Interactive displays are becoming increasingly popular in informal learning environments as an educational technology for improving students’ learning and enhancing their engagement. Interactive displays have the potential to reinforce and maintain collaboration and rich-interaction with the content in a natural and engaging manner. Despite the increased prevalence of interactive displays for learning, there is limited knowledge about how students collaborate in informal settings and how their collaboration around the interactive surfaces influences their learning and engagement. We present a dual eye-tracking study, involving 36 participants, a two-staged within-group experiment was conducted following single-group time series design, involving repeated measurement of participants’ gaze, voice, game-logs and learning gain tests. Various correlation, regression and covariance analyses employed to investigate students’ collaboration, engagement and learning gains during the activity. The results show that collaboratively, pairs who have high gaze similarity have high learning outcomes. Individually, participants spending high proportions of time in acquiring the complementary information from images and textual parts of the learning material attain high learning outcomes. Moreover, the results show that the speech could be an interesting covariate while analyzing the relation between the gaze variables and the learning gains (and task-based performance). We also show that the gaze is an effective proxy to cognitive mechanisms underlying collaboration not only in formal settings but also in informal learning scenarios.  With the advent in interactive display technology, they have become easily accessible and as a result, their use in a variety of domains has been investigated. In the educational domain, interactive displays have been increasingly employed to support informal learning  in museuPrior studies have shown the potential of collaborative eye-tracking  in explaining the cognitive mechanisms responsible for the quality or outcome of collaboration. Previous DUET studies have shown that the eye-tracking data has the capability of explaining the task-based performance , collaboWe present the implications from the first (to the best of our knowledge) collaborative eye-tracking study in the informal learning setting.We present a method to analyze and compare the collaborative interaction of peers across different tasks (learning and gaming) and mediating interfaces .We provide empirical extension of the theoretical framework collaborative learning mechanisms.Moreover, there is a recent trend shown in various learning scenarios to use the physiological data sources to explain the learning processes or to study the relation between the different variables influencing the learning gains or experiences ,12,13,14Recent computer supported collaborative learning (CSCL) research for informal learning has been focused on the process of collaborative learning rather than the outcome of the collaborative effort. For example, Tissenbaum et al.  proposedOne of the theoretical frameworks used to analyze the collaborative learning in informal settings is the collaborative learning mechanisms (CLM) framework . The CLMThere have been other extensions of CLM that provide in depth analysis mechanisms to study the informal collaborative learning processes, such as divergent CLM . DCLM fOne of the common factors that most of the studies in the field of CSCL and informal learning have focused on is the analyses methods. Most of the studies mentioned in the previous sections of the exemplar studies from the theoretical contributions focused on analyzing the dialogues and gestures  and video analyses. This is a significant lack of automatic analyses methods that can be used to further provide feedback to the learners about their individual and/or collaborative learning processes . CLM is One might argue that most of the visitors in museums have diverse goals, for example, adults accompanying children might have different learning goals than those of the children themselves . Thus, CIn this contribution, we extend the CLM framework by having our focus on automatic analyses of collaborative learning in informal settings via multimodal data. We use DUET for measuring joint attention among the collaborating partners and compare the gaze similarity (a measure that captures the convergence of the eye-tracking patterns) for the pairs with the different levels of performance/learning gains. We will also use automatically extracted speech segments to compare the joint attention and other eye-tracking measurements (see Section “Measurements”) while the peers engage in dialogues. By using the automatic ways of analyzing CSCL situations, we could not only understand the process faster than the manual tagging of events, but we might also be able to predict the outcome/experiences in real-time or with fewer data points ,26. ThisWith advances in interactive display technology and increased levels of affordability in recent years, there has been a growing interest in exploring their use within educational contexts. A variety of interactive displays are now available through several vendors and many learning applications have emerged. Informal learning environments, like museums, science centers and aquariums have received attention from the education research community, as supporting social interaction and collaboration is highly related with learning and engagement in informal environments  and inteCallahan et al.  identifi“Read-it”  was one One educational framework that is inspired by Discovery Learning Technique proposed that the educational games if integrated with multi-touch displays in different informal learning spaces could stimulate collaboration, engagement and effective knowledge consolidation . In theiFutura  was a taEvans and Rick  present Eye tracking has been employed to understand the learning processes and different levels of outcome in a multitude of learning scenarios. Prieto et al.  used eyeEye-tracking has also been used in online learning for both in individual ,48,49 anRecent educational research has used eye-tracking in different collaborative (remote and co-located) and individual (video-based and with cognitive-tutoring) settings and for both sides of instruction (teacher and students) in formal learning settings. In this contribution, we utilize eye-tracking capabilities to explain the relation between the learning gains in an informal learning setting, game play and collaboration. Prior work in the field of collaborative or Dual eye-tracking (DUET) has shown that the DUET data can help the researchers explain various cognitive processes responsible for collaboration ,46,51,52Concerning learning gains, Sangin et al.  presenteIn a pair-debugging task, Stein and Brennan  showed tHowever, to the best of our knowledge, DUET has not yet been used to investigate how we learn and collaborate when we use interactive displays in informal learning contexts. Learning is enacted through multiple modalities, especially in informal contexts learners engage in significant multimodal behaviors  to emphasize and de-emphasize different ideas and operate an action inside the informal context. Previous studies have focused in various modalities , for insThe aforementioned studies showcase the importance of DUET and how it can aid in understanding and explaining collaboration quality, expertise and joint performance. The present work utilizes the capabilities of DUET to understand and explain the collaboration and learning gains in an informal learning scenario.Recent studies  have shoQuestion 1: How does learners’ behavior (gaze and actions) affect their performance and the learning gain? We designed a multi-touch game-based system to capture participants’ gaze and actions (from the game-logs) in a “museum-like” setting to study the relation between the gaze and learning gains in an informal setting. There were two versions of the game: collaborative and competitive. We are interested in how individual gaze patterns are related to the performance in the competitive version of the game; and how the dual gaze patterns are related to the collaborative version of the game. Moreover, since there are close ties between gaze and speech , we use the speech segments to have a deeper understanding of such relations.In a recent study, within a formal learning context, Sharma et al.  showed tQuestion 2: How does the gaze change in the different tasks in informal learning context? In the present experiment, we are interested in examining the nature of this relation in an informal learning space. We are also interested in the face how the gaze patterns of the peers change with the presence of speech and during different key moments of the game, such as the use of power ups.In this section, we will provide mapping of the different elements of our system and the design rationales assembled from the previous research. The details about the system, the game and the experiment will follow in the subsections. Collaboration vs. Competition: All the pairs played two sets of games. The collaborative version, where both the participants in a pair were supposed to provide one answer and the team got the points (xp); and the competitive version, where both participants provided answers and were scored individually. It is known in the literature that collaboration promotes synthetic skills whereas competition promotes analytic skills [c skills , and thec skills . Competic skills ,66, howec skills . For insPower Ups: we introduced three different power ups during the game they were provided during both the collaborative as well as the competitive versions of the games. Hint: this showed the participants a clue towards the correct answer.Double xp: this added two times the points awarded for one question to the score of the team/player.Pause time: this stopped the game-play for 15 s to help give the players time to think and answers.Game rules: Following were the rules of the game, they were same for the collaborative and competitive versions: for every correct answer the team/participant gets 100 xp;with every correct answer one of the three power ups increases;three power ups were: pause time double xp, and hint;for each question the team/participant got 30 s.To create the learning material for the experiment presented , we tookSpatial split-attention principle—previous research has shown the beneficial effects of integrating pictures with explanatory text: the text that refers to the picture is typically split up in smaller segments so that the text segment that refers to a particular part of the figure can be linked to this particular part or be included in the picture .Spatial segmentation of text into small paragraphs—the explanation of different brain regions was mapped directly to their position in the anatomical brain. Prior research has shown such segmentation to be particularly useful for low prior-knowledge learners ..Spatial Signaling—to help the students understand the relative positions of the different brain regions were annotated in the posters with a short description of their functionality. Research shows that signaling enhances learners’ appreciation of the learning material [material  and theimaterial ,73).The research design of our study is a single-group time series design , involviOur study consists of two treatments and three measures of learning gains (via tests), one measurement of game performance (during subjects’ interaction with the game—second treatment), as well as continuous measurement of participants’ gaze. To identify the baseline knowledge of the participants, they were asked to fill in a pretest about the content they were going to learn (first learning gain measurement). Then they went through five posters (first treatment) about the structure of neurons, different areas of the brain and