Emotional clues are always expressed in many ways in our daily life, and the emotional information we receive is often represented by multiple modalities. Successful social interactions require a combination of multisensory cues to accurately determine the emotion of others. The integration mechanism of multimodal emotional information has been widely investigated. Different brain activity measurement methods were used to determine the location of brain regions involved in the audio-visual integration of emotional information, mainly in the bilateral superior temporal regions. However, the methods adopted in these studies are relatively simple, and the materials of the study rarely contain speech information. The integration mechanism of emotional speech in the human brain still needs further examinations. In this paper, a functional magnetic resonance imaging (fMRI) study was conducted using event-related design to explore the audio-visual integration mechanism of emotional speech in the human brain by using dynamic facial expressions and emotional speech to express emotions of different valences. Representational similarity analysis (RSA) based on regions of interest (ROIs), whole brain searchlight analysis, modality conjunction analysis and supra-additive analysis were used to analyze and verify the role of relevant brain regions. Meanwhile, a weighted RSA method was used to evaluate the contributions of each candidate model in the best fitted model of ROIs. The results showed that only the left insula was detected by all methods, suggesting that the left insula played an important role in the audio-visual integration of emotional speech. Whole brain searchlight analysis, modality conjunction analysis and supra-additive analysis together revealed that the bilateral middle temporal gyrus (MTG), right inferior parietal lobule and bilateral precuneus might be involved in the audio-visual integration of emotional speech from other aspects. Our senses enable us to receive information about our surroundings, and they also have the ability to perceive specific modalities. Sometimes we may be able to make accurate judgments and responses to the surroundings through information from only one modality, but more often we need the assistance of the integrated multi-sensory information, and our cognition of the world is often multimodal. Therefore, our sensory organs are not isolated from each other. It is their synergy that enables us to respond flexibly to changes in our environment, which depends on the integration of multimodal information by the human brain. As an important dimension of daily communication, emotion is expressed in multimodal ways, such as facial expressions, body movements, emotional speech and music. Studies have shown that when emotions are expressed consistently in visual and auditory modalities, the classification accuracy of emotion is higher than that of unimodal stimuli . Lots ofVisual and auditory emotional information have been adopted as stimulus materials in many studies, revealing the role of the superior temporal sulcus (STS) and superior temporal gyrus in integrating audio-visual emotional contents . Using pA study on audio-visual language processing using EEG has shown that STS is neither the earliest nor the most significant activated site, although it is often considered to be necessary for the integration of audio-visual language . The rolMost studies on audio-visual integration of emotional information used the traditional generalized linear model (GLM) to model the data, and reported the significantly activated voxels by the statistical analysis, such as the modality conjunction analysis and supra-additive analysis. Modality conjunction analysis is defined as the activation of visual and auditory stimuli (AV) stronger than the activation of any unimodal stimuli (AV > A)∩(AV > V). It can be used to locate brain regions that are specific to both auditory and visual stimuli, which may be associated with cross-modal emotional processing, such as the audio-visual integration of emotion. The supra-additive analysis is defined as that the activation intensity of AV is greater than the sum of two unimodality (A+V) which uses a single-cell record directly and is first defined and measured at the cellular level. The supra-additive analysis is also a valid method for obtaining the brain regions of cross-modal integration. It is relatively simple to process data using the modality conjunction analysis and supra-additive analysis, and the fine-grained pattern information can be lost by using the statistical analysis to report significantly activated voxels . As a coIn this study, subjects experienced four emotional stimuli  expressed by three modalities  to explore the brain regions involved in the audio-visual integration of different emotional valences. GLM was first used to obtain the beta files corresponding to each stimulus condition. Next, the ROIs were determined by using the activation of all the subjects under the condition of audio-visual stimuli, and the candidate models were constructed by using hypothesis-driven RSA. The beta file was then generated using RSA based on ROI to obtain the correlation between the neural representation of ROIs and the candidate models. Weighted RSA was used to calculate the weight of each candidate model in the best fitted model for ROIs, thus obtaining the contributions of the models to interpret the representation of ROIs. To obtain brain regions that may be involved in audio-visual integration in the whole brain, a whole-brain searchlight method was then conducted to explore the brain regions significantly related to the audio-visual model, which could be used to verify the results of ROIs and locate other possible brain regions . FinallyTwenty-five healthy volunteers were recruited  from Tianjin University in this study. Nine subjects were excluded for further analysis for the data quality control. All subjects were right-handed with normal or corrected-to-normal vision, and all subjects had no history of neurological and psychiatric disorders. The study was carried out in accordance with the recommendations of Institutional Review Board (IRB) of Tianjin Key Laboratory of Cognitive Computing and Application, Tianjin University. All subjects gave written informed consents in accordance with the Declaration of Helsinki.The stimuli used in this study were collected from Geneva Multimodal Emotion Portrayals (GEMEP) . Four emThe fMRI experiment used an event-related design and contained three runs. The first run was visual stimuli of dynamic facial expressions, the second run was AV of emotional speech and the last run was consistent audio-visual emotional stimuli . Each ruThe imaging data was collected at Tianjin Huanhu Hospital using a 3.0T Siemens magnetic resonance scanner and an eight-channel head coil with the parameters in p = 0.05, FWE corrected). Voxels with a radius of 18 mm within the coordinate were extracted to obtain the main activated brain regions. Then the main activated regions were multiplied with the corresponding region of the AAL template, and the regions that might be involved in audio-visual information processing were obtained finally.The peak activation coordinates were first obtained in the activation results under the audio-visual condition at the group level  expressed by three modalities . The purpose of the GLM analysis is to calculate the beta values corresponding to each condition.The fMRI data was first preprocessed using the SPM12 toolkit in MATLAB software, including slice timing, realign, coregister, segment, normalize and smooth. In addition, the head movement is acceptable, which the horizontal movement is less than 2 mm and the rotation angle is less than 1.5For each ROI, the beta values of all conditions were extracted and expanded to a matrix of 12 × n (n represents the number of voxels in the ROI). Then the traditional RSA was used to compute the representation dissimilarity matrices (RDMs) of ROIs. The RDMs could be obtained by calculating the dissimilarity values between each two conditions, which were defined as one minus Pearson correlation coefficients. Next, the candidate model RDMs were constructed using hypothesis-driven RSA. Five emotion models  and three modality models  were constructed. In the emotion models, the dissimilarity values between different modalities of the same emotion were set to 0 and the dissimilarity between other conditions was set to 1. The generation of modality models were similar to the emotion models.In addition, a weighted RSA method was used to examine the contributions of all