Saccade Target Research Articles

Trans-retinal predictive signals of visual features are precise, saccade-specific and operate over a wide range of spatial frequencies.

Saccadic eye movements successively project the saccade target on two retinal locations: a peripheral one before the saccade, and the fovea after the saccade. Typically, performance in discriminating stimulus features changes between these two projections is very poor. However, a short (~ 200 ms) blanking of the target upon saccade onset drastically improves performance, demonstrating that a precise signal of the peripheral projection is retained during the saccade. While little is known about the nature of that transsaccadic signal, previous reports conjectured that it relies on information processed by the magnocellular system. Across two experiments, we investigated the feature blanking effect for a wide range of spatial frequencies (0.5 to 8 cycles per degree of visual angle, dva), stimulus sizes (1 to 4 dva) and eccentricities (6 to 10 dva). In each trial, participants executed a saccade to a high-contrast grating presented either left or right of fixation. During the saccade, the grating changed orientation (clockwise or counter-clockwise) either instantaneously or after a 200 ms blank, and participants reported the change's direction. We contrasted this saccade condition with a trans-retinal fixation condition mimicking the peripheral-then-foveal sequence of the target stimulus occurring across a saccade. Remarkably, blanking improved performance reliably for each spatial frequency, stimulus size, and eccentricity, but only in the saccade condition. Performance with blanking in saccade trials systematically exceeded performance in the fixation condition. Our results demonstrate a robust feature blanking effect across saccades, suggesting that transsaccadic processes involve low-level visual features beyond those processed in the magnocellular system.

Word length and frequency effects in natural Chinese reading: Evidence for character representations in lexical identification.

Word length and frequency are two of the "big three" factors that affect eye movements in natural reading. Although these factors have been extensively investigated, all previous studies manipulating word length have been confounded with changes in visual complexity (longer words have more letters and are more visually complex). We controlled stroke complexity across one-character (short) and two-character (long) high- and low-frequency Chinese words (to avoid complexity confounds) and recorded readers' eye movements during sentence reading. Both word length and frequency yielded strong main effects for fixation time measures. For saccadic targeting and skipping probability, word length effects, but not word frequency effects, occurred. Critically, the interaction was not significant regardless of stroke complexity, indicating that word length and frequency independently influence lexical identification and saccade target selection during Chinese reading. The results provide evidence for character-level representations during Chinese word recognition in natural reading.

Preselection of potential target spaces based on partial information by the supplementary eye field

Before selecting a saccadic target, we often acquire partial information about the location of the forthcoming target and preselect a region of visual space even before the target becomes visible. To determine whether the supplementary eye field (SEF) represents information signifying the potential target space, we examined neuronal activity in the SEF of monkeys performing a behavioral task designed to isolate the process of visuospatial preselection under uncertainty from the process of selecting a specified location. Our data showed that the activity of SEF neurons represented information about the potential target space instructed by symbolic cues. Increased activity of visuospatially selective SEF neurons encoded the potential target space, which could be a mechanism facilitating subsequent selection of an appropriate target. Furthermore, electrical stimulation of the SEF during the preselection period disrupted subsequent target selection. These results demonstrate that the SEF contributes to the preselection of potential target spaces based on partial information.

Dynamics of Saccade Trajectory Modulation by Distractors: Neural Activity Patterns in the Frontal Eye Field.