their functions, three neurological disorders and the limbic system  the cameras that capture the eyes of the participants and (2) the camera on the nose-bridge of the eye-tracker that records the field view of the participants. The clocks of these two cameras are the same for dual eye-tracking studies, we synchronize the two eye-trackers using a fiducial marker (some of them can be seen in the There were 36 university students (18 randomly formed dyads), who participated in the experiment; there were 13 females among the participants. The average age was 24.4 years (SD = 5 years). The experiment took place in a lab that was designed to simulate a museum space. Upon participants’ arrival in the lab, they filled in a pretest about the poster content; afterwards, they watched the five posters. The simple instruction for the poster phase was “go through the posters as if you were visiting a museum with your friend”. The participants could discuss the content of the posters with their partners a. The dyOnce they finished both the modalities of the game, they filled in a final second posttest. All the participants were rewarded an equivalent of $10. Learning Gain: The three variables used to measure learning gain are the scores in the pre- and posttests. We normalized test scores to be between 0 and 1. We do not consider the learning gain in this experiment, as we observed a floor effect on the pretest scores . This shows that all the participants in the experiment had almost no prior knowledge about the content of the posters. Moreover, there is not enough variance in the pretest score of the participants for it to be a significant predictor of the posttest (first of second) scores. The posttests were developed and piloted to 4 subjects before putting them into practice. The results from the pilot indicated that subjects with no prior experience to the content area (this was our target population) could only respond to very few questions. However, after a small exposure to the content, the subjects were able to attain a better score, but it was very difficult to excel (ranging from 6–8 out of 10). Please see the Game Performance: The participants received individual experience points (xp) during the game (both collaborative and competitive) when they replied correctly to a question. We consider the xp value as their game performance index. This was calculated using the log data from the game.Time on task: This the total time the participants took to answer each question. This was calculated using the log data from the game.Number of “power ups” used in the game: This is the number of different powers used  by the individual players in the game. This was also calculated from the log data from the game. Individual Gaze—AOI Transitions: We divided the posters into different Areas of Interests (AOIs), for example, text blocks and image blocks. Next, we computed the proportions of the gaze transitions from the images in the poster to the corresponding text and the proportions of the gaze transitions from the text to the corresponding images. For example, in the Collaborative Gaze—Gaze Similarity: To compute the metric for the collaborative gaze patterns, we used the same measure as used by Sharma et al. [a et al. ,59. ThisCollaborative Gaze—Gaze Transition Similarity: from the AOI transitions we get the AOI transition graphs  we employed different ANOVAs using the first played phase as the independent variable for all the ANOVAs. The dependent variables were the game score, the pretest score, the first posttest score and the second posttest score. To identify the difference between pretest, the first posttest and the last posttest we employed t-tests. To identify any relation between students pre- and post-scores, as well as the game scores we employed Pearson correlations. To investigate our research question, about the relation of learners’ behavior (gaze and actions) with their learning gain we employed Pearson correlation between AOI transitions and the pretest score, gaze similarity in the poster reading and the pretest score. To investigate the second research question about how gaze changes in the different tasks in informal learning we employed Pearson correlation in gaze similarity in the poster reading and playing in the interactive display. To provide the complete picture in our analysis, we also employed descriptive statistics from the game logs. These logs contain the time on task for each question and the use of power ups in the game. We used Pearson correlation to investigate the relation between the final score of the team and he number of power ups used. We also used Pearson correlation to investigate the relation between the gaze similarity during the game and the number of power ups used. We used pairwise t-tests to compare the different times the teams took to answer a specific question. Finally, to understand the role of the speech segments during the different phases of the experiment and the different versions of the game and their affinity with the similarities (gaze and transition) and the posttest scores (first and second), we used ANCOVA with the speech segment type (speech versus no-speech) as the covariate. The p = .68, d = 0.08). Moreover, we did not observe any order effect of playing collaborative/competitive versions of the game first on the scores from the first  = 1.52, p = .22, d = 0.41) or second  = 0.21, p = .64, d = 0.15) post-tests. This allows us to analyze the collected data without considering the bias that could have been there due to the order of the game modalities (collaborative or competitive). We used ANOVA  = −7.91, p < .0001, d = 1.5 In terms of group performances, we observe a significant average improvement from the pretest score to the first posttest score (t (33.41) = −6.38, p < .0001). The participants who score high in the first posttest also score high in the second posttest (The scores in the first and the second posttests are correlated (r (34) = 0.69, posttest a.p = .01). The participants who score high in the first posttest also perform well in the game (The score in the game is correlated to the score in the first posttest (r (34) = 0.42, the game b.p = .04). The participants who perform well in the game also score high in the second posttest (The score in the game is correlated to the score in the second posttest (r (34) = 0.34, posttest c.The scores in the two posttests were similar for most of the participants. We observe three significant correlations: AOI transitions and the first posttest score: next, we consider the individual gaze patterns during the poster phase. We observe a significant correlation between the transitions from image to text and the first posttest score (r (34) = 0.47, p = .003). The participant having high proportion of the image to text transitions score high in the first posttest (p < .002). Participants that have high proportion of the text to image transitions score high in the first posttest (posttest a. Moreovposttest b. Transition similarity and the first posttest score: we observe a significant positive correlation between the transition similarity during the poster phase and the average first posttest score (r (16) = 0.46, p = .05). The pairs with high transition similarity also have high average first posttest score  on the relationship between the first posttest score and the transition similarity. p = .03, d = 1.05). We also observe that the transition similarity is significantly higher for the speech segments than the transition similarity for the no speech segments  = 8.42, p = .006, d = 1.36). Furthermore, the correlation between the transition similarity and the average first posttest score is higher for the speech segments than that for the no speech segments  = 4.79, p = .03, d = 1.03 Gaze similarity and the first posttest score: further, concerning the collaborative gaze patterns, we observe a significant correlation between the gaze similarity during the poster phase and the first posttest score (r (16) = 0.51, p = .03). The pairs having high gaze similarity have high average first posttest score  on the relationship between the first posttest score and the gaze similarity. p = .02, d = 1.12). We also observe that the gaze similarity is significantly higher for the speech segments than the gaze similarity for the no speech segments  = 15.60, p = .001, d = 1.86). Furthermore, the correlation between the gaze similarity and the average first posttest score is higher for the speech segments than that for the no speech segments  = 10.27, p = .003, d = 1.51, Transition similarity and gaze similarity: we observe a significant positive correlation between the transition similarity during the poster phase and the gaze similarity (r (16) = 0.58, p = .01). The pairs with high transition similarity also have high gaze similarity.Gaze similarity and the second posttest score: further, concerning the collaborative gaze patterns, we observe a significant correlation between the gaze similarity during the game phase and the second posttest score (r (16) = 0.45, p = .05). The pairs having high gaze similarity have high average second posttest score  on the relationship between the second posttest score and the gaze similarity. p = .02, d = 1.10). We also observe that the gaze similarity is significantly higher for the speech segments than the gaze similarity for the no speech segments  = 12.26, p = .001, d = 1.65). Furthermore, the correlation between the gaze similarity and the average second posttest score is higher for the speech segments than that for the no speech segments  = 11.96, p = .001, d = 1.63 Competition vs. collaboration score: we did not observe any significant correlation between the difference in scores of the two players and their average score in the collaborative version of the game (r (16) = -0.10, p = .66).Competition vs. collaboration gaze similarity: we observed a significant difference in the gaze similarity of the two players for the two different versions of the game  = 4.79, p = .02, d = 1.02). The gaze similarity was significantly higher for the collaborative version of the game than the gaze similarity for the competitive version of the game.Time on task for each question: we observed no significant change in time to answer each question  = 0.53, p = .02, p = .04, For all the comparisons in this subsection of results, the gaze similarity in the games is considered from the collaborative phase of the game. The main reason behind this decision is that there is no practical, empirical or theoretical basis of having any considerable gaze similarity in the competitive version of the game. This was also evident when we compared the gaze similarities during the competitive and collaborative versions of the game and found that the gaze similarity during the competitive version of the game is significantly less than the gaze similarity during the collaborative version of the game.Gaze similarity during posters and during the game: we observe a significant correlation between the gaze similarity during the poster phase and the gaze similarity during the game phase (r (16) = 0.49, p < .04). The pairs having high gaze similarity during the poster session also have high gaze similarity during the game phase (me phase a. Gaze similarity during the game and transition similarities during the posters: we observe a significant correlation between the transition similarity during the poster phase and the gaze similarity during the game phase (r (16) = 0.55, p = .01). The pairs having high gaze similarity during the poster session also have high gaze similarity during the game phase (me phase b.Gaze similarity during the game and AOI transitions during the posters: we observe a significant correlation between the image to text transitions during the poster phase and the gaze similarity during the game phase (r (16) = 0.56, p = .01). We also observed a significant correlation