candidate models to the best fitted models of ROIs . The besThe statistical inference was finally made in the ROI analysis. For each ROI, the Kendal rank correlation coefficients between the neural representation RDM and the model RDMs were calculated. The participants were treated as random effects in the group analysis and the Kendall rank correlation coefficients were submitted to a unilateral Wilcoxon sign rank test to evaluate the significance of the correlation.t-test was used to get the significance value corresponding to the candidate model, then the whole-brain significance map (p-Map) was acquired. The whole procedure of data processing is shown in The searchlight analysis was used to obtain the regions that were significantly correlated to a specific candidate model in the whole brain. For each voxel, the beta values of the neighbor voxels with a radius of 6 mm were extracted and expanded to a matrix of 12 × n. Then the searchlight RDM could be obtained by using RSA. The correlation coefficient between data RDM and the candidate model was calculated, which was assigned to the central voxel of the searchlight analysis. The subjects’ whole-brain correlation map (r-Map) was obtained by repeating the process for all subjects on the whole brain. The subjects were treated as random effects in the group analysis and a one-sample t-test, and the significance level is set to p0.05. The activation map of audio-visual stimuli vs. unimodal stimuli was obtained on the group level. Finally, a conjunction analysis of (AV > A)∩(AV > V) was conducted.To further locate which brain region may be involved in audio-visual integration, two contrasts were defined in the first level analysis for all subjects. Then the group level analysis was conducted on all subjects’ result by using one sample t-test with significance level of p0.05 for the group level.Supra-additive analysis can be used to explore brain regions involved in processing other information besides visual and AV, such as audio-visual integration. The contrast of AV > (A+V) was set in the first level analysis for all subjects. The activation map was obtained by using one sample Nine ROIs were defined using the activation map of emotional speech at a group level of all subjects under the condition of audio-visual stimuli. To explore whether these brain regions are truly involved in the audio-visual integration of emotions, it is necessary to examine the association between the representation of brain regions and the emotional models, and determine whether they are significantly correlated with the audio-visual model.A linear combination of the 8 candidate models that constructed in the RSA procedure based on ROIs was used to obtain the optimal fitted model corresponding to each region, so as to minimize the mean square error between the fitted model and the neural representation RDM. The neural representation RDMs and the best fitted model RDMs of all brain regions are shown in SD = 0.020), indicating that the left insula was more likely to participate in the audio-visual integration of emotional speeches among all ROIs.The weight analysis showed that the weights of the sad model and audio-visual model were zero in the bilateral pSTS, and the weights of other emotion models were also not so high, suggesting that the bilateral pSTS might not be involved in the integration of audio-visual emotional speech. For the results of the best fitted models in other ROIs, each of the candidate models showed a great contribution, indicating that they might be associated with the audio-visual integration of emotions. It is worth noting that, compared with other brain regions, the audio-visual model had a more significant contribution to the best fitted model of the left insula  was used to process the results of all subjects, in order to obtain the correlation and significance between the RDMs and the models. For each subject, the Kendall rank correlation coefficients between the neural representation RDMs of the ROIs and the candidate models were further calculated. In the group analysis, the unilateral sign rank test . Further analysis will be carried out to reveal whether audio-visual integration of emotional speech is indeed associated with these brain regions.To further determine which observed regions are really involved in the audio-visual integration of emotional speech, the modality conjunction analysis of (AV > A)∩(AV > V) and the supra-additive analysis of (AV > A+V) were conducted for all subjects.t-test of p = 0.05 and cluster size above 30 voxels, the modality conjunction analysis  of Tianjin Key Laboratory of Cognitive Computing and Application, Tianjin University. Written informed consent was obtained from all participants for their participation in this study.JX proposed the idea. JX and NL designed the experiments. HD and NL performed the experiments and wrote the manuscript. JW, LF, and JX contributed to the manuscript revision. All authors contributed to discuss the results and have approved the final manuscript.


We present a test technique and an accompanying computational framework to obtain data-driven, surrogate constitutive models that capture the response of isotropic, elastic–plastic materials loaded in-plane stress by combined normal and shear stresses. The surrogate models are based on feed-forward neural networks (NNs) predicting the evolution of state variables over arbitrary increments of strain. The feasibility of the approach is assessed by conducting virtual experiments, i.e. Finite Element (FE) simulations of the response of a hollow, cylindrical, thin-walled test specimen to random histories of imposed axial displacement and rotation. In these simulations, the specimen’s material is modelled as an isotropic, rate-independent elastic–plastic solid obeying J2 plasticity with isotropic hardening. The virtual experiments allow assembling a training dataset for the surrogate models. The accuracy of two different surrogate models is evaluated by performing predictions of the response of the material to the application of random multiaxial strain histories. Both models are found to be effective and to have comparable accuracy. This exercise is particularly difficult in the presence of history-dependent responses4. Some authors have attempted using recurring NNs to capture non-linear, path-dependent constitutive responses of different types of solids5; considerable work has explored the response of heterogeneous solids, mainly two-phase composites, and used data-driven approaches to predict the effects of their microstructure on the mechanical behaviour (e.g.6). Some researchers have worked on data-driven models for elastic–plastic solids, collecting training datasets from simulations or measurements of proportional loading histories9, or from the results of structural tests10. We recently proposed a computational procedure to develop surrogate constitutive models for multiphase random composites11 with time- and path-dependent response, suitable for arbitrary multi-axial and non-proportional loading.Applications of machine learning have exponentially increased in number during the last decade and have spread to different fields including image recognition, web search, voice recognition, financial services, healthcare, sales, and more. Recent research also explored applications of machine learning to the mechanics of solids, with the main objective of reducing the computational cost of simulations involving complex material behaviour, by the introduction of surrogate constitutive models or data-driven microstructure-properties relations16. No previous research however has focused on developing data-driven constitutive models for elastic–plastic materials starting from data obtained from measurements and including non-monotonic and non-proportional loading; this is the objective of the present study.Several of the data-driven models described above were trained with numerical simulations of the response of Representative Volume Elements (RVEs) or of single FEs of known constitutive description. Similar approaches can in principle be developed using data obtained directly from measurements, to implement model-free simulations, as shown effectively by11 to obtain surrogate constitutive descriptions of the response of solid materials from measured data collected in lab-scale experiments. The objective is to develop numerical descriptions of the material behaviour which do not rely on any particular theory and are able to predict the material response subject to arbitrary loading, including complex non-monotonic and non-proportional deformation histories. To prove