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When the mind wanders, attention turns away from the external environment and cognitive processing is decoupled from perceptual information. Mind wandering is usually treated as a dichotomy (dichotomy-hypothesis), and is often measured using self-reports. Here, we propose the levels of inattention hypothesis, which postulates attentional decoupling to graded degrees at different hierarchical levels of cognitive processing. To measure graded levels of attentional decoupling during reading we introduce the sustained attention to stimulus task (SAST), which is based on psychophysics of error detection. Under experimental conditions likely to induce mind wandering, we found that subjects were less likely to notice errors that required high-level processing for their detection as opposed to errors that only required low-level processing. Eye tracking revealed that before errors were overlooked influences of high- and low-level linguistic variables on eye fixations were reduced in a graded fashion, indicating episodes of mindless reading at weak and deep levels. Individual fixation durations predicted overlooking of lexical errors 5 s before they occurred. Our findings support the levels of inattention hypothesis and suggest that different levels of mindless reading can be measured behaviorally in the SAST. Using eye tracking to detect mind wandering online represents a promising approach for the development of new techniques to study mind wandering and to ameliorate its negative consequences.
Following up on an exchange about the relation between microsaccades and spatial attention (Horowitz, Fencsik, Fine, Yurgenson, & Wolfe, 2007; Horowitz, Fine, Fencsik, Yurgenson, & Wolfe, 2007; Laubrock, Engbert, Rolfs, & Kliegl, 2007), we examine the effects of selection criteria and response modality. We show that for Posner cuing with saccadic responses, microsaccades go with attention in at least 75% of cases (almost 90% if probability matching is assumed) when they are first (or only) microsaccades in the cue target interval and when they occur between 200 and 400 msec after the cue. The relation between spatial attention and the direction of microsaccades drops to chance level for unselected microsaccades collected during manual-response conditions. Analyses of data from four cross-modal cuing experiments demonstrate an above-chance, intermediate link for visual cues, but no systematic relation for auditory cues. Thus, the link between spatial attention and direction of microsaccades depends on the experimental condition and time of occurrence, but it can be very strong.
Reading requires the orchestration of visual, attentional, language-related, and oculomotor processing constraints. This study replicates previous effects of frequency, predictability, and length of fixated words on fixation durations in natural reading and demonstrates new effects of these variables related to previous and next words. Results are based on fixation durations recorded from 222 persons, each reading 144 sentences. Such evidence for distributed processing of words across fixation durations challenges psycholinguistic immediacy-of-processing and eye-mind assumptions. Most of the time the mind processes several words in parallel at different perceptual and cognitive levels. Eye movements can help to unravel these processes.
Reading requires the orchestration of visual, attentional, language-related, and oculomotor processing constraints. This study replicates previous effects of frequency, predictability, and length of fixated words on fixation durations in natural reading and demonstrates new effects of these variables related to previous and next words. Results are based on fixation durations recorded from 222 persons, each reading 144 sentences. Such evidence for distributed processing of words across fixation durations challenges psycholinguistic immediacy-of-processing and eye- mind assumptions. Most of the time the mind processes several words in parallel at different perceptual and cognitive levels. Eye movements can help to unravel these processes
The zoom lens of attention simulating shuffled versus normal text reading using the SWIFT model
(2012)
Assumptions on the allocation of attention during reading are crucial for theoretical models of eye guidance. The zoom lens model of attention postulates that attentional deployment can vary from a sharp focus to a broad window. The model is closely related to the foveal load hypothesis, i.e., the assumption that the perceptual span is modulated by the difficulty of the fixated word. However, these important theoretical concepts for cognitive research have not been tested quantitatively in eye movement models. Here we show that the zoom lens model, implemented in the SWIFT model of saccade generation, captures many important patterns of eye movements. We compared the model's performance to experimental data from normal and shuffled text reading. Our results demonstrate that the zoom lens of attention might be an important concept for eye movement control in reading.
The aim of this work was to verify the processing of pronominal anaphora by children that have attention deficit hyperactivity disorder or dyslexia. The sample studied consisted of 75 children that speak German, which read two texts of 80 words containing pronominal anaphora. The eye movements of all participants were recorded and, to make sure they were reading with attention, two activities that tested reading comprehension were proposed. Through the analysis of eye movements, specifically the fixations, the data indicate that children with disorders have difficulty to process the pronominal anaphora, especially dyslexic children.