between the text to image transitions during the poster phase and the gaze similarity during the game phase (r (16) = 0.50, p = .03).We presented a dual eye-tracking study in the context of an informal collaborative setting. Dyads of participants were asked to explore and discuss the material provided in a “museum-like” setup. They were then required to play a gamified quiz. In this contribution, we used automatic gaze and speech analyses to explain the collaborative learning mechanisms (CLM) involved in the informal learning scenarios. Using the DUET data one can understand both the individual and collaborative learning processes. For example, we observe that those individuals who understood the relation between the text and the visualizations correctly (high number of image to text and back transitions) had higher learning gains. Moreover, we also observe that those dyads who put efforts into establishing the common ground  learned more (high posttest and game scores).We also provided an analysis that combined different tasks and showed that it is important to consider the behavior in both the interaction media  to understand the successful learning processes. For example, we observe that the gaze similarity in the poster and game phases, and the scores (posttests and game) are correlated to each other.Finally, we empirically show how collaborative learning mechanisms could be understood using DUET data. For example, coordination of collaboration, joint attention and narration, can be captured using the overall gaze similarity and the similarity measures during speech episodes. Furthermore, collaborative discussion can be measured using the transition similarity during the speech episodes.From the results of the present DUET study we can explain the following:In this section, we elaborate on our contributions and provide detailed implications of our findings.Regarding the game and test scores, the results show no significant improvement from the first posttest score to the second posttest score. Looking at the means and the standard deviation of the first  and the second  posttest, one can reason that there was a very small room for improvement for the students in the second posttest. However, there is a slight but nonsignificant improvement. The results also indicate towards a positively significant correlation between the two posttest scores, which shows that the interactive multi-touch display does not obstruct the learning process of the teams. This is similar to the results reported in the prior works done by Sluis et al.  and ZahaThe results, based on the eye-tracking data, presented in the previous section represent two behavioral gaze patterns , both of which are correlated to participants’ learning outcomes. Concerning the individual gaze patterns reported in this study, the gaze transitions between images and the corresponding text pieces play an important role in explaining the posttest scores. The results show that the students with a higher first posttest scores connect the text and images/graphics in a better manner and in higher proportions than the students with the low first posttest scores. The complementarity of the information presented in the textual form and the images is of utmost importance when it comes to understanding a learning material . By conConcerning the collaborative gaze patterns reported in this study, the gaze similarity between the peers depicts the amount of time spent by the partners looking together at the similar sets of objects in their field of view. This contribution measures the joint attention of the partners using gaze similarity. Joint attention is one of the key aspects of creating and sustaining high levels of mutual understanding. The results show a significant and positive correlation between the obtained knowledge and the gaze similarity of the pair. One plausible reason for this correlation could be the fact that while looking at the similar objects the peers might discuss and reflect upon the content of the posters which in turn sustains a high level of mutual understanding of the team. On the other hand, this process might be difficult if the peers are not looking at the similar set of objects together. Such results were also reported in different educational contexts ,51,53,59We also compared the gaze similarity during the collaborative and the competitive phases of the game. The results show that the gaze similarity during the collaborative phase of the game is significantly higher than the gaze similarity during the competitive phase of the game. On the other hand, the scores in the two phases were not significantly different. The difference in the collaborative gaze behavior during two game phases is driven by the need of the respective phases. For example, during the collaborative phase the peers would need to discuss the answer before answering the question and this would lead them to point to the different parts of the questions and the multiple choices available to them. This would in turn increase the gaze-similarity (as our results show that during speech episodes the gaze-similarity increases). On the other hand, during the competitive phase no such dialogue is necessary among the peers and most of them answered the questions quietly, this could also explain the lower values of the gaze-similarity. One might argue that in the competitive phase the gaze similarity should be zero. However, this would not be the case because the questions were made available to the peers at the same time hence, they would read part (or full) question at the same time. This would result in a non-zero value gaze similarity (still significantly less than the gaze-similarity during the collaborative phase) during the competitive phase.We also computed the transitions similarity between the peers in a dyad. Transition similarity is an extension of the gaze similarity. Gaze similarity captures if the two peers are looking at the similar sets of the objects in their respective field of view in a given time window. On the other hand, transition similarity denotes that the peers are also shifting their attention among the different sets of objects in a similar manner. In other words, gaze similarity is the similarity in attention distribution, while the transition similarity is the similarity in the attention changes. We found that the transition similarity is higher for the pairs with high posttest scores than that for the pairs with low posttest scores. This shows that the pairs with high posttest score did not only focused on the similar object, but they also had similar change of the focus. Furthermore, this paper also presents the relationship between the collaborative gaze patterns in the two very different phases of the experiment, poster phase that was physical and the game phase that was digital. Another difference between the two phases was rooted in the script of the experiment. In the poster/physical phase of the experiment the students were not forced/told/asked to collaborate, they were simply told to “watch the posters as if they were in a museum with their friend”. This made the collaboration during the poster phase a voluntary effort of the students. On the other hand, during the game/digital phase of the experiment, according to the script of the experiment, the participants collaborated. Despite these two major differences, the gaze similarities in the poster/physical and the game/digital phases were significantly and positively correlated. This result indicates towards the validation of the interaction styles hypothesis by Sharma et al. , statingFinally, while comparing the gaze patterns across the different speech segments, we observe that the speech episodes have higher gaze and transition similarity then the no-speech episodes and this difference is wider for the participants with the high posttest score. In addition, this difference exists in both the poster and the game phases. This shows that there is higher amount of joint attention (measured by gaze similarity) and attention shift (measured by transition similarity) accompanying the verbal actions of peers in a dyad. Additionally, the gaze similarity is higher during the moments when the participants were using the power ups in the collaborative version of the game. This depicts that beneficial coordinated actions and joint attention episodes occur together. The correlation between the average posttest score for the dyads and the measures of their joint attention shows that there is a convergence of conceptual change. These results also show that CLM can be used in an automatic manner, although up to an extent. For example, the coordination of collaboration, joint attention and narration, can be captured using the overall gaze similarity and the similarity measures during speech episodes. The triumvirate relation between the posttest score, gaze similarity and the type of speech episodes indicates that there was a process responsible for creating and sustaining the mutual understanding trough references. Previous research has shown a close relation between the mutual understanding and the joint attention ,79).On the other hand, the collaborative discussion can be measured using the transition similarity during the speech episodes. Transition similarity indicates a deeper level of mutual understanding as it does not merely capture the attention similarity but the similarity between peers’ shift of attention. This might be a result of more engaging dialogue process then simple deictic references since the high levels of transition similarity co-occur more with the speech episodes than the no-speech episodes. We used a simple script for the present study, which consisted of two phases based on the framework presented by Leftheriotis et al. . In the In this contribution, we showed that there are individual and collaborative gaze patterns, which can explain the learning outcomes/processes of the participants in a collaborative informal educational setting using automatic methods in a museum-like setting and through the utilization of interactive surfaces. These explanations are coherent with studies conducted in more formal educational settings and other in-the-wild studies that employ interactive surfaces and collect data utilizing other techniques . HowThe present study is one of the first to use eye-tracking data to examine the relation between gaze, collaboration and learning gain in an informal learning scenario. However, our study entails some limitations. Mobile eye tracking devices are fragile, need frequent recharging and of course demand good calibration and thus additional time for the experiment was needed; in addition, the equipment is expensive. Due to the above limitations, there was a relatively small sample size, the total number of participants was 36 and most of them were males. With a small sample size, there is less statistical power. However, in most metrics the differences we found are significantly important. Moreover, the participants were volunteers from our university which may somewhat limit the generalizability of our results, so other sampling methods could have been applied to ensure a more consistent sample was obtained in terms of the age and reading skills. In addition, the experiment took place in a lab in the university and not in a museum or a similar real-life setting. Finally, this study lacked structured qualitative data , which would be a fruitful opportunity for further research. Future studies could compare the role of gaze in alternative learning environments, as well as obtaining deeper insights from longitudinal collection of eye-tracking data. In addition, instead of posters with information, we are in discussions to run a similar study in a museum with real artefacts where participants could also interact with them and thus understand the role of gaze while interacting collaboratively in a real museum setting.