the feasibility of the approach, we conduct virtual tests by performing FE simulations of the response of a hollow, cylindrical, thin-walled test specimen to random histories of imposed non-proportional axial displacement and torsional rotation. The results of the simulations are processed in the same way as in actual experiments, obtaining time histories of the average direct and shear stresses and strains in the specimen’s gauge portion. Repeated virtual experiments are conducted by imposing multiple random deformation histories, such to adequately sample the space of the applied deformation. Such strain and stress histories are subdivided in small time increments, and the stresses and strains at the beginning and at the end of each increment are used as inputs and outputs, respectively, for the surrogate models. Additional history-dependent inputs are also included in the model. NNs are used to establish a correspondence between the inputs and the outputs, after appropriate training. The choice of obtaining the training dataset from virtual  experiments is driven by two reasons: (i) the fact that in virtual experiments the material’s response is well-defined and known in detail and (ii) the desire to perform a feasibility study for this approach, before embarking in an extensive experimental campaign.Here we follow similar steps as inThe paper is structured as follows. In section “Performing an accurate and complete characterisation of the multiaxial stress–strain response of solids is challenging, costly and requires equipment such as triaxial test machines, which are unavailable to most materials engineers. However, applying a combination of axial strain and torsional rotation to a thin-walled axisymmetric material specimen (which is the strategy pursued in this study) is relatively inexpensive and it results in approximately uniform normal and shear stresses on the specimen’s gauge portion; this allows exploring the material’s response in plane stress.20. The detailed sizing of the specimen was performed with the aid of FE simulations of its elastic–plastic response in pure tension, pure compression and pure torsion; the simulations served to assess and maximise the uniformity of the strains and stresses in the gauge portion; checks were performed to ensure that compressive and torsional elastic buckling did not occur, based on theoretical predictions for a thin-walled hollow cylinder (from21), with the conservative assumption of simply-supported boundary conditions at the ends of the cylinder. The final dimensions are indicated in Fig. The design of the test specimen was performed to minimise the variability of the normal and shear strains and stresses within the gauge portion, and to prevent compressive and torsional buckling and wrinkling during the  experiments. The geometry of the specimen, sketched in Fig. der from2, with th22. The material of the virtual specimens was taken as isotropic linear elastic  on the specimen, with the objective of determining the elastic compliance matrix of the material S were determined by a least square fit of Eq.  were used here to construct surrogate constitutive models based on the data presented above. A summary of how NNs work can be found inTwo different surrogate models are presented in this study, and their architecture is summarised in Fig. n is an index denoting the current state while n + 1 denotes the state at the end of the simulation increment considered.Before proceeding to describe the details the two surrogate models, we defineConsidering the relatively small deformations applied to the specimens, we assume that additive strain decomposition applies, i.e.We shall also make use of the current accumulated von Mises plastic strain, defined asThis model performs, at every increment, the regression.25, and ReLU26 was the chosen activation function for all hidden layers. The training dataset was split into two portions, equal to 10% and 90% of the total, which were randomly selected as testing and training data, respectively. The Mean Absolute Error (MAE25) was used as the loss function after a preliminary study. The training of the NN was performed by backpropagation using the Adam optimiser27, with a number of epochs set to 70,000, a batch size of 200 and a learning rate of 0.001.As the material studied is elastic–plastic, its response is expected to be history-dependent. In this model, gression , the incS, while predicting the non-linear and history-dependent elastic–plastic response represents the real challenge. In Model II, we separate the two types of predictions, in an attempt to improve the surrogate model and to reduce its computational cost.In a general increment in an FE simulation, two distinct behaviours (elastic or elastic–plastic) can be activated at each material point. The elastic response is simple to predict from knowledge of the compliance matrix Y is the flag defined in Eq.  with 11. The training of the NN was performed by backpropagation using the Adam optimiser27, with 10,000 epochs, a batch size of 100 and a learning rate of 0.001. The analysis of the confusion matrix25 showed that the classification was accurate in 99.84% of the cases.As shown in Fig. d in Eq.  ; the pltor  which had not been seen by the surrogate models during their training. These were generated using the same procedure described in section “Both Model I and Model II were used to predict the stress versus strain responses corresponding to the unseen random strain histories. For each of such histories, starting from the initial stress- and strain-free configuration  in Figs. We find that both surrogate models are in excellent agreement with the virtual tests. Both models capture the expected isotropy and symmetry of the material’s response, the yield locus corresponding to von Mises plasticity, and the details of the strain hardening characteristic of the solid. The accuracy of the surrogate predictions persists along most of the complex, non-monotonic, non-proportional strain paths considered; minor errors can be seen in the final parts of the random strain paths, due to accumulation of the error after a large number of increments, but also due to the relative scarcity of training datapoints for the NNs in those final parts of the random strain paths. We refer the reader to the 11 we showed that similar architectures of the surrogate models were also adequate for fully dense solids displaying a pressure-sensitive response.The accuracy of the predictions reassures us that the proposed architecture of the surrogate models, including the history-dependent evolution of the accumulated plastic strain, is adequate to capture the material response of the isotropic von Mises solid considered in this study. We note that in29: this would involve modifying the architecture of the surrogate models by enforcing appropriate constraints , including additional terms in the loss-function; it would however imply assuming a priori some features of the constitutive response. An additional development could be to include in the training dataset data measured in experiments involving non-uniform stress and strain fields, such as instrumented indentation or bending tests. We discuss this in the The obvious limitation of the surrogate models presented here that they are not necessarily accurate in regions of the input space scarcely populated by training datapoints. Such limitation can, however, be overcome by including additional coupon-level tests  to those considered here, for example biaxial or triaxial experiments. A complementary strategy could be to resort to physics-informed neural networksWe proposed a methodology to develop data-driven surrogate constitutive models which do not rely on any constitutive theory and are informed exclusively from the results of carefully designed random non-proportional, non-monotonic multiaxial tests. The aim of this study is to develop accurate numerical tools to predict the elastic–plastic response of materials prior to establishing valid theories describing their behaviour, and without any knowledge of their microstructure.We described a strategy to conduct relatively inexpensive experiments on the material of interest and to accurately capture its response by surrogate models based on small feed-forward NNs, including the design of suitable specimens and of the imposed random strain histories.We demonstrated that the proposed framework is very effective in the specific case examined, and that the surrogate models presented capture all details of the constitutive response assigned to the specimens in the virtual experiments.Supplementary Information.