Fixation durations in reading are longer for within-word fixation positions close to word center than for positions near word boundaries. This counterintuitive result was termed the Inverted-Optimal Viewing Position (IOVP) effect. We proposed an explanation of the effect based on error-correction of mislocated fixations [Nuthmann, A., Engbert, R., & Kliegl, R. (2005). Mislocated fixations during reading and the inverted optimal viewing position effect. Vision Research, 45, 2201-2217], that suggests that the IOVP effect is not related to word processing. Here we demonstrate the existence of an IOVP effect in "mindless reading", a G-string scanning task. We compare the results from experimental data with results obtained from computer simulations of a simple model of the IOVP effect and discuss alternative accounts. We conclude that oculornotor errors, which often induce mislocalized fixations, represent the most important source of the IOVP effect. (c) 2006 Elsevier Ltd. All rights reserved.
Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that it is the question of competitors in the “game” of word skipping that must be solved in eye movement research.
Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that it is the question of competitors in the "game" of word skipping that must be solved in eye movement research
The fast and the slow of skilled bimanual rhythm production : parallel versus integrated timing
(2000)
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
Real-world scene perception is typically studied in the laboratory using static picture viewing with restrained head position. Consequently, the transfer of results obtained in this paradigm to real-word scenarios has been questioned. The advancement of mobile eye-trackers and the progress in image processing, however, permit a more natural experimental setup that, at the same time, maintains the high experimental control from the standard laboratory setting. We investigated eye movements while participants were standing in front of a projector screen and explored images under four specific task instructions. Eye movements were recorded with a mobile eye-tracking device and raw gaze data were transformed from head-centered into image-centered coordinates. We observed differences between tasks in temporal and spatial eye-movement parameters and found that the bias to fixate images near the center differed between tasks. Our results demonstrate that current mobile eye-tracking technology and a highly controlled design support the study of fine-scaled task dependencies in an experimental setting that permits more natural viewing behavior than the static picture viewing paradigm.
Real-world scene perception is typically studied in the laboratory using static picture viewing with restrained head position. Consequently, the transfer of results obtained in this paradigm to real-word scenarios has been questioned. The advancement of mobile eye-trackers and the progress in image processing, however, permit a more natural experimental setup that, at the same time, maintains the high experimental control from the standard laboratory setting. We investigated eye movements while participants were standing in front of a projector screen and explored images under four specific task instructions. Eye movements were recorded with a mobile eye-tracking device and raw gaze data were transformed from head-centered into image-centered coordinates. We observed differences between tasks in temporal and spatial eye-movement parameters and found that the bias to fixate images near the center differed between tasks. Our results demonstrate that current mobile eye-tracking technology and a highly controlled design support the study of fine-scaled task dependencies in an experimental setting that permits more natural viewing behavior than the static picture viewing paradigm.
Mathematical models have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (Engbert, Longtin, & Kliegl, 2002)were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements we observe in reading experiments. Here, we present an advanced version of SWIFT which integrates properties of the oculomotor system and effects of word recognition to explain many of the experimental phenomena faced in reading research. We propose new procedures for the estimation of model parameters and for the test of the model’s performance. A mathematical analysis of the dynamics of the SWIFT model is presented. Finally, within this framework, we present an analysis of the transition from parallel to serial processing.
SWIFT explorations
(2003)
Mathematical, models,have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (R. Engbert, A. Longtin, & R. Kliegl, 2002) were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements observed in reading experiments. The authors present an advanced version of SWIFT that integrates properties of the oculomotor system and effects of word recognition to explain many of the experimental phenomena faced in reading research. They propose new procedures for the estimation of model parameters and for the test of the model's performance. They also present a mathematical analysis of the dynamics of the SWIFT model. Finally, within this framework, they present an analysis of the transition from parallel to serial processing
Scene viewing is used to study attentional selection in complex but still controlled environments. One of the main observations on eye movements during scene viewing is the inhomogeneous distribution of fixation locations: While some parts of an image are fixated by almost all observers and are inspected repeatedly by the same observer, other image parts remain unfixated by observers even after long exploration intervals. Here, we apply spatial point process methods to investigate the relationship between pairs of fixations. More precisely, we use the pair correlation function, a powerful statistical tool, to evaluate dependencies between fixation locations along individual scanpaths. We demonstrate that aggregation of fixation locations within 4 degrees is stronger than expected from chance. Furthermore, the pair correlation function reveals stronger aggregation of fixations when the same image is presented a second time. We use simulations of a dynamical model to show that a narrower spatial attentional span may explain differences in pair correlations between the first and the second inspection of the same image.
