed in the long run, and how they will affect people's life and interactions.

Figure 2 :

 2 Figure 2: Breeze, a pendant for shared breathing biofeedback [2].


Cecilia Nardini

Balázs Kozma

Alain Barrat

Who's talking first? Consensus or lack thereof in coevolving opinion formation models

Keywords: numbers: 89.75.-k, -87.23.Ge, 05.40.-a

We investigate different opinion formation models on adaptive network topologies. Depending on the dynamical process, rewiring can either (i) lead to the elimination of interactions between agents in different states, and accelerate the convergence to a consensus state or break the network in non-interacting groups or (ii) counter-intuitively, favor the existence of diverse interacting groups for exponentially long times. The mean-field analysis allows to elucidate the mechanisms at play. Strikingly, allowing the interacting agents to bear more than one opinion at the same time drastically changes the model's behavior and leads to fast consensus.

In the recent years, agent based models have been more and more used in the area of social sciences. Through a rather simple modeling approach for the individual processes of social influence, these models focus on the emergence of social behavior at the global population level. Statistical physics models and tools provide therefore a natural framework for such studies, and have been widely applied, leading to the appearance of the field called sociophysics (see [1] for a recent review on the application of statistical physics models to social dynamics).

The growing field of complex networks [START_REF] Pastor-Satorras | Evolution and structure of the Internet: A statistical physics approach[END_REF][START_REF] Newman | [END_REF][START_REF] Dorogovtsev | Evolution of networks: From biological nets to the Internet and WWW[END_REF] has moreover allowed to obtain a better knowledge of social networks [START_REF] Granovetter | [END_REF][START_REF] Wasserman | Social Network Analysis: Methods and applications[END_REF], and in particular to show that the typical topology of the networks on which social agents interact is not regular. Many studies have therefore considered the evolution of models of interacting agents when agents are embedded on more realistic networks, and studied the influence of various complex topologies on the corresponding dynamical behavior [START_REF] Boccaletti | [END_REF]. An additional feature of networks, that may have a strong impact on the model's behavior, lies in their dynamical nature. They may indeed evolve on various timescales, and the evolution of the topology and the dynamical processes can drive each other with complex feedback effects. Studies of this coevolution are more recent and still limited [8,9,10,11,12,13,14,15,16,17], with many open issues.

In this Letter, we provide new insights into such feedback effects by an investigation of Voter-like models (VM), in which agents update their opinions by imitating their neighbors, and can also break and establish connections with other agents. More precisely, we show how slight modifications in the evolution rule, which have minor consequences if the topology of interactions is kept fixed, can change drastically the model's behavior as soon as the topology can evolve on the same timescale as the agents' opinions. On the other hand, the simple fact of allowing agents to have several opinions at the same time, in the spirit of the Naming Game [18] or of the AB model [19], leads to more robust behavior.

The Voter model [20] considers a population of size N in which each individual i has an opinion characterized by a binary variable s i = ±1: only two opposite opinions are here allowed (for example a political choice between two parties) [25]. Starting from a random configuration of opinions, the dynamical evolution of the direct VM (d-VM) is the following: at each elementary step, an agent (i) is randomly selected, chooses one of its neighbors (j) at random and adopts its opinion, i.e. s i is set equal to s j (one timestep consists of N such updates). In the reverse case (r-VM), the first agent i instead convinces its neighbor j (s j is set equal to s i ). The distinction between d-and r-VM is necessary since the two interacting nodes do not play the same role. Moreover, the degrees of the first and the second chosen nodes have different distributions, and the second is a large-degree node with larger probability [START_REF] Pastor-Satorras | Evolution and structure of the Internet: A statistical physics approach[END_REF]. The asymmetry in the opinion update between the two interacting nodes can then couple to the asymmetry between a randomly-chosen node and its randomly-chosen neighbor, leading to different dynamical properties. No important difference is expected on homogeneous networks but, on heterogeneous networks, the probability for a hub to update its state will vary strongly from one rule to the other. The basic imitation process of the VM mimics the homogenization of opinions but, since interactions are binary and random, do not guarantee the convergence to a uniform state. Since a consensus in which all individuals share the same opinion is an absorbing state of the dynamics, any finite population reaches a consensus, but the time needed t c (N ) depends on its size N and on the topology of interactions, and diverges as N → ∞. On static networks, t c (N ) grows as a power-law of N , with an exponent depending on the degree distribution, and on the updating rule [21,22,23]. On homogeneous networks in particular, t c (N ) ∝ N for both d-and r-VM.