The sudden appearance of a visual distractor shortly before saccade initiation can capture spatial attention and modulate the saccade trajectory in spite of the ongoing execution of the initial plan to shift gaze straight to the saccade target. To elucidate the neural correlates underlying these curved saccades, we recorded from single neurons in the frontal eye field (FEF) of two male rhesus monkeys shifting gaze to a target while a distractor with the same eccentricity appeared either left or right of the target at various delays after target presentation. We found that the population level of pre-saccadic activity of neurons representing the distractor location encoded the direction of the saccade trajectory. Stronger activity occurred when saccades curved toward the distractor, and weaker when saccades curved away. This relationship held whether the distractor was ipsilateral or contralateral to the recorded neurons. Meanwhile, visually responsive neurons showed asymmetrical patterns of excitatory responses that varied with the location of the distractor and the duration of distractor processing relating to attentional capture and distractor inhibition. During earlier distractor processing, neurons encoded curvature towards the distractor. During later distractor processing, neurons encoded curvature away from the distractor. This was observed when saccades curved away from distractors contralateral to the recording site and when saccades curved towards distractors ipsilateral to the recording site. These findings indicate that saccadic motor planning involves dynamic push-pull hemispheric interactions producing attraction or repulsion for potential but unselected saccade targets.Significant Statement This study not only advances our understanding of oculomotor function in dynamic environments but also has potential clinical relevance for diagnosing and understanding disorders characterized by abnormal saccade trajectories. Our research elucidates the neural mechanisms behind saccade trajectories that are not always linear due to the brain's integration of multiple visual cues and/or motor plans. By analyzing the frontal eye field (FEF) activity in rhesus monkeys, we found that saccade directionality and timing are influenced by the interaction between FEF visual neurons representing target and distractor stimuli. The FEF's role extends beyond a winner-takes-all approach, incorporating saccade vector averaging computations that produce curved saccades. Furthermore, ipsilateral visual neurons encode distractor suppression that drives curvature away from the distractor.

The Effect of Visual Word Segmentation Cues in Tibetan Reading.

In languages with within-word segmentation cues, the removal or replacement of these cues in a text hinders reading and lexical recognition, and adversely affects saccade target selection during reading. However, the outcome of artificially introducing visual word segmentation cues into a language that lacks them is unknown. Tibetan exemplifies a language that does not provide visual cues for word segmentation, relying solely on visual cues for morpheme segmentation. Moreover, previous studies have not examined word segmentation in the Tibetan language. Therefore, this study investigated the effects of artificially incorporated visual word segmentation cues and basic units of information processing in Tibetan reading. We used eye-tracking technology and conducted two experiments with Tibetan sentences that artificially incorporated interword spaces and color alternation markings as visual segmentation cues. The results indicated that interword spaces facilitate reading and lexical recognition and aid in saccade target selection during reading. Color alternation markings facilitate reading and vocabulary recognition but do not affect saccade selection. Words are more likely to be the basic units of information processing and exhibit greater psychological reality than morphemes. These findings shed light on the nature and rules of Tibetan reading and provide fundamental data to improve eye movement control models for reading alphabetic writing systems. Furthermore, our results may offer practical guidance and a scientific basis for improving the efficiency of reading, information processing, and word segmentation in Tibetan reading.

Presaccadic Attention Enhances and Reshapes the Contrast Sensitivity Function Differentially around the Visual Field.

Contrast sensitivity (CS), which constrains human vision, decreases from fovea to periphery, from the horizontal to the vertical meridian, and from the lower vertical to the upper vertical meridian. It also depends on spatial frequency (SF), and the contrast sensitivity function (CSF) depicts this relation. To compensate for these visual constraints, we constantly make saccades and foveate on relevant objects in the scene. Already before saccade onset, presaccadic attention shifts to the saccade target and enhances perception. However, it is unknown whether and how it modulates the interplay between CS and SF, and if this effect varies around polar angle meridians. CS enhancement may result from a horizontal or vertical shift of the CSF, increase in bandwidth, or any combination. In addition, presaccadic attention could enhance CS similarly around the visual field, or it could benefit perception more at locations with poorer performance (i.e., vertical meridian). Here, we investigated these possibilities by extracting key attributes of the CSF of human observers. The results reveal that presaccadic attention (1) increases CS across SF, (2) increases the most preferred and the highest discernable SF, and (3) narrows the bandwidth. Therefore, presaccadic attention helps bridge the gap between presaccadic and postsaccadic input by increasing visibility at the saccade target. Counterintuitively, this CS enhancement was more pronounced where perception is better-along the horizontal than the vertical meridian-exacerbating polar angle asymmetries. Our results call for an investigation of the differential neural modulations underlying presaccadic perceptual changes for different saccade directions.