In humans and in foveated animals visual acuity is highly concentrated at the center of gaze, so that choosing where to look next is an important example of online, rapid decision-making. Computational neuroscientists have developed biologically-inspired models of visual attention, termed saliency maps, which successfully predict where people fixate on average. Using point process theory for spatial statistics, we show that scanpaths contain, however, important statistical structure, such as spatial clustering on top of distributions of gaze positions. Here, we develop a dynamical model of saccadic selection that accurately predicts the distribution of gaze positions as well as spatial clustering along individual scanpaths. Our model relies on activation dynamics via spatially-limited (foveated) access to saliency information, and, second, a leaky memory process controlling the re-inspection of target regions. This theoretical framework models a form of context-dependent decision-making, linking neural dynamics of attention to behavioral gaze data.
Visuospatial attention and gaze control depend on the interaction of foveal and peripheral processing. The foveal and peripheral regions of the visual field are differentially sensitive to parts of the spatial frequency spectrum. In two experiments, we investigated how the selective attenuation of spatial frequencies in the central or the peripheral visual field affects eye-movement behavior during real-world scene viewing. Gaze-contingent low-pass or high-pass filters with varying filter levels (i.e., cutoff frequencies; Experiment 1) or filter sizes (Experiment 2) were applied. Compared to unfiltered control conditions, mean fixation durations increased most with central high-pass and peripheral low-pass filtering. Increasing filter size prolonged fixation durations with peripheral filtering, but not with central filtering. Increasing filter level prolonged fixation durations with low-pass filtering, but not with high-pass filtering. These effects indicate that fixation durations are not always longer under conditions of increased processing difficulty. Saccade amplitudes largely adapted to processing difficulty: amplitudes increased with central filtering and decreased with peripheral filtering; the effects strengthened with increasing filter size and filter level. In addition, we observed a trade-off between saccade timing and saccadic selection, since saccade amplitudes were modulated when fixation durations were unaffected by the experimental manipulations. We conclude that interactions of perception and gaze control are highly sensitive to experimental manipulations of input images as long as the residual information can still be accessed for gaze control. (C) 2016 Elsevier Ltd. All rights reserved.
Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
(2021)
Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.
When searching a target in a natural scene, it has been shown that both the target’s visual properties and similarity to the background influence whether and how fast humans are able to find it. So far, it was unclear whether searchers adjust the dynamics of their eye movements (e.g., fixation durations, saccade amplitudes) to the target they search for. In our experiment, participants searched natural scenes for six artificial targets with different spatial frequency content throughout eight consecutive sessions. High-spatial frequency targets led to smaller saccade amplitudes and shorter fixation durations than low-spatial frequency targets if target identity was known. If a saccade was programmed in the same direction as the previous saccade, fixation durations and successive saccade amplitudes were not influenced by target type. Visual saliency and empirical fixation density at the endpoints of saccades which maintain direction were comparatively low, indicating that these saccades were less selective. Our results suggest that searchers adjust their eye movement dynamics to the search target efficiently, since previous research has shown that low-spatial frequencies are visible farther into the periphery than high-spatial frequencies. We interpret the saccade direction specificity of our effects as an underlying separation into a default scanning mechanism and a selective, target-dependent mechanism.
Saccades move objects of interest into the center of the visual field for high-acuity visual analysis. White, Stritzke, and Gegenfurtner (Current Biology, 18, 124-128, 2008) have shown that saccadic latencies in the context of a structured background are much shorter than those with an unstructured background at equal levels of visibility. This effect has been explained by possible preactivation of the saccadic circuitry whenever a structured background acts as a mask for potential saccade targets. Here, we show that background textures modulate rates of microsaccades during visual fixation. First, after a display change, structured backgrounds induce a stronger decrease of microsaccade rates than do uniform backgrounds. Second, we demonstrate that the occurrence of a microsaccade in a critical time window can delay a subsequent saccadic response. Taken together, our findings suggest that microsaccades contribute to the saccadic facilitation effect, due to a modulation of microsaccade rates by properties of the background.