As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A major challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well with the times of publicly announced interventions. Thereby, we can quantify the effect of interventions, and we can incorporate the corresponding change points into forecasts of future scenarios and case numbers. Our code is freely available and can be readily adapted to any country or region. During the initial outbreak of an epidemic, reliable short-term forecasts are key to estimate medical requirements and capacities, and to inform and advise the public and decision makers  model  with Bayesian parameter inference and augment the model by a time-dependent spreading rate. The time dependence is implemented via potential change points that reflect changes in the spreading rate driven by governmental interventions. Based on three distinct measures taken in Germany, we detect three corresponding change points in the reported COVID-19 case numbers. by April 1, 2020 we reported evidence for the first two change points, and predicted the third , as well as the figures are all available on Github . In Germany, the first serious interventions occurred around March 9, 2020 and affected the case reports after an observation delay  sampling . The cenrameters .As median estimates, we obtain for the spreading rate  and 3.3  and cumu and 3.3 , which sTo quantify the impact of possible interventions, we concentrate on the effective growth of active infections before and after the intervention. As long as the number of infections and recoveries are small compared to the population size, the number of active infections per day can be approximated by an exponential growth  with effkelihood . This stn λ*=28% . The conTo simulate the effect of different possible interventions, we model the effects of interventions as change points in the spreading rate (Methods). We consider different, hypothetical interventions following the initial phase to show that both, the amount of change in behavior (leading to a change in spreading rate (i) No social distancing: Public behavior is unaltered and spread continues with the inferred rate ((ii) Mild social distancing: The spreading rate decreases to (iii) Strong social distancing: Here, the spreading rate decreases to In this, the timing of an intervention matters: Apart from the strength of an intervention, its onset time has great impact on the total case number . For exaWhile we find that the timing of an intervention has a great effect on case numbers, the duration over which the change takes place has only minor effect if the intervals of change are centered around the same date. In To model real-world data, we further refined the SIR model. Most importantly, we account for systematic variations of case reports throughout the week, in particular lower case numbers on the weekend, by explicitly modeling a weekly reporting modulation (see Methods). Indeed, comparisons confirm that models with this correction outperform those without (see table S2). In the supplemental material, we further generalize our model to include an explicit incubation period  that yields results consistent with our main model.We incorporate the effect of governmental interventions into our models by introducing flexible change points in the spreading rate (see Methods). During the COVID-19 outbreak in Germany, governmental interventions occurred in three stages from (i) the cancellation of large events with more than 1000 participants (around March 9), through (ii) closing of schools, childcare facilities and the majority of stores (in effect March 16), to (iii) the contact ban and closing of all non-essential stores (in effect March 23). The aim of all these interventions was to reduce the (effective) growth rate Detecting change points in the spreading rate and quantifying the amount of change as quickly as possible becomes a central modeling challenge when short-term forecasts are required. To address this challenge, we assume an initial spreading rate The inferred parameters for the models with change points are consistent with the inferred parameters from the exponential onset phase  cross-validation-based Bayesian model comparison . HoweverWhen comparing our inference based on three change points to the number of confirmed cases, we find them to largely match . The domIdeally, detected changes can be related to specific mitigation measures, so that one gains insights into the effectiveness of different measures . Indeed,We presented a Bayesian approach for monitoring of the effect of non-pharmaceutical governmental interventions on the epidemic spread of an infectious respiratory disease. Using the example of the COVID-19 outbreak in Germany, we applied this approach to infer the central epidemiological parameters and three change points in the spreading rate from the number of reported cases. We showed that change points in the spreading rate affect the confirmed case numbers with a delay of about two weeks  theOur results indicate that the full extent of interventions was necessary to stop exponential growth. The first two interventions brought a reduction of the growth rate We used a formal Bayesian model comparison to validate the presence of change points. Our model comparison ruled out models with fewer than two change points , additional details may become important, such as explicit modeling of incubation time distributions  model. We also test the robustness of our results by means of more sophisticated models, in particular an SEIR-like model that explicitly incorporates an incubation period (fig. S3). While the SIR model-dynamics is well understood in general, here our main challenge is to estimate model parameters specifically for the COVID-19 outbreak, and to use them for forecasting. To that end, we combined a Bayesian approach — to incorporate prior knowledge — with Markov Chain Monte Carlo (MCMC) sampling — to compute the posterior distribution of the parameters and to sample from it for forecasting. Put simply, we first estimate the parameter distribution that best describes the observed situation, and then we use many samples from this parameter distribution to evolve the model equations and thus forecast future developments.The data used comes from the Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE) dashboard  (Each chain performs 1000 burn-in (tuning) steps using NUTS, which are not recorded. This serves as equilibration in order to sample from an equilibrium distribution in the next step.Each chain performs 4000 steps, which are used to approximate the posterior distribution. To ensure that the chains are equilibrated and sampled from the whole posterior distribution (ergodicity), we verified that the R-hat statistic is below 1.05, which is implemented in PyMC3. The rank normalized R-hat diagnostic tests for lack of convergence by comparing the variances within chains and between chains: For identical within-chain and between-chain variances R-hat becomes 1, indicating convergence. For well-converged chains the resulting samples will describe the real-world data well, so that consistent forecasts are possible in the forecast phase.For the forecast, we take all samples from the MCMC step and continue time integration according to different forecast scenarios explained below. Note that the overall procedure yields an ensemble of forecasts — as opposed to a single forecast that would be solely based on one set of (previously optimized) parameters.Each MCMC step requires to propose a new set of parameters As short-term forecasts are time-critical at the onset of an epidemic, the available real-world data are typically not informative enough to identify all free parameters, or to empirically find their underlying distributions. We therefore chose informative priors on initial model parameters where possible and complemented them with uninformative priors otherwise. Our choices are summarized in In order to constrain our simple model, an SIR model with stationary spreading rate for the exponential onset phase, we chose the following informative priors. Because of the ambiguity between the spreading and recovery rate in the exponential onset phase (see description of simple model), we chose a narrow log-normal prior for the recovery rate The remaining model parameters are constrained by uninformative priors, in practice the Half-Cauchy distribution  leads to a reduction (and not an increase) of For the spreading rates, we chose log-normal distributed priors as in the simple model. In particular, we chose for the initial spreading rate the same prior as in the simple model, Kontaktsperre), which includes the prohibition of even small public gatherings as well as complete closing of restaurants and non-essential stores was imposed by the government authorities. Further policy changes may occur in future; however, for now, we do not include more change points.For the timing of change points, we chose normally distributed priors. In particular, we chose The change points take effect over a certain time period of cases . We assuThe number of tests that are performed and reported vary regularly over the course of a week and are especially low during weekends. To account for this periodic variation, we modulated the number of inferred cases by the absolute value of a sine function with in total a period of 7 days. We chose this function as it is a non-symmetric oscillation, fitting the weekly variation of cases on a phenomenological level. For the amplitude of the modulation we chose a weakly informative Beta prior: Since change point detection entails evaluating models with different numbers of parameters, some form of fair model comparison is needed. This is necessary to compensate for the higher flexibility of more complex models, as this flexibility carries the risk of overfitting and overconfident forecasts. The standard approach to avoid over-fitting in machine learning is cross-validation, and cross validation has recently also been advocated for Bayesian model comparison (e.g., (