Prior work has shown that accurately perceiving the risk for COVID-19 is associated with higher adherence to protective health behaviors, like face mask use, and more acceptance of governmental restrictive measures such as partial or complete banning of indoor activities and social gatherings. In this study we explored these associations at the beginning of the second wave of COVID-19 in Argentina through a national representative probabilistic survey that evaluated personal and contextual risk perception, self-reported compliance with protective health behaviors, attitude to governmental restrictive measures, and political orientation and psychological distress as potential modulators. Also, going beyond measures of association, here we sought to test whether messages highlighting potential risks increased acceptance of restrictive measures. Three types of messages were randomized to the participants. Two messages conveyed risk-related content  and the third a prosocial, altruistic content. Between March 29th and 30th, 2021, 2,894 participants were recruited . 74.64% of those surveyed evaluated the current health situation as “quite serious” or “very serious” and 62.03% estimated that the situation will be “worse” or “much worse” in the following 3 months. The perception of personal risk and the level of adherence to protective behaviors gradually increased with age. Through a regression model, age, perceived personal risk, and contextual risk appraisal were the variables most significantly associated with protective behaviors. In the case of the acceptance of restrictive measures, political orientation was the most associated variable. We then found messages aimed at increasing risk perception  had a significantly greater effect on increasing the acceptance of restrictive measures than the prosocial message, mainly for government supporters but also for non-supporters. However, the level of response was also modulated by the political orientation of the participants. We propose a mechanism of “ideological anchoring” to explain that participants were responsive to risk modulation, but within the limits established by their pre-existent political views. We conclude that messages highlighting risk can help reinforce the acceptance of restrictive measures even in the presence of polarized views, but must be calibrated by age and political orientation. During the last weeks of March 2021, the number of new cases of COVID-19 increased progressively in Argentina, raising the level of alert among experts, government officials, and the general public about the possibility of a second wave of cases in the country. In the weeks that followed, the concerns became reality and the incidence of new cases and mortality surpassed the worst numbers seen during 2020. By March 28th, 2021, vaccination coverage against COVID-19 in Argentina  was not strong enough to protect against the dissemination of new strains of SARS-CoV-2 and the beginning of winter in the global south. In this context, people’s adherence to individual protection measures, such as the use of face masks, physical distancing, and the avoidance of enclosed social spaces, became essential to prevent the uncontrolled spread of the virus.Previous knowledge about the adoption of health protection behaviors during pandemics emphasized the role of risk perception in motivating the behavioral response . PerceivMeanwhile, risk perception seems to be influenced by multiple different factors. Older age, identifying as female gender (with a binary item), prosocial tendencies, higher self-efficacy, and confidence in science and medicine tend to be associated with a higher perception of risk; in contrast, younger age, identifying as male, and individualistic worldviews are more commonly associated with lower perception of risk . FinallyTogether with the reinforcement of individual protective behaviors, the imminence of a second wave rekindled public debate on the need for new restrictive measures on general mobility by the government after a more relaxed period during the previous summer months. During the COVID-19 pandemic’s first wave, Argentina has been considered one of the countries with the highest restrictions  with a The first aim of this study was to evaluate the population’s risk perception in the face of the second wave of COVID-19 in Argentina and its relationship with the adoption of protective health behaviors and the acceptance of restrictive measures. We also measured the following potential confounds: psychological distress, political orientation of the participants, vaccination status, and sociodemographic characteristics. A national probabilistic representative survey was conducted early on when the incidence of new cases began to increase in the last days of March 2021. We expected that health protective behaviors would be associated with perceived risk. Regarding confounders, we expected that being younger and experiencing greater psychological distress would be associated with less adherence to health protective behaviors. Instead, we anticipated that the acceptance of restrictive measures could also be influenced by political orientation, in addition to risk perception, due to polarization observed during the first wave.The second aim of this study was to assess the effect of risk-based messages on the acceptance of restrictive directives from the government. Previous research has shown that messages that heighten risk appraisals change intentions and behaviors related to health protection and safety in different domains, such as vaccination, dieting, dental hygiene, sun protection, driving, or medical testing . HoweverTo evaluate this, three alternative messages were randomized to the participants in the final section of the survey. The first message was designed as an informational update aimed at increasing risk perception from a cognitive appraisal process. The second message was designed to increase risk perception by triggering emotional arousal. Finally, the third message was conceived as a control message aimed to achieve a prosocial effect, rather than increasing the perception of risk. We hypothesized that the risk-targeted messages, and in particular the emotionally charged message, will have a greater effect than the pro-social message in promoting acceptance of restrictions.The information obtained could be useful in formulating recommendations to guide public policies based on behavioral and communication factors.1 Data collection took place between 29th and 30th March 2021.We carried out a representative probabilistic population survey at the national level through the Aresco Instant Research Platform.The first part of the survey explored COVID-19 risk perception and protective health behaviors, as well as socio-demographical characteristics of the participants and other variables of interest.In the final section of the survey, the effect of three types of randomized messages on the intention to accept stricter government restrictive measures against COVID-19 in the next 3 months was evaluated. The three types of messages were based on: (1) increasing perceived risk through an informational update based on comparative epidemiological facts (“cognitive risk enhancement message”); (2) increasing perceived risk through an emotionally loaded description of the new strains of the COVID-19 ; (3) activating prosocial attitudes targeted to take care of more vulnerable people .This project was approved by the Ethics Committee of the Favaloro Foundation.The survey explored the following dimensions:Data were collected on age range, gender, educational level, socioeconomic status, and the region of the country where the participants live.Two questions were included as measures of contextual risk perception  were surveyed. See The survey included a question that evaluated the participant’s agreement with different levels of hypothetical mobility restrictions as a response to a sustained increase in new cases. The question included five incremental options ranging from “allow all activities” to “total lockdown,” and the participants had to choose the one they considered the more adequate in case of a sustained worsening of the health scenario. See The level of psychological distress was assessed using the patient health questionnaire-4 (PHQ-4). The PHQ-4 is an ultra-brief self-report standardized questionnaire that integrates the two-item screening scale for depression PHQ-2 and the two-item screening scale for anxiety GAD-2 . The gloThe political orientation of the participants was assessed by asking which candidate they voted for in the previous 2019 presidential elections in Argentina (where the incoming president won with 48% of the votes). For a categorical analysis, the participants were grouped as “government supporters” if they voted for the president of the country at the time of the survey in 2021, and as “opposition supporters” if they had voted for any other candidate.Following the randomized messages , we performed stratified 5-fold cross-validation using sklearn’s StratifiedShuffleSplit function  with a 80:20 train:test split for each fold to compute the mean out-of-sample (OOS) R2 and standard deviation across test-set folds. Again, to avoid overfitting, the L1-penalty alpha coefficient was determined through nested cross-validation using 10-fold cross-validation on the training set by testing 30 equally spaced values on a log scale from 0.0001 to 1. Then, the optimal penalty coefficient was used to train a model and predict the test set of each fold to estimate how the model performs on samples it did not use for training . To compute coefficients and p-values for statistical explanatory inference purposes, we used Python’s statsmodels implementation of LASSO given p-values are not provided in the sklearn implementation and conversely, statsmodels does not provide the nested stratified cross-validation procedure we performed for prediction. We use the average L1-penalty derived from the prior cross-validation and fit LASSO on the entire dataset as is customary when computing regression coefficients and p-values  can be predicted from the remaining variables, we fit Least absolute shrinkage and selection operator (LASSO) multiple regression models for each of the three dependent variables. Our metric of interest is p-values  , an ordinal logistic regression was performed with treatment group as factor. This analysis allowed us to obtain the odds ratio of the effect of the two risk-related messages compared to the pro-social message.Given political orientation has been shown to influence attitudes toward restrictions in previous literature and it was also the main variable predicting support for restrictions in the LASSO regression analysis, we wanted to ascertain its effect on acceptance of restrictions together with the type of message received. For this reason, we included political orientation in the ordinal regression as a covariate. However, after including the new independent variable, goodness-of-fit testing of the ordinal logistic regression was not adequate. Hence, we changed regression link function to complementary log–log, instead of logit, as the former yielded the best fitting. In the “Results” section we preserved the two