Microsaccades - i.e., small fixational saccades generated in the superior colliculus (SC) - have been linked to spatial attention. While maintaining fixation, voluntary shifts of covert attention toward peripheral targets result in a sequence of attention-aligned and attention-opposing microsaccades. In most previous studies the direction of the voluntary shift is signaled by a spatial cue (e.g., a leftwards pointing arrow) that presents the most informative part of the cue (e.g., the arrowhead) in the to-be attended visual field. Here we directly investigated the influence of cue position and tested the hypothesis that microsaccades align with cue position rather than with the attention shift. In a spatial cueing task, we presented the task-relevant part of a symmetric cue either in the to-be attended visual field or in the opposite field. As a result, microsaccades were still weakly related to the covert attention shift; however, they were strongly related to the position of the cue even if that required a movement opposite to the cued attention shift. Moreover, if microsaccades aligned with cue position, we observed stronger cueing effects on manual response times. Our interpretation of the data is supported by numerical simulations of a computational model of microsaccade generation that is based on SC properties, where we explain our findings by separate attentional mechanisms for cue localization and the cued attention shift. We conclude that during cueing of voluntary attention, microsaccades are related to both - the overt attentional selection of the task-relevant part of the cue stimulus and the subsequent covert attention shift.(C) 2017 Elsevier Ltd. All rights reserved.
During reading, saccadic landing positions within words show a pronounced peak close to the word center, with an additional systematic error that is modulated by the distance from the launch site and the length of the target word. Here we show that the systematic variation of fixation positions within words, the saccadic range error, can be derived from Bayesian decision theory. We present the first mathematical model for the saccadic range error; this model makes explicit assumptions regarding underlying visual and oculomotor processes. Analyzing a corpus of eye movement recordings, we obtained results that are consistent with the view that readers use Bayesian estimation for saccade planning. Furthermore, we show that alternative models fail to reproduce the experimental data.
Skilled reading requires information processing of the fixated and the not-yet-fixated words to generate precise control of gaze. Over the last 30 years, experimental research provided evidence that word processing is distributed across the perceptual span, which permits recognition of the fixated (foveal) word as well as preview of parafoveal words to the right of fixation. However, theoretical models have been unable to differentiate the specific influences of foveal and parafoveal information on saccade control. Here we show how parafoveal word difficulty modulates spatial and temporal control of gaze in a computational model to reproduce experimental results. In a fully Bayesian framework, we estimated model parameters for different models of parafoveal processing and carried out large-scale predictive simulations and model comparisons for a gaze-contingent reading experiment. We conclude that mathematical modeling of data from gaze-contingent experiments permits the precise identification of pathways from parafoveal information processing to gaze control, uncovering potential mechanisms underlying the parafoveal contribution to eye-movement control.
Skilled reading requires information processing of the fixated and the not-yet-fixated words to generate precise control of gaze. Over the last 30 years, experimental research provided evidence that word processing is distributed across the perceptual span, which permits recognition of the fixated (foveal) word as well as preview of parafoveal words to the right of fixation. However, theoretical models have been unable to differentiate the specific influences of foveal and parafoveal information on saccade control. Here we show how parafoveal word difficulty modulates spatial and temporal control of gaze in a computational model to reproduce experimental results. In a fully Bayesian framework, we estimated model parameters for different models of parafoveal processing and carried out large-scale predictive simulations and model comparisons for a gaze-contingent reading experiment. We conclude that mathematical modeling of data from gaze-contingent experiments permits the precise identification of pathways from parafoveal information processing to gaze control, uncovering potential mechanisms underlying the parafoveal contribution to eye-movement control.
Skilled reading requires information processing of the fixated and the not-yet-fixated words to generate precise control of gaze. Over the last 30 years, experimental research provided evidence that word processing is distributed across the perceptual span, which permits recognition of the fixated (foveal) word as well as preview of parafoveal words to the right of fixation. However, theoretical models have been unable to differentiate the specific influences of foveal and parafoveal information on saccade control. Here we show how parafoveal word difficulty modulates spatial and temporal control of gaze in a computational model to reproduce experimental results. In a fully Bayesian framework, we estimated model parameters for different models of parafoveal processing and carried out large-scale predictive simulations and model comparisons for a gaze-contingent reading experiment. We conclude that mathematical modeling of data from gaze-contingent experiments permits the precise identification of pathways from parafoveal information processing to gaze control, uncovering potential mechanisms underlying the parafoveal contribution to eye-movement control.