Neural correlates of perisaccadic visual mislocalization in extrastriate cortex

When interacting with the visual world using saccadic eye movements (saccades), the perceived location of visual stimuli becomes biased, a phenomenon called perisaccadic mislocalization. However, the neural mechanism underlying this altered visuospatial perception and its potential link to other perisaccadic perceptual phenomena have not been established. Using the electrophysiological recording of extrastriate areas in four male macaque monkeys, combined with a computational model, we were able to quantify spatial bias around the saccade target (ST) based on the perisaccadic dynamics of extrastriate spatiotemporal sensitivity captured by a statistical model. This approach could predict the perisaccadic spatial bias around the ST, consistent with behavioral data, and revealed the precise neuronal response components underlying representational bias. These findings also establish the crucial role of increased sensitivity near the ST for neurons with receptive fields far from the ST in driving the ST spatial bias. Moreover, we showed that, by allocating more resources for visual target representation, visual areas enhance their representation of the ST location, even at the expense of transient distortions in spatial representation. This potential neural basis for perisaccadic ST representation also supports a general role for extrastriate neurons in creating the perception of stimulus location.

An early effect of the parafoveal preview on post-saccadic processing of English words.

A key aspect of efficient visual processing is to use current and previous information to make predictions about what we will see next. In natural viewing, and when looking at words, there is typically an indication of forthcoming visual information from extrafoveal areas of the visual field before we make an eye movement to an object or word of interest. This "preview effect" has been studied for many years in the word reading literature and, more recently, in object perception. Here, we integrated methods from word recognition and object perception to investigate the timing of the preview on neural measures of word recognition. Through a combined use of EEG and eye-tracking, a group of multilingual participants took part in a gaze-contingent, single-shot saccade experiment in which words appeared in their parafoveal visual field. In valid preview trials, the same word was presented during the preview and after the saccade, while in the invalid condition, the saccade target was a number string that turned into a word during the saccade. As hypothesized, the valid preview greatly reduced the fixation-related evoked response. Interestingly, multivariate decoding analyses revealed much earlier preview effects than previously reported for words, and individual decoding performance correlated with participant reading scores. These results demonstrate that a parafoveal preview can influence relatively early aspects of post-saccadic word processing and help to resolve some discrepancies between the word and object literatures.

Saccadic targeting in the Landolt-C task: Implications for Chinese reading.

Participants in an eye-movement experiment performed a modified version of the Landolt-C paradigm (Williams & Pollatsek, 2007) to determine if there are preferred viewing locations when they searched for target squares embedded in linear arrays of spatially contiguous clusters of squares (i.e., sequences of one to four squares having missing segments of variable size and orientation). The results of this experiment indicate that, although the peaks of the single- and first-of-multiple-fixation landing-site distributions were respectively located near the centers and beginnings of the clusters, thereby replicating previous patterns that have been interpreted as evidence for the default saccadic-targeting hypothesis, the same dissociation was evident on nonclusters (i.e., arbitrarily defined regions of analysis). Furthermore, properties of the clusters (e.g., character number and gap size) influenced fixation durations and forward saccade length, suggesting that ongoing stimulus processing affects decisions about when and where (i.e., how far) to move the eyes. Finally, results of simulations using simple oculomotor-based, default-targeting, and dynamic-adjustment models indicated that the latter performed better than the other two, suggesting that the dynamic-adjustment strategy likely reflects the basic perceptual and motor constraints shared by a variety of visual tasks, rather than being specific to Chinese reading. The theoretical implications of these results for existing and future accounts of eye-movement control are discussed. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Presaccadic Attention Depends on Eye Movement Direction and Is Related to V1 Cortical Magnification.

With every saccadic eye movement, humans bring new information into their fovea to be processed with high visual acuity. Notably, perception is enhanced already before a relevant item is foveated: During saccade preparation, presaccadic attention shifts to the upcoming fixation location, which can be measured via behavioral correlates such as enhanced visual performance or modulations of sensory feature tuning. The coupling between saccadic eye movements and attention is assumed to be robust and mandatory and considered a mechanism facilitating the integration of pre- and postsaccadic information. However, until recently it had not been investigated as a function of saccade direction. Here, we measured contrast response functions during fixation and saccade preparation in male and female observers and found that the pronounced response gain benefit typically elicited by presaccadic attention is selectively lacking before upward saccades at the group level-some observers even showed a cost. Individual observer's sensitivity before upward saccades was negatively related to their amount of surface area in primary visual cortex representing the saccade target, suggesting a potential compensatory mechanism that optimizes the use of the limited neural resources processing the upper vertical meridian. Our results raise the question of how perceptual continuity is achieved and how upward saccades can be accurately targeted despite the lack of-theoretically required-presaccadic attention.

Inhibitory tagging both speeds and strengthens saccade target selection in the superior colliculus during visual search.