ordinal regression analyses, as long as the logit regression allowed us to calculate the odds ratio as a direct measure of the comparative effects of the message, while the complementary log-log regression allowed us to establish whether the message effects were significant after including political orientation as a covariate.Finally, the odds of eliciting the highest outcome category (“complete response”) was compared between the three types of messages. Odds ratios were obtained for the total sample and for subgroups according to political orientation.The final sample included 2,894 participants . Most of the participants (74.64%) appraised the current health context at the moment of the survey as “quite serious” or “very serious” . The rate of non-compliance in the age group under 29 years old was 37.61%, doubling the percentage of the total sample (18.56%). Rates on non-compliance also differed between political orientation groups , even if both supporters of government and opposers were mostly compliant , PHQ-2 (p = 0.126), or GAD-2 (p = 0.748) according to Kruskal–Wallis test.Regarding depressive symptoms, 25% of the participants showed scores of 3 or more on the PHQ-2, which is the cut-off point suggested to identify people who are likely to be depressed. For anxiety symptoms, 22.6% of the sample scored 3 or more in the GAD-2, indicating a possible anxiety disorder. There were no differences between age groups in PHQ-4 , between the PRI and the PHBI , and between the PRI and support for restriction measures . PHQ-4 was positively correlated with PRI , but not with PHBI or support for restrictions.The variables most significantly associated to PRI were current health context appraisal, followed by psychological distress, future health context appraisal, PHBI, support for restriction, being politically opposed (negatively), and age. Together these variables accounted for 21% of the variance of PRI.The variables most significantly associated to PHBI were age, followed by PRI, current health context appraisal, and support for restrictions. The model accounted for 17% of the variance of PHBI.Finally, the variables most significantly associated to Supporting restriction measures was being politically opposed followed by PRI and PHBI. The model accounted for 15% of the variance of the dependent variable.2 = 9.038, p = 0.011) and the assumption of proportional odds was met (p = 0.527). The obtained estimates indicated that the two risk-related messages outperformed the pro-social message. Participants that received the cognitive risk enhancement were significantly more likely to endorse a higher level of acceptance of restrictions than those who received the pro-social message . The effect of the emotional risk enhancement messages was also significant . Both the effects of cognitive risk messages  and emotional risk messages  remained significant. Political orientation also showed a significant effect on the result , with government supporters more likely to support a higher level of restrictions  perceived themselves as compliant with the protective health behaviors; however, older age groups tended to comply more. Participants who failed to comply with protective behaviors perceived a lower risk and had more mood symptoms. A negative mood may contribute to non-compliance by increased fatigue, social isolation, impaired cognitive functioning, or helplessness , but it In the regression analysis, the perceptions of personal risk and contextual risk appraisal were both associated with greater compliance with protective behaviors, and together with age, they were the most important variables to explain protective behaviors. These findings confirmed the hypothesis derived from classic models of health psychology about the relationship between risk perception and adoption of protective health behaviors , and werUp to this point, the expectations of a “rational” actor in the health domain were met for most people: participants perceived the external health situation in a realistic way, configured their personal risk based on prior information on susceptibility and severity, cognition and emotion were aligned, and then they adopted protective measures according to the level of perceived risk.However, a factor outside the health domain also seems to influence perceived risk and health behaviors. In the present study, we confirmed the modulating role of political orientation on risk perception observed in previous studies during the COVID-19 pandemic . CitizenInstead, the modulating effect of political orientation was especially evident in the support for restrictive measures: it was the variable that was most associated to the endorsement of restrictive measures in the regression analysis, over other health and demographic variables. This result is consistent with a previous report in Argentina .Why was support for restriction measures so influenced by political orientation, to a much greater extent than other health protective behaviors? The long period of restrictions adopted by the government of Argentina in response to the first wave of COVID-19 ignited a strong political debate because, unlike individual protective behaviors such as wearing a mask or maintaining physical distancing, the adoption of restrictive measures entailed high economical and emotional costs . This destatus quo” or the relaxation of restrictive measures, since 67% of the participants consider it necessary to adopt more restrictive measures than those in force at the moment of the survey, although with a preference for measures of intermediate intensity. These preferences for active but moderate measures suggest an “intelligent” decision process, rather than an automatic polarized alignment. Consequently, in many cases, the influence of political orientation may be a matter of degrees, rather than a dichotomy between extreme positions.Nevertheless, it should be noted that in our study the endorsement of restrictive measures does not appear to be completely polarized or irrationally detached from public health considerations. Regardless of the political orientation, there is a preference in most of the participants for the adoption of active measures over the maintenance of the “Finally, risk-based messages showed a significantly greater effect than prosocial messages in the intention to adopt stricter restriction measures. The first risk message was designed to elicit cognitive appraisal and make an informative update comparing the rates of infection and mortality the days before the survey with the rates of the first wave. The second risk message was intended to provoke emotional arousal by highlighting the more aggressive features of the new strains of the virus. The two risk messages worked better than a prosocial message reinforcing the importance of adopting restrictions for helping the more vulnerable population. These results showed that participants are in general permeable to interventions that modulate risk perception as previous studies on the matter have shown . Even ifTaking into account the results of the survey and the effects of the messages as a whole, we can affirm that both health-related and health-unrelated variables influence risk perception and the adoption of health protective measures. A matter of further study would be to understand how the two types of information interact. One possible account comes from the application of the anchoring and adjustment heuristic . A hypotDue to the action of the anchoring bias and the changes in health conditions themselves, it is conceivable that the adjustment process needs to be repeatedly updated at different times of the pandemic. Also, as shown in the experimental part of this study, the messages that increase the sense of risk through health-related information may serve as tools for adjusting the initial highly biased estimations, but the adjustment will be probably still constrained within the surroundings of the basal estimation. The right messages may reduce the bias, but will not make pre-existing differences between groups attributable to the ideologic anchoring disappear. This two-steps risk estimation process based on anchoring and adjustment heuristic could account for the influence of both non-health and health variables on risk estimation and the adoption of protective measures. Future experimental studies could test this.From the pragmatic perspective, and even within the limits created by this sort of ideologic anchoring, we have shown that health protective behaviors are linked to risk perception, and that risk perception may be enhanced by messages that operate at both informational and emotional levels of the risk perception process. Timely and accurate health information held by neutral non-partisan sources may result in desirable changes in the intention to support and to adopt protective behaviors, even if limited in magnitude.The present study has several limitations. First, the survey is based on self-report methods and therefore carries the biases typical of this type of subjective measurement. Second, our analyses are not intended to estimate the causal relationships between the variables assessed in the first part of the survey before the messaging. Third, the amount of variance explained in the three regression analyses was small, leaving a lot of room for unrecognized variables in explaining the phenomena studied. Fourth, the effect of the messages was measured as self-reported intentions, not as actual behaviors, and it is known that intentions do not always materialize as anticipated.As a matter of future studies, other factors not included in this report may have influenced the observed results and may help to understand the unexplained variance of the regression analyses. Non-health variables, such as institutional trust  or econoIn conclusion, the model that emerges from this study is that of health behavior governed by risk perceptions, with both elements moderated by political ideology. Risk perceptions respond to contextual factors and to information related to health and medical issues, but political orientation also is associated with the perceptions and behaviors toward health, especially in the more polarizing topics. Despite this, political ideology does not seem to be completely decoupled from health information, since even within the parameters of each group, certain rational relationships between the variables linked to health are maintained. At the individual level, those who perceive greater risk take more care of themselves. Most people prefer selective and intelligent measures, over the most extreme. Also, the modulation of risk through health-related information seems to exert an effect that is not completely neutralized by the influence of political ideology.github.com/danielmlow/covid19_risk.The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: The studies involving human participants were reviewed and approved by Comité de Ética Independiente de la Fundación Favaloro, Buenos Aires, Argentina. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.FT and AY conceived the design, performed the data analysis, and drafted the manuscript. DL contributed to the data analysis and writing. All authors provided feedback for the discussion.