Zygomatic implants have been proposed in literature for atrophic maxillary fixed oral rehabilitations. The aim of the present research was to evaluate, by a clinical and tomography assessment, a surgical complication of a zygomatic implant penetration to the orbit.A 56 year-old female patient was visited for pain and swelling in the left orbit after a zygomatic implant protocol. The orbit invasion of the zygomatic implant screw was confirmed by the CBCT scan. The patient was treated for surgical implant removal and the peri- and post-operative symptoms were assessed. No neurological complications were reported at the follow-up. The ocular motility and the visual acuity were well maintained. No purulent secretion or inflammatory evidence were reported in the post-operative healing phases.The penetration of the orbit during a zygomatic implant positioning is a surgical complication that could compromise the sight and movements of the eye. In the present case report, a zygomatic implant removal resulted in an uneventful healing phase with recovery of the eye functions. Dental implants are extensively used in clinical practice for replacing missing teeth and as an adjunct in the reconstruction of jaws and teeth. Severe maxillary atrophy can be observed in patients with an edentulous state. In fact, dental extractions induce bone loss and alveolar bone leading to expansion of the maxilla sinuses, to severe atrophy and to a decrease in volume, making it difficult to insert dental implants. So the rehabilitation of severe maxillary atrophies related to the oncologic resection, traumatic loss or the loss of dental elements, requires treatment with bone regeneration or reconstructive surgical procedures, preparatory to implant-prosthetic support . DiffereIn the literature different geometries and implant designs have been proposed in order to facilitate an optimal positioning of the fixture and a long-term maintenance of osseointegration of the placed implants –12.In this case report, we present a case of invasion of the orbital cavity after placement of a zygomatic denture-anchoring implant and it is described in line with the SCARE criteria .The present study was conducted according the ethical principles of the Declaration of Helsinki amended in 2013. A 56-year-old woman was seen in our Outpatient Clinic for pain and swelling in her left eye, which developed following a zygomatic implant  should be made only by surgeons with extensive experience, to reduce post-operative complications. In fact, different anatomical structures adjacent to the zygomatic bone, such as the orbit, can be damaged during zygomatic implant placement . Severe The authors performed an active drainage of blood from within the orbit with Penrose drains and prescription of methylprednisolone 40 mg (four times a day) and acetazolamide 500 mg. After many months, it is possible to observe in some cases infection or cutaneous fistula in the zygomatic-orbital area. The use of two or three zygomatic implants on each side increases these complications because the height and thickness of the zygomatic bone are small and distance between implant and orbit is very short .Takamaru et al.  measuredThese anatomical considerations of the patient are important during zygomatic implant placement. So, it is prudent to modify the implant angulation based on anatomic patient considerations. Computed tomography is important for evaluation of the zygomatic implant site and the sinus status, as well as for the implant path. In fact, cone beam computed tomography is crucial to determine the amount of bone in the zygomatic arch and in the residual alveolar crest which have to be explored in both horizontal and vertical dimensions. It is important to take a stereolithography model realized by the DICOM files and a 3D printer, that is a good aid for this type of surgery as it faithfully reproduces the bony anatomy of the patient, allowing to assess the exact size and position of the implants. In this case report, the surgeon who placed the implants used the intranasinus technique. This technique increases the risk of orbit invasion, because there is no vision and control of the drills during implant bed preparation. To avoid this complication a concept called the zygomatic anatomy-guided approach (ZAGA)  was propIn conclusion, the placement of zygomatic implants should be made only by surgeons with extensive experience, to reduce the post-operative complications, especially in a period in which there is an increase in the use of zygomatic implants.However the zygomatic implant technique represents a noble alternative to regenerative bone procedures taking advantage of the available bone, anchored in the zygomatic region to native and non-regenerated bone, with obvious biomechanical advantages , 8.


The complex interfacial condition between the human brain and the skull has been difficult to emulate in a surrogate system. Surrogate head models have typically been built using a homogeneous viscoelastic material to represent the brain, but the effect of different interfacial conditions between the brain and the skull on pressure transduction into the brain during blast has not been studied. In the present work, three interfacial conditions were generated in physical surrogate human head models. The first surrogate consisted of a gel brain separated from the skull by a layer of saline solution similar in thickness to the cerebrospinal fluid (CSF) layer in the human head: the fluid interface head model. The second surrogate head had the entire cranial cavity filled with the gel: the fixed interface head model. The third surrogate head contained a space-filling gel brain wrapped in a thin plastic film: the stick-slip interface head model. The human head surrogates were evaluated in a series of frontal blast tests to characterize the effect of skull-brain interfacial conditions on overpressure propagation into the gel brains. The fixed and the stick-slip interface head models showed nearly equal peak brain overpressures. In contrast, the fluid interface head model had much higher in-brain peak overpressures than the other two models, thus representing the largest transmission of forces into the gel brain. Given that the elevated peak overpressures occurred only in the fluid interface head model, the presence of the saline layer is likely responsible for this increase. This phenomenon is hypothesized to be attributed to the incompressibility of the saline and/or the impedance differences between the materials. The fixed interface head model showed pronounced high frequency energy content relative to the other two models, implying that the fluid and the stick-slip conditions provided better dampening. The cumulative impulse energy entering the three brain models were similar, suggesting that the interface conditions do not affect the total energy transmission over the positive phase duration of a blast event. This study shows that the fidelity of the surrogate human head models would improve with a CSF-emulating liquid layer. Blast overpressure (OP) from explosive detonations and heavy weapon systems has been linked to transient, but measurable effects of deteriorated performance and symptomologies in law enforcement and military personnel –4. HowevNumerous models have been used to investigate the effect of blast on the human body. Broadly, these models can be characterized as either pre-clinical animal models or human facsimile surrogates. Animal models can give information on changes to biology and behavior in response to OP. However, there are many caveats in translating this research to humans, given the differences in biology and circumstances of injury Human facsimile surrogates often use simplified geometries, such as ellipsoidal plastic shells filled with silicone gel as a brain simulant –14, soliIn the most basic sense, the human skull contains the meninges, the tri-layer membrane that surrounds the brain and spinal cord and contains the cerebrospinal fluid (CSF), in which the brain is suspended. Simulation-based research on the role of the meninges in OP loading of the brain notes that the accurate construction of surrogate materials can have a critical influence on the transfer of blast forces to the brain, and subsequent brain responses , but valOur experimental approach evaluated three surrogate head models with different interfacial conditions between the brain and skull to assess how these may affect OP propagation into the brain. The three conditions are: (A) stick-slip—the brain surrogate fills the entire skull cavity, however, the surrogate brain is wrapped in a thin plastic film allowing sliding between the brain and skull, (B) fluid—a layer of saline exists between the skull and the surrogate brain, and (C) fixed—the entire brain cavity is filled with the surrogate brain material and the two materials (skull and brain) are tightly coupled. These surrogates were then subjected to various OP insults during explosive training courses and the results were analyzed to determine if the interfacial conditions affected OP propagation into the brain.Each surrogate head is comprised of a commercial, anatomically accurate human skull with a removable plastic skull cap  and gel brain, attached to a Hybrid III neck . Each head has three 50 psi (345 kPa) acceleration compensated sensors , one in the left eye socket and two in the brain. The two pressure sensors in the brain have the same orientation and positioning for all three heads, with a positional accuracy of <3 mm .The manufacturing method for the stick-slip head is detailed in O'Shaughnessy et al.  where itA CT scan of the stick-slip head shows the position of the sensors inside the plastic skull . The scaThe fluid head was fabricated in the same manner as the stick-slip head but with slight modifications. The CSF layer was created in a two-step process. The first step was to make a smaller brain that would leave a large gap between the brain and skull. A sacrificial layer was first added to the inside of the brain mold. This allowed the resulting brain to be slightly smaller than the original brain without altering the location of pressure sensors within the brain. This smaller brain was placed on the Sylgard platform in the lower half of the skull. The second step created the actual CSF layer thickness. To accomplish this, the thickness of the skull cap was increased by forming an approximate 5 ± 2 mm layer of Dragon Skin  on the inside of the skull cap. This skull cap was placed on the bottom half of the skull with the reduced-size brain in place. More Sylgard 3-6636 was added to fill any space between the skull cap and brain through a hole in the top of the skull cap. Once the cavity was fully filled and the Sylgard 3-6636 fully cured, the Dragon Skin coated skull cap was removed and the original skull cap was refitted to the lower skull section. The two skull pieces were sealed together with silicone caulk. Prior to testing, approximately 130 ml of fresh 0.9% saline was added into the gap formed by the difference in thickness between the Dragon Skin-coated skull cap and the original skull cap, through a hole in the top of the skull cap. Once the gap was full of saline, the hole in the skull cap was sealed with a silicone plug to prevent leaking.For this headform, the eye sockets were filled with, and the platform covering the neck mount was made from, Sylgard 3-6636 (as opposed to Sylgard 184 in the stick-slip head). This allowed for material continuity between the platform and the gel brain. Unlike the stick-slip head, the gel brain in the fluid head is not removable. Because of this, there is a continuity of material between the gel brain and the platform is important to ensure proper curing between the two objects. The surrogate brain and platform were polymerized together with a thin coat of uncured Sylgard 3-6636 applied on each surface.A CT