It has been suggested that, during difficult visual search tasks involving time pressure and multiple saccades, inhibitory tagging helps to facilitate efficient saccade target selection by reducing responses to objects in the scene once they have been searched and rejected. The superior colliculus (SC) is a midbrain structure involved in target selection, and recent findings suggest an influence of inhibitory tagging on SC activity. Precisely how, and by how much, inhibitory tagging influences target selection by SC neurons, however, is unclear. The purpose of this study, therefore, was to characterize and quantify the influence of inhibitory tagging on target selection in the SC. Rhesus monkeys performed a visual search task involving time pressure and multiple saccades. Early in the fixation period between saccades in the context of this task, a subset of SC neurons reliably discriminated the stimulus selected as the next saccade goal, consistent with a role in target selection. Discrimination occurred earlier and was more robust, however, when unselected stimuli in the search array had been previously fixated on the same trial. This indicates that inhibitory tagging both speeds and strengthens saccade target selection in the SC during multisaccade search. The results provide constraints on models of target selection based on SC activity.NEW & NOTEWORTHY An important aspect of efficient behavior during difficult, time-limited visual search tasks is the efficient selection of sequential saccade targets. Inhibitory tagging, i.e., a reduction of neural activity associated with previously fixated objects, may help to facilitate such efficient selection by modulating the selection process in the superior colliculus (SC). In this study, we characterized and quantified this modulation and found that, indeed, inhibitory tagging both speeds and strengthens target selection in the SC.

Presaccadic attention does not facilitate the detection of changes in the visual field.

Planning a rapid eye movement (saccade) changes how we perceive our visual world. Even before we move the eyes visual discrimination sensitivity improves at the impending target of eye movements, a phenomenon termed "presaccadic attention." Yet, it is unknown if such presaccadic selection merely affects perceptual sensitivity, or also affects downstream decisional processes, such as choice bias. We report a surprising lack of presaccadic perceptual benefits in a common, everyday setting-detection of changes in the visual field. Despite the lack of sensitivity benefits, choice bias for reporting changes increased reliably for the saccade target. With independent follow-up experiments, we show that presaccadic change detection is rendered more challenging because percepts at the saccade target location are biased toward, and more precise for, only the most recent of two successive stimuli. With a Bayesian model, we show how such perceptual and choice biases are crucial to explain the effects of saccade plans on change detection performance. In sum, visual change detection sensitivity does not improve presaccadically, a result that is readily explained by teasing apart distinct components of presaccadic selection. The findings may have critical implications for real-world scenarios, like driving, that require rapid gaze shifts in dynamically changing environments.

The representation of priors and decisions in the human parietal cortex.

Animals actively sample their environment through orienting actions such as saccadic eye movements. Saccadic targets are selected based both on sensory evidence immediately preceding the saccade, and a "salience map" or prior built-up over multiple saccades. In the primate cortex, the selection of each individual saccade depends on competition between target-selective cells that ramp up their firing rate to saccade release. However, it is less clear how a cross-saccade prior might be implemented, either in neural firing or through an activity-silent mechanism such as modification of synaptic weights on sensory inputs. Here, we present evidence from magnetoencephalography for 2 distinct processes underlying the selection of the current saccade, and the representation of the prior, in human parietal cortex. While the classic ramping decision process for each saccade was reflected in neural firing rates (measured in the event-related field), a prior built-up over multiple saccades was implemented via modulation of the gain on sensory inputs from the preferred target, as evidenced by rapid frequency tagging. A cascade of computations over time (initial representation of the prior, followed by evidence accumulation and then an integration of prior and evidence) provides a mechanism by which a salience map may be built up across saccades in parietal cortex. It also provides insight into the apparent contradiction that inactivation of parietal cortex has been shown not to affect performance on single-trials, despite the presence of clear evidence accumulation signals in this region.