Rotating machinery often works under complex and variable working conditions; the vibration signals that are widely used for the health monitoring of rotating machinery show extremely complicated dynamic frequency characteristics. It is unlikely that a few certain frequency components are used as the representative fault signatures for all working conditions. Aiming at a general solution, this paper proposes an intelligent bearing fault diagnosis method that integrates adaptive variational mode decomposition (AVMD), mode sorting based deep belief network (DBN) and extreme learning machine (ELM). It can adaptively decompose non-stationery vibration signals into temporary frequency components and sort out a set of effective frequency components for online fault diagnosis. For online implementation, a similarity matching method is proposed, which can match the online-obtained frequency-domain fault signatures with the historical fault signatures, and the parameters of AVMD-DBN-ELM model are set to be the same as the most similar case. The proposed method can decompose vibration signals into different modes adaptively and retain effective modes, and it can learn from the idea of an attention mechanism and fuse the results according to the weight of MIV. It also can improve the timeliness of the fault diagnosis. For comprehensive verification of the proposed method, the bearing dataset from the University of Ottawa is used, and some recent methods are repeated for comparative analysis. The results can prove that our proposed method has higher reliability, higher accuracy and higher efficiency. Bearing fault diagnosis plays a crucial role in rotary machines. Accurate detection and isolation of early-stage bearing faults will contribute to more safe and more efficient operation of the rotary machines . An analHowever, the many existing methods are supposed to handle the dataset collected from constant working conditions . In practice, the working conditions of rotary machines are complex and varying, so the vibration signals are often non-stationary. In recent years, some fault diagnosis methods have been proposed under variable working conditions ,18.As an example, Aiming at more practical solutions, many recent studies used signal decomposition techniques ,14,15, sThis paper proposes a data-driven AVMD-DBN-ELM model for bearing fault diagnosis. First, the WOA-VMD algorithm is used to adaptively decompose vibration signals into different frequency components, and then, an MIV-DBN algorithm is used for the mode sort. After mode selection, reference to the idea of attention mechanisms, and according to the weights obtained by using the MIV algorithm, the diagnosis result of each mode is fused. The DBN-ELM model for fault diagnosis is established by training the selected modes. Finally, a similarity match method is used to match the most similar data, and the parameters are set according to the similar data parameter setting. After acquiring the retained modes, the fault diagnosis model handles these modes and acquires the result of fault diagnosis.The advantages of the proposed method are as follows. First, the proposed method can decompose vibration signals into different modes adaptively and retain effective modes. The second advantage is that it can learn from the idea of attention mechanism and fuse the results according to the weight of MIV; the third advantage is that it can improve the timeliness of the fault diagnosis.The rest of this paper is organized as follows. The overview of the proposed adaptive bearing fault diagnosis method is shown in K, but the value of α and K may be different under different working conditions. In this paper, the WOA algorithm is used to optimize the values of the two main input parameters.VMD is an adaptive and completely non-recursive method and uses signals to decompose modes . The corWOA  is an opWhen When When Next, we judge whether α and K. Given the vibration signal N is the number of sampling points, and The envelope entropy can reflect the sparse nature of the vibration signal. The maximum value of envelope entropy reflects the most uncertain probability distribution . The minimum values of envelope entropy are the optimal solution of tropy Ep  is:(5){EThe implementation steps of the WOA-VMD algorithm for decomposing vibration signal are as follows: Step 1: Pre-process the vibration signals;Step 2: Set the parameters of WOA;Step 3: Set the parameters of VMD;Step 4: Decompose the vibration signal into different frequency components using the VMD algorithm;Step 5: Judge whether the value of envelope entropy is minimum;Step 6: According to the judgment result of Step 5, return to Step 3 if the result dissatisfies Step 5. If the result satisfies Step 5, output the result of the variational mode;Step 7: Complete the process of decomposing the vibration signal adaptively.The MIV algorithm  reflectsThe second step in Step 1: Take the variational mode obtained from the WOA-VMD algorithm as the training dataset;Step 2: Use the DBN algorithm to train a normal fault diagnosis model;Step 3: Increase the value of the training dataset (here named P) by 10% to form a new training dataset P1, and reduce the value of the training dataset by 10% to form a new training dataset P2;Step 4: Use the VMD algorithm to decompose the vibration signal into different frequency components;Step 5: Based on the P1 and P2, use the fault diagnosis model to obtain the simulation results A1 and A2;Step 6: Calculate the MIV, and sort the mode according to the absolute value of the MIV to complete the process of mode sorting.The mode sort can highlight the role of the components that contain fault information and to screen out the parts of the signal that are not useful for diagnosis.This paper combines the DBN algorithm with the ELM algorithm. The DBN algorithm is used to extract features, while the ELM algorithm is used for classification. The BP algorithm used in the DBN algorithm must be iterative, whereas the use of the ELM algorithm can rapidly learn without iteration. Compared with only using the DBN algorithm, the DBN-ELM method has faster learning speed and better generalization performance, and its structure is shown in step 3 of The detailed process of the DBN-ELM method is described as follows:Step 1: Take the selected mode obtained from the MIV-DBN algorithm as the training dataset, and the number of training dataset is equal to the number of selected mode;Step 2: With different training datasets, the DBN-ELM algorithm is used to train the fault diagnosis model;Step 3: Refer to the idea of attention mechanisms , and accStep 4: Complete the process to build the fault diagnosis model.The above steps solve the problem of establishing a diagnostic model based on offline data, but in fact, the rotating machinery’s continuous operation and online data are generated all the time. Because the online data is generated all the time, the online data fault diagnosis needs to be completed in a timely manner, but the process of parameter optimization takes too much time. Therefore, in this section, a strategy of online diagnosis is simulated, a similarity match method is used to match the most similar data, and the parameters are set according to the similar data parameter setting. This method reduces the time by removing the process of parameter optimization; after acquiring the retained modes, the fault diagnosis model handles these modes and acquires the result of fault diagnosis, and its structure is shown in step 3 of Step 1: Use the similarity matching method to match the high similar data, and use the maximum mean discrepancy (MMD)  to calcuStep 2: Set the VMD and MIV algorithm parameters according to the most similar data parameter setting;Step 3: Acquire the modes by using the MIV algorithm;Step 4: Use the fault diagnosis model to train these modes and acquire the result of fault diagnosis.This paper proposed an adaptive VMD and mode sort based DBN-ELM