scan was taken without any fluid in the gap for greater contrast between the brain surrogate and the gap for CSF. The CT scan showed that the gap between the skull and the brain ranged from approximately 3 to 7 mm . Foam torsos were attached to the fixture so that each head had a torso with soft armor vest to replicate OP reflections off a warfighter's chest during an explosive breaching event. The heads and torsos were placed side by side with a center-to-center distance between the heads of 46 cm. The height of the stand was 1.4 m (not including the height of the heads and necks). Three pencil gauges  were attached to the stand at three different locations, left and right shoulders and at the center. These gauges measured the incident pressures in the vicinity of the three heads. The test fixture configurations, pencil gauge locations, and sensor locations within the skulls and brains are shown in Two USB-6356 X Series DAQs , connected through two signal conditioners  and operated via a laptop running SignalExpress 2014 , were used to acquire data. The system triggered off the “eye” pressure sensor of the center head. Data were collected with a 10 ms pre-trigger buffer for up to 0.5 s at a 1 MHz sample rate. Data analyses were performed using Igor Pro v6 . Pressure data were scaled using the calibration sensitivities of each sensor and filtered at 100 kHz with Igor Pro's digital finite impulse response low-pass filter with a Hanning window.Data was collected during explosive breacher training classes at two sites: Quantico, VA, with the US Marine Corps Methods of Entry (MOE) School and Fort Leonard Wood, MO, with the US Army Urban Mobility Breacher Course (UMBC). At Quantico, the test fixture was oriented parallel to the breaching wall directly in front of the explosive charge . At FortEach of the three surrogates was tested in the same configuration on the test fixture and exposed to a range of overpressures levels. To facilitate the discussion, these pressure ranges have been categorized into three general levels—low, medium and high. The average incident pressures and standard deviations (as measured with the right pencil gauge) for each of the three levels are listed in Likewise, the eye sensor data showed little variation across all three heads for each of the tests. In contrast to the external sensors (pencil gauge and eye), the forward and upward sensors in the brain showed differences in pressures across the three head types . The aveWith the upward sensor, peak pressure relationships between the three conditions changed slightly . While tDespite the differences in peak pressures between each of the three interfacial conditions, the overall durations of the positive phase of the three heads were similar . The impWhen comparing the peak pressures of the in-brain sensors to the initial peak pressures of the eye, a pattern emerges . CompariThe power spectral map in This study sought to expand current head surrogate models by introducing and validating a CSF layer between skull and brain to investigate the role of interfacial conditions on blast propagation into the human head. The fluid head exhibited much higher in-brain peak pressures than either fixed or stick-slip heads. These results indicate that the addition of a CSF layer to the surrogate model does influence results, while providing explosive blast validation for previous shock tube efforts  and inclThe higher peak pressures seen by the fluid interface could be due in part to the incompressibility of water. The other potential cause for increased pressure could be due to the fluid head being a sealed system. In living organisms, CSF flows between the head and spine. Since this fluid movement is mainly driven by respiration , 22, hol2PED) headform incorporated a CSF layer in addition to a falx  and a fluid layer exhibit mixed results. Work by Salzer et al.  with salIn looking at the other two conditions, the in-brain pressures of the fixed head were only slightly higher than that of the stick-slip head for the forward sensors. This suggests that any possible small air gaps in the stick-slip head did not affect pressure wave transmission noticeably. The difference in the upward facing sensors between the fixed and stick-slip heads might be due to the air gap in the stick-slip condition or reduced coupling due to the sliding potential in the stick-slip interface.The other main difference between the three types of surrogate heads was the frequency component. We suspect that for the fixed head the tight coupling between the brain and the skull likely allows for better transmission of vibrational effect into the surrogate brain. This coupling could explain the high frequency components in the pressure data in the fixed head whereas the sliding boundary condition in the stick-slip head (where the brain was wrapped in a thin plastic film) decoupled the brain from the skull. The fluid head also showed minimal high frequency response suggesting that the fluid layer also decouples this response.It is important to note some of the limitations of this work. To study the effect of interfacial conditions on blast propagation into the head, a number of simplifications were made. In reality, the interfaces between the fluid and the solid in the brain are significantly more complex than a simple fluid (CSF) layer surrounding the brain. The arachnoid and sub-arachnoid structures, dura and pia mater would be difficult to physically simulate at this time. This study also did not consider the implications of fluid/structure interfaces inside the brain such as ventricles and vasculature. Each of these systems has the potential to further affect pressure propagation into and through the brain, but also significantly increase the complexity of the surrogate needed for testing. Given the results from this work on the CSF layer, future efforts addressing these other systems are warranted.Another limitation involved the skull. The use of a commercially available stiff polymer skull consisting of skullcap, base of skull and mandible closely represents the geometry of a human skull. However, its response to blast-induced shock and overpressure loading are likely different from those of living bone in a human head. However, the use of the plastic skull does not prevent collection of useful information even though the shock front pressure transmissions through the skull and elastic skull deformation may not fully replicate living bone. Since the same skull is used in all three interfacial head-brain models tested, differences between the three models are reasonably assumed to be due to the variable parameter . While the absolute magnitudes of the responses may be different than real bone, the relative changes would persist.Results from this research suggest that interfacial conditions can affect the pressure wave transmission of OP exposure into the brain. The presence of a fluid layer, even 3–7 millimeters thick, seems to amplify the peak pressure within the brain surrogate. However, the increased peak pressures did not produce a corresponding increase in the impulse due to their short durations, suggesting that the fluid layer does not affect overall shock wave energy transmission into the brain. The fluid and stick-slip conditions seemed to dampen the higher frequency components of the shock waves entering the brain. Given that the introduction of a CSF layer into a gel-based surrogate human head resulted in notable pressure differences within the surrogate brain, it would be prudent to determine the effects of other internal anatomical structures, such as ventricles, on pressure propagation into the brain.The datasets generated for this study are available on request to the corresponding author, pending security approval from NRL.YC, TO'S, and AB contributed to the concept and design of the study. YC, TO'S, GK, DH, and AB participated in data collection events. YC and ME drafted the manuscript. All authors contributed to manuscript revision.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


In the pressure of excessive resource consumption and serious environmental pollution, governments provide various consumer subsidies to promote sales of energy-saving vehicles, including the energy-saving fuel vehicle (FV) and the pure electric vehicle (EV) in the automobile industry. Utilizing a Hotelling model, this paper explores two competing firms’ decisions on the selection of green technology innovations for vehicles, namely producing either the energy-saving FV or the pure EV, while the two vehicles are different from each other on not only the energy-saving level but also the consumer’s acceptance. We further explore the impact of the government’s consumer subsidy on the profits, environment, and consumer surplus. We find that the two competing firms’ equilibrium selections of green technology innovations for vehicles change as the variable manufacturing cost of the pure EV varies. In particular, when the variable manufacturing cost of the pure EV is moderate, the firm with a lower technology capacity for improving the energy-saving level of the FV  will produce the pure EV while the other firm  produces the energy-saving FV, and the converse is not true. In this case, the decreasing variable manufacturing cost of the pure EV will benefit firm 2 and make firm 1 lose in a competing context. In particular, both firms would charge lower retail prices as the variable manufacturing cost of the EV decreases. In addition, we find that although the consumer subsidy could reduce the purchasing cost for the consumer and promote both firms to produce higher energy-saving level vehicles, a firm can still reduce its retail price under certain conditions because of the competition between the two firms. Finally, we prove that the consumer subsidy can be always beneficial to the environment, while it may hurt the consumer surplus and the firms’ profits under certain conditions. The results provide suggestions for governments to adopt an appropriate consumer subsidy program from perspectives of the consumer, environment, and economy.  