Sound reduces saccadic chronostasis illusion

The saccadic chronostasis illusion refers to the duration overestimation of the first visual stimulation after saccadic eye movement, which is also known as “stopped clock illusion.” The present study investigated whether saccadic chronostasis would be observed in the auditory modality and whether the saccade-induced time dilation in the visual modality would be reduced by a synchronously presented sound. In each trial, a unisensory visual stimulus, unisensory sound, or bimodal audio-visual stimulus with a duration of 200–800 ms (probe stimulus) was presented at the saccade target location and temporally around the offset of the saccade, followed by a unisensory visual or auditory standard stimulus for a fixed 500 ms. Participants were required to identify which of the two stimuli (probe or standard) presented in the target modality (visual or auditory) was perceived as longer. The results showed that no saccadic chronostasis was observed in the auditory modality, regardless of whether the sound was presented alone or synchronously accompanied by a visual stimulus. Interestingly, the magnitude of the saccadic chronostasis illusion was reduced by the synchronously presented sound. Moreover, the combined effect of the saccade and sound on visual time perception fits well with the standard scalar model, and the weight of the cross-modal effect was higher than that of saccadic visual time dilation. These results suggest that sound dominates vision in time processing during saccades and linearly modulates saccadic chronostasis, which follows the Scalar Expectancy Theory.

Pre-saccadic Neural Enhancements in Marmoset Area MT.

Each time we make an eye movement, attention moves before the eyes, resulting in a perceptual enhancement at the target. Recent psychophysical studies suggest that this pre-saccadic attention enhances the visual features at the saccade target, whereas covert attention causes only spatially selective enhancements. While previous nonhuman primate studies have found that pre-saccadic attention does enhance neural responses spatially, no studies have tested whether changes in neural tuning reflect an automatic feature enhancement. Here we examined pre-saccadic attention using a saccade foraging task developed for marmoset monkeys (one male and one female). We recorded from neurons in the middle temporal area with peripheral receptive fields that contained a motion stimulus, which would either be the target of a saccade or a distracter as a saccade was made to another location. We established that marmosets, like macaques, show enhanced pre-saccadic neural responses for saccades toward the receptive field, including increases in firing rate and motion information. We then examined if the specific changes in neural tuning might support feature enhancements for the target. Neurons exhibited diverse changes in tuning but predominantly showed additive and multiplicative increases that were uniformly applied across motion directions. These findings confirm that marmoset monkeys, like macaques, exhibit pre-saccadic neural enhancements during saccade foraging tasks with minimal training requirements. However, at the level of individual neurons, the lack of feature-tuned enhancements is similar to neural effects reported during covert spatial attention.

Cross-linguistic comparison in reading sentences of uniform length: Visual-perceptual demands override readers' experience.

Accurate saccadic targeting is critical for efficient reading and is driven by the sensory input under the eye-gaze. Yet whether a reader's experience with the distributional properties of their written language also influences saccadic targeting is an open debate. This study of Russian sentence reading follows Cutter et al.'s (2017) study in English and presents readers with sentences consisting of words of the same length. We hypothesised that if the readers' experience matters as per discrete control account, Russian readers would produce longer saccades and farther landing positions than the ones produced by English readers. On the contrary, if the saccadic targeting is primarily driven by the immediate perceptual demands that override readers' experience as per the dynamic adjustment account, the saccades of Russian and English readers would be of the same length, resulting in similar landing positions. The results in both Cutter et al. and the present study provided evidence for the latter account: Russian readers showed rapid and accurate adjustment of saccade lengths and landing positions to the highly constrained input. Crucially, the saccade lengths and landing positions did not differ between English and Russian readers even in the cross-linguistically length-matched stimuli.

The Effect of Stimulus Contrast and Spatial Position on Saccadic Eye Movement Parameters.

(1) Background: Saccadic eye movements are rapid eye movements aimed to position the object image on the central retina, ensuring high-resolution data sampling across the visual field. Although saccadic eye movements are studied extensively, different experimental settings applied across different studies have left an open question of whether and how stimulus parameters can affect the saccadic performance. The current study aims to explore the effect of stimulus contrast and spatial position on saccadic eye movement latency, peak velocity and accuracy measurements. (2) Methods: Saccadic eye movement targets of different contrast levels were presented at four different spatial positions. The eye movements were recorded with a Tobii Pro Fusion video-oculograph (250 Hz). (3) Results: The results demonstrate a significant effect of stimulus spatial position on the latency and peak velocity measurements at a medium grey background, 30 cd/m2 (negative and positive stimulus polarity), light grey background, 90 cd/m2 (negative polarity), and black background, 3 cd/m2 (positive polarity). A significant effect of the stimulus spatial position was observed on the accuracy measurements when the saccadic eye movement stimuli were presented on a medium grey background (negative polarity) and on a black background. No significant effect of stimulus contrast was observed on the peak velocity measurements under all conditions. A significant stimulus contrast effect on latency and accuracy was observed only on a light grey background. (4) Conclusions: The best saccadic eye movement performance (lowest latency, highest peak velocity and accuracy measurements) can be observed when the saccades are oriented to the right and left from the central fixation point. Furthermore, when presenting the stimulus on a light grey background, a very low contrast stimuli should be considered carefully.