In this Letter, we consider the scenario in which agents can rewire their "unsatisfied" connections. More precisely, the initial configuration is given by a random homogeneous network of interacting agents, with average number of neighbors k and random opinions. At each timestep, an agent i and one of its neighbors j are cho- sen. With probability Φ, an attempt to rewire the link is made, if s i = s j . A new agent k is then chosen at random and the link (i, j) is rewired to (i, k) [26]. With probability 1 -Φ, an opinion update takes place instead.

The rewiring, which conserves the total number of links, is made at random: the new link is established without prior knowledge of the new neighbor's opinion.

If the frequency of rewirings is small (Φ → 0), the system still reaches a global consensus and the network remains connected. For fast rewiring rates on the other hand, (Φ → 1) the network breaks into (typically two for the VM) separate connected components, each one with a local consensus. These two regimes are separated by a non-equilibrium phase transition at a critical value Φ c of the rewiring probability. Similar transitions have already been reported in co-evolving models of opinion formation [13,16,17] and we will not focus on this aspect here.

A more surprising aspect of the dynamics is revealed by the behavior of the convergence time t c (N ), which grows linearly with N on a static network for both the dand the r-VM [22,23]. Strikingly, the network's adaptivity has completely opposed effects in these models (Fig. 1). Consensus is strongly favored in the d-VM, for which t c (N ) becomes ∝ ln N [START_REF]Close to the transition Φ ∼ Φc, tc(N ) ∼ N a[END_REF]; in contrast, for the r-VM t c (N ) grows exponentially with the system size. The system therefore remains for exponentially long times in a state in which two groups of different opinions co-exist and remain connected to each other. It is noteworthy that the system therefore is not frozen, with agents continuously updating their links and opinions.

In order to understand the different behavior of the d-and r-VM on adaptive networks, we note that the state of the system is characterized by three independent quantities: (i) the density n + of agents with opinion +1, or equivalently the magnetization m = n + -n -(n -= 1 -n + is the density of agents with opinion -1); (ii) the number of links joining agents in the + opinion, N l ++ ; and (iii) the number of links joining agents of opposite opinions, i.e. of active links N l -+ = N l +-(since the total number of links is preserved, k /2 = l ++ +l +-+l --). At the mean-field (MF) level, we can derive the evolution equation of these quantities. Let us first consider the magnetization: it changes of -2/N when an agent changes its states from + to -, and of +2/N in the opposite case. For the d-VM, the probability of the first event is proportional to the density n + of agents in the + state, times the probability that it chooses to interact with a neighbor that has -opinion, i.e. k +-/k + where k + is the average degree of a + node, and k +-= l +-/n + is the average number of -neighbors of a + node. The probability of the second event (-→ +) is obtained in the same way, and finally

dm dt dVM = - 2(1 -Φ) N l +- 1 k + - 1 k - . (1)
In the case of the r-VM, the probabilities of the two processes are simply interchanged: dm/dt rVM = -dm/dt dVM . On an adaptive network, it is essential to distinguish k + from k -: as shown in Fig. 2, one has

indeed k + > k > k -if n + > n -.
In other words, the nodes of the majority opinion have more neighbors. This is a simple consequence of the rewiring dynamics: if m > 0, any rewiring event (i, j) → (i, k) has a higher chance to randomly pick a + node as a new neighbor due to their larger number. Therefore, nodes of the larger group gain new links with larger probability. Equation ( 1) then immediately shows that for m > 0, dm/dt dVM > 0 and dm/dt rVM < 0. In summary, the coevolution of opinions and topology generates a positive feedback for the d-VM driving the system to a consensus state, m stable = ±1, and a negative feedback for the r-VM resulting in m stable = 0. This readily explains the strong differences between these models. For the d-VM the adaptivity leads to an accelerated consensus, while it hinders the convergence for the r-VM and keeps the system in a dynamically evolving state with zero average magnetization. It is moreover possible to write the evolution equations for the various types of links. It is easy to understand that, according to the model's definition, the vector x = (m, l +-, l ++ ) can evolve in 4 ways at each elementary update: x → x + v a , a = 1, • • • , 4, with respective probabilities w a . Let us start with the d-VM. The displacement vectors and the associated probabilities read then:

N v 1 = (2, k ---k -+ , k -+ ), w 1 = (1 -Φ) n -k -+ /k -; N v 2 = (-2, k ++ -k +-, -k ++ ), w 2 = (1-Φ) n + k +-/k + ; N v 3 = (0, -1, 0), w 3 = Φ n 2 -k -+ /k -; N v 4 = (0, -1, + 1), w 4 = Φ n 2 + k +-/k + . v 1
and v 2 correspond to opinion changes, for which the change in magnetization (±2/N ) is associated with changes in the densities of links. For example, when a -node is transformed to +, its --links become +-and its +-links become ++ ones (hence l +-varies of (k ---k +-)/N ). The corresponding probabilities w 1 and w 2 are obtained as for Eq. (1). v 3 and v 4 correspond to rewiring events: when a +-link is rewired it can be either transformed to --(v 3 ) or to ++ (v 4 ). For the r-VM, the displacement vectors are exactly the same as for the d-VM, but the transition probabilities w 1 and w 2 are interchanged. w 3 and w 4 remain the same since the rewiring rules are the same for both models. Figure 2 shows the result of the numerical integration of the evolution equations dx/dt = a v a w a , compared with numerical simulations of the models. It is clear that these equations correctly account for the difference between k + and k -and for the system's evolution in the phase space. Of course, the real systems are moreover submitted to fluctuations that are not taken into account in the MF description. In particular, looking at single runs (Fig. 2) shows clearly the difference between the d-and r-VM. For the d-VM, the density of active links decreases rapidly to 0 and the system is driven to one of the consensus states. For the r-VM on the contrary, the system performs a random walk in a sort of potential well around m = 0 with a non-zero density of active links, which ends only because of a finite-size fluctuation which leads it into one of the absorbing boundaries at m = ±1.

Let us now consider that agents cannot pass directly from one opinion to another, but can keep both opinions in their "memory", being then in an intermediate state that we call 0. This is the case in the Naming Game (NG) model, in which agents try to agree on the name to assign to a given object [18], or also of the AB model [19]. If only two names are available (that we can call + and -for simplicity), the dynamical rules of the direct NG (d-NG) are the following: at each timestep, an agent i and one of its neighbors, j, are chosen at random to be respectively Hearer (H) and Speaker (S). S proposes a name to H. If S has both names in memory, it chooses one at random. Let us suppose for instance that S proposes +. If H does not know the name uttered (i.e., it is in state -), it absorbs this possibility by changing to the intermediate state, 0. If H instead has the name in memory (i.e., it is in state + or 0), the interaction is successful and both H and S agree on this particular name and set in state + after the interaction. In the reverse case (r-NG), the first randomly selected agent is S and its neighbor is H, and the update rules remain the same [28]. When agents interact on a static topology, these dynamical rules lead to a global consensus. On homogeneous networks, we obtain t c (N ) ∼ ln N (while t c (N ) ∼ N for the VM). The difference between the two models is due to the fact that in the VM, consensus is reached by a finite-size fluctuation of the average magnetization while in the NG, consensus is reached due to the surface-tension introduced by the 0 states, which tends to minimize the interface between the agents of different opinions and hence drive the system to a homogeneous consensus state [19,24]. For adaptive networks, Fig. 3 clearly shows that the convergence time remains logarithmic for both the direct and reverse version, even if the r-NG is slower. The MF analysis allows to understand this strong difference with the VM. We can indeed write the evolution equation for the magnetization n + -n -, by introducing the average degree of 0 nodes k 0 and the density of +0 and -0 links, as