Bottom-up saliency is often cited as a factor driving the choice of fixation locations of human observers, based on the (partial) success of saliency models to predict fixation densities in free viewing. However, these observations are only weak evidence for a causal role of bottom-up saliency in natural viewing behaviour. To test bottom-up saliency more directly, we analyse the performance of a number of saliency models---including our own saliency model based on our recently published model of early visual processing (Schütt & Wichmann, 2017, JoV)---as well as the theoretical limits for predictions over time. On free viewing data our model performs better than classical bottom-up saliency models, but worse than the current deep learning based saliency models incorporating higher-level information like knowledge about objects. However, on search data all saliency models perform worse than the optimal image independent prediction. We observe that the fixation density in free viewing is not stationary over time, but changes over the course of a trial. It starts with a pronounced central fixation bias on the first chosen fixation, which is nonetheless influenced by image content. Starting with the 2nd to 3rd fixation, the fixation density is already well predicted by later densities, but more concentrated. From there the fixation distribution broadens until it reaches a stationary distribution around the 10th fixation. Taken together these observations argue against bottom-up saliency as a mechanistic explanation for eye movement control after the initial orienting reaction in the first one to two saccades, although we confirm the predictive value of early visual representations for fixation locations. The fixation distribution is, first, not well described by any stationary density, second, is predicted better when including object information and, third, is badly predicted by any saliency model in a search task.
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
When we fixate our gaze on a stable object, our eyes move continuously with extremely small involuntary and autonomic movements, that even we are unaware of during their occurrence. One of the roles of these fixational eye movements is to prevent the adaptation of the visual system to continuous illumination and inhibit fading of the image. These random, small movements are restricted at long time scales so as to keep the target at the centre of the field of view. In addition, the synchronisation properties between both eyes are related to binocular coordination in order to provide stereopsis. We investigated the roles of different time scale behaviours, especially how they are expressed in the different spatial directions (vertical versus horizontal). We also tested the synchronisation between both eyes. Results show different scaling behaviour between horizontal and vertical movements. When the small ballistic movements, i.e., microsaccades, are removed, the scaling behaviour in both axes becomes similar. Our findings suggest that microsaccades enhance the persistence at short time scales mostly in the horizontal component and much less in the vertical component. We also applied the phase synchronisation decay method to study the synchronisation between six combinations of binocular fixational eye movement components. We found that the vertical-vertical components of right and left eyes are significantly more synchronised than the horizontal-horizontal components. These differences may be due to the need for continuously moving the eyes in the horizontal plane in order to match the stereoscopic image for different viewing distances.
The launch-site effect, a systematic variation of within-word landing position as a function of launch-site distance, is among the most important oculomotor phenomena in reading. Here we show that the launch-site effect is strongly modulated in word skipping, a finding which is inconsistent with the view that the launch-site effect is caused by a saccadic-range error. We observe that distributions of landing positions in skipping saccades show an increased leftward shift compared to non-skipping saccades at equal launch-site distances. Using an improved algorithm for the estimation of mislocated fixations, we demonstrate the reliability of our results.
Using a serial search paradigm, we observed several effects of within-object fixation position on spatial and temporal control of eye movements: the preferred viewing location, launch site effect, the optimal viewing position, and the inverted optimal viewing position of fixation duration. While these effects were first identified by eye-movement studies in reading, our approach permits an analysis of the functional relationships between the effects in a different paradigm. Our results demonstrate that the fixation position is an important predictor of the subsequent saccade by influencing both fixation duration and the selection of the next saccade target.
In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.
Active motor processes are present in many sensory systems to enhance perception. In the human visual system, miniature eye movements are produced involuntarily and unconsciously when we fixate a stationary target. These fixational eye movements represent self-generated noise which serves important perceptual functions. Here we investigate fixational eye movements under the influence of external noise. In a two-choice discrimination task, the target stimulus performed a random walk with varying noise intensity. We observe noise-enhanced discrimination of the target stimulus characterized by a U-shaped curve of manual response times as a function of the diffusion constant of the stimulus. Based on the experiments, we develop a stochastic information-accumulator model for stimulus discrimination in a noisy environment. Our results provide a new explanation for the constructive role of fixational eye movements in visual perception.