The role of visual crowding in eye movements during reading: Effects of text spacing.

Visual crowding, generally defined as the deleterious influence of clutter on visual discrimination, is a form of inhibitory interaction between nearby objects. While the role of crowding in reading has been established in psychophysics research using rapid serial visual presentation (RSVP) paradigms, how crowding affects additional processes involved in natural reading, including parafoveal processing and saccade targeting, remains unclear. The current study investigated crowding effects on reading via two eye-tracking experiments. Experiment 1 was a sentence-reading experiment incorporating an eye-contingent boundary change in which reader's parafoveal processing was quantified through comparing reading times after valid or invalid information was presented in the parafovea. Letter spacing was jointly manipulated to compare how crowding affects parafoveal processing. Experiment 2 was a passage-reading experiment with a line spacing manipulation. In addition to replicating previously observed letter spacing effects on global reading parameters (i.e., more but shorter fixations with wider spacing), Experiment 1 found an interaction between preview validity and letter spacing indicating that the efficiency of parafoveal processing was constrained by crowding and visual acuity. Experiment 2 found reliable but subtle influences of line spacing. Participants had shorter fixation durations, higher skipping probabilities, and less accurate return sweeps when line spacing was increased. In addition to extending the literature on the role of crowding to reading in ecologically valid scenarios, the current results inform future research on characterizing the influence of crowding in natural reading and comparing effects of crowding across reader populations.

A presaccadic perceptual impairment at the postsaccadic location of the blindspot.

Saccadic eye movements are preceded by profound changes in visual perception. These changes have been linked to the phenomenon of 'forward remapping', in which cells begin to respond to stimuli that appear in their post-saccadic receptive field before the eye has moved. Few studies have examined the perceptual consequences of remapping of areas of impaired sensory acuity, such as the blindspot. Understanding the perceptual consequences of remapping of scotomas may produce important insights into why some neurovisual deficits, such as hemianopia are so intractable for rehabilitation. The current study took advantage of a naturally occurring scotoma in healthy participants (the blindspot) to examine pre-saccadic perception at the upcoming location of the blindspot. Participants viewed stimuli monocularly and were required to make stimulus-driven vertical eye-movements. At a variable latency between the onset of saccade target (ST) and saccade execution a discrimination target (DT) was presented at one of 4 possible locations; within the blindspot, contralateral to the blindspot, in post-saccadic location of the blindspot and contralateral to the post-saccadic location of the blindspot. There was a significant perceptual impairment at the post-saccadic location of the blindspot relative to the contralateral post-saccadic location of the blindspot and the post-saccadic location of the blindspot in a no-saccade control condition. These data are consistent with the idea that the visual system includes a representation of the blindspot which is remapped prior to saccade onset.

Sensory tuning in neuronal movement commands

Movement control is critical for successful interaction with our environment. However, movement does not occur in complete isolation of sensation, and this is particularly true of eye movements. Here, we show that the neuronal eye movement commands emitted by the superior colliculus (SC), a structure classically associated with oculomotor control, encompass a robust visual sensory representation of eye movement targets. Thus, similar saccades toward different images are associated with different saccade-related "motor" bursts. Such sensory tuning in SC saccade motor commands appeared for all image manipulations that we tested, from simple visual features to real-life object images, and it was also strongest in the most motor neurons in the deeper collicular layers. Visual-feature discrimination performance in the motor commands was also stronger than in visual responses. Comparing SC motor command feature discrimination performance to that in the primary visual cortex during steady-state gaze fixation revealed that collicular motor bursts possess a reliable perisaccadic sensory representation of the peripheral saccade target's visual appearance, exactly when retinal input is expected to be most uncertain. Our results demonstrate that SC neuronal movement commands likely serve a fundamentally sensory function.