dm dt dNG = 1 2 dm dt dVM + 1 -Φ N l +0 k 0 - l -0 k 0 ( 2
)
dm dt rNG = 1 2 dm dt rVM + 1 -Φ N l +0 k + - l -0 k - . (3)
The first terms on the rhs represent the change in the magnetization mediated by the l +-links. The factor 1/2 stems from the fact that + and -nodes are not transformed instantly to their opposite counterpart but to the intermediate state 0. The remaining terms correspond to the transformation of the 0 nodes to ± ones. For example, in the d-NG, the second term on the right-hand side is generated by the process when a 0 node is converted to + by first picking a 0 node, with probability n 0 , then one of its + neighbors, with probability k 0+ /k 0 , and so on. Even though the first terms in Eq.-s ( 2) and (3) change sign for the d-and the r-variants of the NG just as for the VM, this effect is suppressed by the remaining terms associated with the transitions (0 → ±) which will always generate a positive feedback to the change of magnetization. As shown in Fig. 4 indeed, l +0 -l -0 is of the sign of m, which is expected since then n + > n -. This effect overcomes the difference between k + and k -; as a result, dm/dt remains of m's sign even in the r-NG, leading to logarithmic convergence times. Very interestingly, the possibility for agents to remain in an intermediate state before updating their opinion strongly enhances the trend towards consensus.

In summary, we have shown how slight modifications of the interaction rules can have drastic consequences in the global behavior of opinion formation models in the case of dynamically evolving networks. In the case of the paradigmatic Voter model, adaptivity of the network can either accelerate the convergence to consensus, or on the contrary hinders it strongly, by maintaining the system in a dynamically evolving state for exponentially long times. A mean-field analysis allows to account for such differences, which are due to the coupling of the asymmetry between the interacting agents to the asymmetry in their degrees. Such coupling is known to change the scaling of the convergence time in heterogeneous static networks, which however remains a power-law of time [22,23], and in fact does not have consequences in homogeneous networks. In strong contrast, and even if the adaptive network remains homogeneous, the fact that the majority has a slightly larger average degree suffices to change from a very fast convergence in logarithmic time for the d-VM to a dynamical state surviving for exponentially long times for the r-VM. Interestingly, if the agents cannot change opinion so easily, and have to go through an intermediate state, such as in the NG or AB models, convergence to consensus is enhanced also for adaptive networks, and irrespective of the order of interactions (d-NG vs. r-NG). The connections with nodes in the intermediate state determine then the dominant evolution of the magnetization, leading to a more robust behavior.

FIG. 1 :

 1 FIG.1: (Color online) Convergence time for the r-VM as a function of the population size, for various rewiring probabilities. Throughout this paper, the data from simulations were averaged over 100 realizations of the system. Inset: same for the d-VM. Note the difference of scales.

FIG. 2 :

 2 FIG.2:(Color online) Top: k+/ k vs m for the VM. The symbols correspond to averages obtained from numerical simulations with N = 1000, k = 10, while the continuous lines are the numerical solution of the MF equations for the evolution of x = (m, l+-, l++), starting from initial conditions with m close to 0. Bottom: l++ and l+-vs m. The continuous black lines correspond to the numerical solution of the MF equations. The red symbols and the grey and brown lines correspond to single runs of the d-and r-VM, respectively (N = 500, k = 10, Φ = 0.4). The inset in the middle shows the evolution of m for the same runs (red symbols for the d-VM and dashed line for the r-VM).

5 FIG. 3 :

 53 FIG. 3: Convergence time for the direct (filled symbols) and reverse (open symbols) NG.

FIG. 4 :

 4 FIG.4: dm/dt vs m (symbols) for the r-NG. According to Eq. (3), changes in the magnetization come from r-VM-like interactions (dashed line) and those mediated by the 0-links, l+0 and l-0 (dash-dotted line). The upper inset gives l+0 and l-0, the other k+/ k , k-/ k . Φ = 0.2, k = 10, N = 10 4 .

Acknowledgements -BK and AB are partially supported by the EU under contract 001907 (DELIS).