algorithm for bearing fault diagnosis. The adaptive decomposition process of vibration signal is completed by using the WOA-VMD method. The MIV algorithm is used to complete the mode sorting process. The DBN-ELM algorithm is used to achieve the establishment of fault diagnosis model. The similarity matching method is used to complete the online fault diagnosis process. Compared with traditional bearing fault diagnosis methods under constant speed working conditions, the proposed method can be applied to more working conditions, and the timeliness of fault diagnosis is also considered.In this section, the bearing fault diagnosis dataset from the University of Ottawa  is used In this section, the experimental study is conducted by using the bearing fault diagnosis dataset from the University of Ottawa, in which 5 kinds of faults are considered, and each kind of fault has 4 kinds of time-varying rotational speed working conditions. The 5 kinds of faults includes healthy status (here marked as H), the outer raceway fault (here marked as OF), the inner raceway fault (here marketed as IF), the ball fault (here marked as BF) and a combination fault (here marked as CF). The 4 kinds of working conditions include the speed increasing working conditions (here marked as SI), speed decreasing working conditions (here marked as SD), speed increasing and then decreasing working conditions (here marked as SID), speed decreasing and then increasing working conditions (here marked as SDI). α and K [α and K are different under different working conditions.The main parameters of VMD are α and K , and wheAfter the VMD completes the vibration signal decomposition, the VMD decomposed spectrum is used as the training dataset. The MIV-DBN algorithm is used to train the frequency spectrum data. The MIV value is obtained, and the mode sorting process is completed. With the DBN-ELM, the fault diagnosis accuracies of five kinds of faults are shown in This paper proposes an adaptive VMD and mode sort based DBN-ELM method for bearing fault diagnosis. This method can handle the vibration signals collected from different working conditions in which multiple frequency components are mixed. This method contains four main processes: first, the WOA-VMD is used to decompose the vibration signal into different modes; second, according to the influence level of input neuron to output neuron, the MIV method is used to sort the different modes; third, the DBN-ELM method is used to build the fault diagnosis model; finally, according to the similarity matching method, the process of online fault diagnosis is completed.The proposed method focuses on the vibration signal collected from complex working conditions in which multiple frequency components are mixed. The method of this paper has three advantages: the first advantage is that it can decompose vibration signal into different modes, and according to the influence level of input neuron to output neuron, the different modes allow sorting. The mode sort can highlight the role of the components that contain fault information and to screen out the parts of the signal that are not useful for diagnosis. The second advantage is that it can learn from the idea of the attention mechanism and fuse the results according to the weight of MIV; the third advantage is that it can improve the timeliness of the fault diagnosis. Therefore, this method is hopeful to be applied in practical industrial conditions to optimize the reliability, accuracy and timeliness of the fault diagnosis.


This study provides a promising approach for achieving optical measurements with comprehensive high performance and may have great significance in various applications, such as vision-controlled directional navigation and high-dynamic target tracking, formation and obstacle avoidance of unmanned aerial vehicles.Optical measurement systems suffer from a fundamental tradeoff between the field of view (FOV), the resolution and the update rate. A compound eye has the advantages of a wide FOV, high update rate and high sensitivity to motion, providing inspiration for breaking through the constraint and realizing high-performance optical systems. However, most existing studies on artificial compound eyes are limited by complex structure and low resolution, and they focus on imaging instead of precise measurement. Here, a high-performance lensless compound eye microsystem is developed to realize target motion perception through precise and fast orientation measurement. The microsystem splices multiple sub-FOVs formed by long-focal subeyes, images targets distributed in a panoramic range into a single multiplexing image sensor, and codes the subeye aperture array for distinguishing the targets from different sub-FOVs. A wide-field and high resolution are simultaneously realized in a simple and easy-to-manufacture microelectromechanical system (MEMS) aperture array. Moreover, based on the electronic rolling shutter technique of the image sensor, a hyperframe update rate is achieved by the precise measurement of multiple time-shifted spots of one target. The microsystem achieves an orientation measurement accuracy of 0.0023° (3σ) in the  Optical systems in nature can be roughly divided into three types: human eyes, fish eyes and compound eyes (ref. 7). The distinctive characteristics of these architectures can provide inspiration to meet the increasing requirements for high-performance optical measurement. Unlike vertebrate single-aperture eyes, compound eyes (refs. 9) are multiaperture systems made up of small eyes with different viewing angles; thus, their FOV can be as wide as that of fish eyes. Moreover, due to independent sensing neurons, with each corresponding to an ommatidium, and the parallel processing procedure, compound eyes have the advantages of a high update rate and high sensitivity to motion that human eyes and fish eyes do not have. If the high resolution of human eyes can be achieved in compound eyes without largely complicating the structure, high-performance optical measurement systems can be realized.Realizing the compatibility of a wide field of view (FOV), high resolution and a high update rate is a challenging scientific problem in the field of optical measurement. The orientation measurement of moving targets with high resolution and a high update rate in a wide FOV is also a common requirement in various applications, such as vision-controlled directional navigation and high-dynamic target tracking, formation and obstacle avoidance of unmanned aerial vehicles (refs. 22). As a result, the FOV is limited by the planar-distributed subeyes. To achieve a wide FOV, artificial compound eye systems with both curved lens arrays and photosensitive arrays are designed from the bionic perspective (refs. 25). Relying on flexible electronic techniques, curved photosensitive arrays are difficult to manufacture and incompatible with existing planar image sensors. Therefore, some studies have turn to a compound eye system combining a curved lens array with a planar pixel array. Due to the mismatch of the two components, it is necessary to design a relay device (refs. 31) or waveguide device (refs. 33). However, these devices only serve the purpose of light transmission and do not increase the focal length, retaining the low resolution typical for common compound eye systems. In addition to the low resolution and manufacturing difficulty (ref. 34), most existing compound eye systems focus on the restoration of observed images, and there are a few studies (refs. 32) on precise target motion measurement  and a planar pixel array (refs. e refs. 3 or waveg6).Here, we develop a lensless compound eye (LCE) microsystem with a wide FOV, high resolution and high update rate. As shown in Fig. osxsyszs) can be determined. Specifically, in the LCE coordinate system with the center of the image sensor as the origin, the target orientation can be represented by the angle vector  formed by the zs axis