Environmental awareness has grown drastically over the last several decades. As concerns developed, consumer taste and preference for green products became ubiquitous ,2. In reIn order to protect the environment, governments introduce various policies to support the development of green vehicles, including the consumer subsidy, the R&D subsidy, and the tax preference. Among them, the consumer subsidy is a general government incentive subsidy focusing on subsidizing the consumers who purchase the green vehicles, such as the energy-saving FVs and the EVs. Typically, a consumer purchasing a greener vehicle would receive a higher consumer subsidy. For instance, the government in China provides subsidies up to RMB 30,000 for each plug-in hybrid electric vehicle and up to RMB 55,000 for each battery EV in 2016 .With the increasing competition in the area of FV and the government financial supports, more and more automotive firms choose to produce pure EVs, especially for the emerging automotive firms. Obviously, the firms producing more environment friendly vehicles will receive more green allowances from the government and be more attractive to consumers with environmental concerns . HoweverMotivated by these observations, we seek to study the firms’ selection of the energy-saving vehicle design with the government subsidy support in a competing market. To be specific, we try to answer the following questions: (i) what factors would influence the firm’s selection of the energy-saving vehicle design, namely producing an energy-saving FV or a pure EV? (ii) how does a consumer subsidy program influence the firms’ equilibrium decisions, such as pricing and degree of greenness of vehicles, especially in a competing context? (iii) what are the implications of the effects of the consumer subsidy on the environment, the firms’ profits, and the consumer surplus?To address these issues, we first consider a base model where two automotive firms compete with each other in a market with no subsidy from the government. Each firm chooses to produce an energy-saving vehicle, either the energy-saving FV or the pure EV. Without loss of generality, we assume that all pure EVs have the undifferentiated energy-saving level because the pure EVs are driven by electric energy only, which releases little carbon emission. In addition, the two firms are assumed to possess different levels of technology capacities related to production of the energy-saving levels of the FVs. Therefore, in addition to the firms’ decisions on the vehicle type , the firms should make the decisions on the energy-saving level of the FV. For either the energy-saving FV or the pure EV, we consider that all additional costs in improving the energy-saving levels of vehicles  are variable manufacturing costs. They are incurred by additional green devices to install , more material and parts in the vehicles, more expensive materials and parts to use, and more assembly work to make the vehicles . In partBy employing a Hotelling model, we obtain the equilibrium outcomes of two competing firms without and with the consumer subsidy following Nash game theory. We obtain some interesting results.Firstly, there are changing Nash equilibriums as the variable manufacturing cost of the pure EV varies. In addition to both firms choosing the same vehicle type, i.e., producing energy-saving FVs or pure EVs, if the two firms choose different vehicle types, the firm with a lower technology capacity of improving the energy-saving level of the FV  would offer the pure EV, and the other firm  offers the energy-saving FV, while the converse is not true. In this case, the decreasing variable manufacturing cost of the pure EV will benefit firm 2 and make firm 1 lose in a competing context. Therefore, the development of the EV technology may hurt some vehicle firms having the advanced technologies used to produce the energy-saving FV. This finding can well explain why Toyota, the leader of firms producing hybrid vehicles, has disclosed its key technologies in order to shorten the gap of technology capacity with other competitors. We also find that both firms would charge lower retail prices as the variable manufacturing cost of the EV decreases. We further derive conditions under which each Nash equilibrium exists. We see that the consumer subsidy can influence not only the conditions but also the two firms’ equilibrium decisions, and eventually influence the environment, profits, and consumer surplus.Secondly, we prove that consumer subsidy programs could reduce carbon emissions in a competing context in two ways. The first is making both firms more likely to produce pure EVs instead of energy-saving FVs, and the second is encouraging both firms to increase the energy-saving levels of FVs if they decide to produce FVs. These results reveal approaches of the consumer subsidy to improve the environment. In particular, it indicates that although some consumer subsidies are not high enough to promote sales of pure EVs just as the government expects, they could increase energy-saving levels of FVs, and eventually reduce the carbon emissions. In addition, while one may expect that the consumer subsidy can encourage a firm to charge a higher price for the energy-saving FV and EV, we find that the firm producing the less energy-saving vehicle than the other firm will charge a lower price under the consumer subsidy program than that under no subsidy program. This is because the consumer subsidy would enhance the competitive advantages of the firm producing the higher energy-saving vehicle. The firm producing vehicles with the lower energy-saving vehicle would have to reduce its price to retain its potential consumers. This result proves the effectiveness of consumer subsidiary in improving the environment and provides guidance for firms to charge prices for consumers in a competitive context.Thirdly, we find the conflicting effects of the consumer subsidy on the two firms’ profits because of the competition between them. Specifically, the firm that offers the higher energy-saving vehicle will get benefits while the other firm always gets the loss from the increasing consumer subsidy. In addition, we are surprised to find that the consumer subsidy could hurt the total profits of the two firms if they offer different vehicle types and the consumer subsidy is in a low level; otherwise, the consumer subsidy always increases the total profit of the two firms.Finally, we find that the consumer subsidy always benefits the consumers if both two firms offer the energy-saving FVs. This is because the consumer subsidy not only improves the energy-saving levels of the FVs but also subsidizes the consumer who purchases the FV directly. However, if the firm with the lower technology capacity decides to offer the EV while the firm with the higher technology capacity offers the FV, the consumer surplus would be harmed by increasing the consumer subsidy under certain conditions, namely the government offering a small subsidy and there is a high degree of inconvenience of the EV to the consumer. This is because the increased consumer subsidy could induce more consumers to purchase the EVs and the large inconvenience of the EV to the consumer makes such a shift harmful for the consumer surplus. This result indicates that the government should take the supporting infrastructure of EVs into account while launching a consumer subsidy program.The remainder of the paper is organized as follows. In This paper is closely related to the literature about green production, government policy, and competition.As consumer environmental awareness and social responsibility rose, lots of researchers began to pay attention to the issues of green production, including green product line design and pricing. Based on the theory of market segmentation, Chen  formulatNote that most literature on green production of vehicles only involves a type of green technology innovation, namely the energy-saving FV ,17 or thZhu and He  propose Our work is closely related to the research that considers government policy as an instrument to improve the environment ,21,22,23Research on consumer subsidy policy is the most related to our work ,26,27,28Besides the environmental impacts, a large number of studies also explore the impact of government policy on firms’ profit and social welfare ,30,31,32In our paper, the impacts of the consumer subsidy on the environment, the firms’ profits, and the consumer welfare are all taken into account. In particular, we study the impacts of the consumer subsidy in a competing context while the two types of green technology innovation of vehicles are both considered.Another related body of literature is the research about the competition of green products ,34,35,36Different from this research mentioned above, we consider two automotive firms competing with not only the quality  and prices but also the type of the green technology innovations of the vehicles. Specifically, a firm has to choose a type of green vehicle to produce, such as the energy-saving FV or the pure EV, while competing with the other firm.This paper’s position in the literature is summarized in There are two vehicle firms, labeled by firm 1 and firm 2. Each of the two vehicle firms chooses to produce either an energy-saving fuel vehicle (FV) or an electric vehicle (EV). They compete with each other in the same market. For the energy-saving FV Generally, the government provides subsidies for consumers who purchase green vehicles in the automotive industry ,25,33. Aproducts ,35. WithWe utilize the Hotelling model to depict the consumer’s heterogeneous preference over two firms. The consumers are uniformly distributed on a  line, with the two firms at the two ends. Denote By purchasing a FV produced by firm 1 and firm 2, a consumer’s valuations are given by:By purchasing an EV produced by firm 1 and firm 2, a consumer’s valuations are given by:We suppose that consumers’ basic production valuation, g models ,38, and For either the energy-saving FV or the pure EV, we consider that all additional costs in improving the energy-saving levels of vehicles  are variable manufacturing costs. They are incurred by additional green devices to install, more material and parts in the vehicles, more expensive material and parts to use, and more assembly work to make the vehicles . In partIn particular, because technologies for producing the EV are immature for the majority of vehicle firms, the difference in technologies for producing the EVs is much less than that for producing the FVs in the automotive industry. Without loss of generality, we suppose a fixed variable manufacturing cost The timing of events is as follows. First, both firms simultaneously decide to produce either an energy-saving FV or an EV. Then, the firms that choose to produce the energy-saving FV determine the energy-saving levels for the FV. Finally, simultaneously the two firms set prices for the vehicles they produce.