and the projection of the incident light on the osxszs and osyszs planes  that we measure can be calculated byh is the distance from the aperture array to the image sensor,  is the coordinate of a matched subaperture center, and  is the coordinate of the corresponding spot.The LCE realizes target motion perception through precise and fast orientation measurement. The perceived target of the LCE is a point-like target whose opening angle relative to aperture is much smaller than the sub-FOV of the LCE. When a point-like target is in the FOV of the LCE, the emitted or reflected light passes through the coded subeye aperture array and forms a series of projected coded spots on the single multiplexing image sensor. By decoding the position information of the spots, we can match the spots with the corresponding subeye apertures using perceptual algorithms . In this paper, multiple sub-FOV splicing and single-image sensor multiplexing are adopted to solve the contradiction between a large FOV and high resolution in a simple and easy-to-manufacture MEMS aperture array. The lens array size of a common planar artificial compound eye is close to the size of the image sensor, and the lens is near the image sensor (refs. 20). To achieve high resolution, we lift the planar subeye aperture array away from the image sensor to create a long focal length. At the same time, the size of the subeye aperture array is much larger than that of the image sensor, so the incident light from a wide range can reach the image sensor through different regions of the subeye aperture array, which ensures the realization of a wide FOV. The subeye aperture array is coded to recognize which region of the array or which sub-FOV the light is incident from.In the measurement, there exists a fundamental tradeoff between high resolution and a wide FOV. For single-aperture optical systems, a long focal length results in high resolution but a narrow FOV. Existing studies have achieved a large FOV by using multiple high-resolution single-aperture systems as a multiaperture system, which leads to a large instrument structure, data volume surge and low resource utilization (refs. 37). By acquiring and processing the images line by line, instead of frame by frame, we realize a hyperframe update rate in the LCE for real-time orientation measurement.Furthermore, we utilize the ERS imaging mode of the image sensor to enable the capability of tracking high-dynamic targets. The subeyes are densely arranged to ensure that photons from a target pass through multiple subeyes and form corresponding spots. The spots located on different rows of the image sensor are exposed at different moments Fig.  due to tThe basic optical parameters of the LCE are first determined for the convenience of subsequent analysis. Considering that several instruments can be used together to achieve a FOV of 360°, we choose 120° as the FOV of the LCE. Since the existing spot-centering methods can reach subpixel (submicron) accuracy, we set 7 mm as the focal length of the LCE to ensure arc-second angular resolution  without greatly increasing the volume of the microsystem. Next, we mainly optimize the subeye aperture array, the key component of the LCE, from two aspects: the aperture size for image quality and the aperture distribution for sub-FOV recognition.zs axis  of each rectangular aperture and has no components on the other side (with the length of lv). Then, the optimal lp is different for each incident angle, while the optimal lv remains unchanged. Note that each incident angle corresponds to a concentric circle in the subeye aperture array plane. The apertures at one concentric circle have the same lp but different rotations, and all the apertures have the same lv, which equals the lp of the aperture on the zs axis . For convenience, we radially place the apertures around the xis Fig.  so that xis Fig. . The simx and y directions). The acquired images contain the coding information of one or more subregions. By analyzing the positions of the spots, the subregions and apertures corresponding to the spots can be determined by the perception algorithm (see Supplementary Note 3c), and its manufacturing process is easy  of the LCE and the minimum distinguishable displacement (Δl) of the spot, and this Δl is determined by the centering precision limit related to the spot profile (ref. 38). The update rate is affected by the frame rate and the number of spots that can be distributed in different exposure rows of the detector. Details of the performance analysis are illustrated in the Materials and methods. The analysis shows that the FOV of the LCE reaches 120°. The centering precision limit over the incident angle is shown in Fig. The FOV of the LCE depends on the geometric arrangement of the subeye apertures and the image sensor. The resolution for orientation measurement is determined by the focal length  in the y direction across a wide FOV of 120°  Fig. . Differe20° Fig. . This ex39). Our approach is not limited to this because the update rate can be significantly improved by arranging the apertures more densely and improving the frame rate of the image sensor. More results for the dynamic target measurement can be seen in Supplementary Note Then, we conduct a high-dynamic target orientation measurement experiment. The turntable is rotated at a high speed of ~30°/s. The exposure time of the LCE is 20 ms, and the readout time interval between adjacent exposure rows is 20 μs. Taking the sampled image when the target is in the central sub-FOV as an example Fig. , the spoA lensless compound eye microsystem is developed for target orientation measurement with high performance, which consists of a planar coded subeye aperture array and a planar multiplexing image sensor. Both simulation and experimental results show that the LCE has the advantages of high resolution, a wide FOV, a hyperframe update rate, and a small and simple structure, even though in usual cases these capacities are restricted with each other. The work provides a promising approach for achieving optical measurements with comprehensive high performance and can be easily adapted to meet the requirements of various real-time motion measurement applications. A higher resolution can be achieved by choosing a longer focal length. A wider FOV can be realized by increasing the size of the subeye aperture array if the system volume limit is not strict. A higher update rate can be achieved by arranging the subeye apertures more densely, which also results in better accuracy because the number of spots increases. In addition, the LCE can simultaneously measure multiple sparse targets as long as the spots of these targets are distinguishable (see Supplementary Note 8). Different regions of the coded subeye aperture array are projected to the single multiplexing image sensor, which is consistent with superposition eyes. Target-orientation measurement is achieved by matching a single imaging spot and a single aperture, which is consistent with apposition eyes . For near-parallel light, the intensity distribution becomes  of the LCE for orientation measurement meetsThe angular resolution (α is the incident angle of the light and Δl is the minimum displacement of the spot that can be resolved by the image sensor. Δl can be determined by estimating the limit of subpixel centering precision based on the spot profile simulation (ref. 38). Combined with the long focal length (h) of the microsystem, LCE enables high orientation measurement resolution.Thus,Umax of our approach can be estimated by (ref. 41)nfps is the frame rate of the image detector and lamin is the minimum length of the spot that can be formed. Here, we select 37% of the maximum intensity as the extracting threshold and assume that the length of the extracted spot region is la. The lamin of the spot for the vertically incident light (Fig. The maximum update rate ght Fig.  is 0.050ght Fig.  is 0.164Supplementary Information