(i)In case FF,(ii)In case FE,(iii)In case EF,(iv)In case EE,It is straightforward to derive four possible cases based on the two firms’ selections, denoted by the case FF, FE, EF, EE. In the case FF, both firms choose to produce the energy-saving FVs; in the case FE (EF), firm 1 (2) chooses to produce the energy-saving FV, and the other chooses to produce the EV, and in the case EE, both firms choose to produce the EVs. We can derive the demand for firm Therefore, firm In this section, we consider that the government provides no consumer subsidy for consumers  if, then  is the unique pure Nash equilibrium (NE) and the equilibrium outcomes are,,, and(ii) if, then  is the unique pure NE and the equilibrium outcomes are,(iii) if, then  is the unique pure NE and the equilibrium outcomes arewhere,,andProposition 1 shows that the two firms’ production selections follow two thresholds, including a low threshold  shows that if a firm’s technology capacity for improving the energy-saving level of the FV is higher  shows the impact of consumer’s social responsibility on the price of FV and EV. Specifically, as the consumer’s social responsibility is higher . To further analyze the impact of the emergence of the EV on the two firms, we derive the effect of the cost of the EV on the firms’ profits.Corollary 2.When the variable manufacturing cost of the EV is moderate so that firm 2 decides to produce the EV and firm 1 produces the FV, firm 1′s profit will increase in In this section, we examine the scenario in which the government provides consumer subsidies for green vehicles. We develop the following propositions and corollaries to examine the impact of the consumer subsidies on the firms’ selections of vehicle type, equilibrium energy-saving levels for the FVs, equilibrium pricing for the FV/EV, total environmental benefits, and the firms’ profits. We use superscript Proposition 2.Under the consumer subsidy program, supposeand, we have:(i) if, then  is the unique pure NE and the equilibrium outcomes are(ii) if, then  is the unique pure NE and the equilibrium outcomes are(iii) if, then  is the unique pure NE and the equilibrium outcomes arewhere,,andProposition 2 shows similar results to that of Proposition 1. When the government offers the consumer subsidy, both firms choose to adopt the same vehicle type, namely offering the energy-saving FVs  shows that the consumer subsidy increases the two thresholds for the two firms lower than when the two firms would produce the EV instead of producing the energy-saving FV. Specifically, Corollary 3/(iii) see  shows thCorollary 3/(iv) see  shows thNotice that if the two firms offer the EVs simultaneously, neither would dominate the other. We find that the consumer subsidy makes no effect on the firms’ equilibrium pricing decisions, which is shown by Corollary 3/(v).As discussed above, the government’s consumer subsidy program can influence the two firms’ selections of green technology innovations and environmental efforts on improving the energy-saving levels of the FVs, as well as the prices for the vehicles. In this section, we discuss sequentially the impact of the consumer subsidy program on the profit, environment, and consumer surplus. As such, we firstly examine the impact of the consumer subsidy on the profits in Proposition 3.Proposition 3.whereProposition 3 shows the impact of the consumer subsidy coefficient on the profit of firm 1 and 2, and the total channel profit  shows see , when fiAs Proposition 3/(ii) see  demonstrIn summary, an increasing consumer subsidy cannot be beneficial for both competing firms. In particular, the firm that offers the vehicle with the higher energy-saving level will get benefits from the consumer subsidy. The consumer subsidy could hurt the total profits of the two firms if the two firms offer different vehicle types in NE and the consumer subsidy is at a low level, otherwise the consumer subsidy always increases the total profit of the two firms.We then define a metric for measuring total environmental benefits. As Shen et al.  and FiglWe see that the total carbon emissions are determined by three factors: i) the selection of green technology innovations of the two firms, ii) the demand for vehicles, and iii) the energy-saving levels of the vehicles. By comparing the total carbon emissions with and without the consumer subsidy, we can obtain Proposition 4.Proposition 4.Comparing the carbon emissions with and without the consumer subsidy shows thatProposition 4 indicates significant effects of the consumer subsidy in terms of protecting the environment. It is generally believed that the consumer subsidy could encourage firms to provide EVs with no carbon emissions and benefit the environment. In particular, when the two firms both produce FVs and no EV is provided, the total carbon emission of all vehicles with the consumer subsidy is still lower than that without the consumer subsidy . In the following, we evaluate the impacts of the consumer subsidy on the consumer surplus, denoted by  subsidy .By comparing the consumer surpluses with and without the consumer subsidy, we can get Proposition 5.Proposition 5.whereandProposition 5 points out the relationship between the consumer surplus and the consumer subsidy. Combining Propositions 3 and 5, we can see that the consumer subsidy offered by the government could hurt the consumer and the firms simultaneously if the subsidy is at a low level and the degree of inconvenience of the EV to consumers is high, when the two competing firms choose the different types of vehicles.In order to slow the speed of environmental pollution, it is generally accepted that the government supports the consumer with an incentive subsidy to promote the development of green vehicles in the automobile industry. While the government usually provides a higher subsidy  for the consumer to purchase a vehicle with a higher energy-saving level, the pure electric vehicle (EV) would be more attractive to consumers than the energy-saving fuel vehicle (FV) because of its higher energy-saving level. However, the limited supporting infrastructure for the operation of the EV  reduces the consumer’s valuation on the pure EV. Therefore, the vehicle firms need to decide to produce either the energy-saving FV or the pure EV, especially in a competing context.This paper constructs an oligopolistic competition game model where two vehicle firms choose to produce the pure EV or the energy-saving FV. The analysis of Nash equilibrium results shows each firm’s optimal green technology innovation selections and price decision for FV or EV, as well as the energy-saving level for the FV (if it decides to produce the FV). Furthermore, while the consumer subsidy supported by the government is taken into account, the impacts of the consumer subsidy on the firms’ profit, environment, and the consumer surplus are examined by comparing the equilibrium outcomes with and without the consumer subsidy.We find the following results. Firstly, there are changing Nash equilibriums as the variable manufacturing cost of the pure EV varies. In addition to both firms choosing the same vehicle type, i.e., producing energy-saving FVs or pure EVs, if the two firms choose different vehicle types, the firm with a lower technology capacity for improving the energy-saving level of the FV  would offer the pure EV and the other firm  offers the energy-saving FV, while the converse is not true. In this case, the decreasing variable manufacturing cost of the pure EV will benefit firm 2 and make firm 1 lose in a competing context. Therefore, the development of the EV technology may hurt some vehicle firms having the advanced technologies and producing the energy-saving FV. This finding can well explain why Toyota, the leader of firms producing hybrid vehicles, disclosed its key technologies in order to shorten the gap of technology capacity with other competitors. We also find that both firms would charge lower retail prices as the variable manufacturing cost of the EV decreases. We further derive conditions under which each Nash equilibrium exists. We see that the consumer subsidy can influence not only the conditions but also the two firms’ equilibrium decisions, and eventually influence the environment, profits, and consumer surplus.Secondly, we prove that consumer subsidy programs could reduce carbon emissions in a competing context in two ways. The first is making both firms more likely to produce pure EVs instead of energy-saving FVs, and the second is encouraging both firms to increase energy-saving levels of FVs if they decide to produce FVs. These results reveal approaches of the consumer subsidy to improve the environment. In particular, it indicates that although some consumer subsidies are not high enough to promote sales of pure EVs, just as the government expects, they could increase energy-saving levels of FVs and eventually reduce the carbon emissions. In addition, while one may expect that the consumer subsidy can encourage a firm to charge a higher price for the energy-saving FV and EV, we find that the firm producing the less energy-saving vehicle will charge a lower price under the consumer subsidy program than that under no subsidy program. This is because the consumer subsidy would enhance the competitive advantage of the firm producing the higher energy-saving vehicle. The firm producing vehicles with the lower energy-saving vehicle would have to reduce its price to retain its potential consumers. This result proves the effectiveness of consumer subsidiary in improving the environment and provides guidance for firms to charge prices for consumers in a competitive context.Thirdly, we find the conflicting effects of the consumer subsidy on the two firms’ profits because of the competition between them. Specifically, the firm that offers the higher energy-saving vehicle will get benefits while the other firm always gets the loss from the increasing consumer subsidy. In addition, we are surprised to find that the consumer subsidy could hurt the total profits of both firms if they offer different vehicle types and the consumer subsidy is at a low level; otherwise, the consumer subsidy always increases the total profit of the two firms.Finally, we find that the consumer subsidy always benefits the consumers if both two firms offer the energy-saving FVs. This is because the consumer subsidy not only improves the energy-saving levels of the FVs but also subsidizes the consumer who purchases the FV directly. However, if the firm with the lower technology capacity decides to offer the EV while the firm with the higher technology capacity offers the FV, the consumer surplus would be harmed by increasing the consumer subsidy under certain conditions, namely if the government offers a small subsidy and there is a high degree of inconvenience of the EV to the consumer. This is because increasing the consumer subsidy could induce more consumers to purchase the EVs, and the large inconvenience of the EV to the consumer makes such a shift harmful for the consumer surplus. This result indicates that the government should take the supporting infrastructure of EVs into account while launching a consumer subsidy program.Our research can be further extended in several directions. First, the environmental quality level of EV could be considered in future. In fact, although the percentage of greenhouse gas emissions by electric-driving vehicles is much smaller than that of fuel-driving vehicles, the battery life of EV could also influence the environmental quality indirectly. Second, to be more realistic, we could consider both environmentally and not environmentally conscious consumers in a market. Finally, it is more meaningful to investigate the difference in efficiencies between the consumer subsidy and other policies, such as the manufacturer subsidy, R&D subsidy, and credit policy.