Better than expected performance effect depends on the spatial location of visual stimulus

doi:10.21203/rs.3.rs-4985593/v1

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Better than expected performance effect depends on the spatial location of visual stimulus

https://doi.org/10.21203/rs.3.rs-4985593/v1

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The process of perceptual decision-making in the real world involves aggregation of pieces of evidence into a final choice. The visual evidence is usually presented in different pieces, distributed along time and space. We wondered whether by adding variation in the location of the receiving information, subjects showed differences in how they integrated visual information. Seven participants viewed two pulses of random dots motion stimulus, separated by time gaps and in different areas of the visual field. Our findings suggest that subjects accumulate discontinuous information (over space or time), not in the same way as when they are presented continuously, at the same location or with no gaps between them. These findings indicate that the discontinuity of evidence impacts the process of evidence integration in a manner more nuanced than presumed by the theory positing the perfect integration of evidence.

Biological sciences/Neuroscience

Biological sciences/Psychology

Perception

Decision-making

Spatiotemporal integration

We make decisions all the time, from selecting our future career to the brand of our clothing. But how do we integrate all the information reaching us from different locations and separated by temporal gaps? Various efforts have been made to discover the neural ^1–4 and behavioral ^5–7 representations of decision-making process. Studies show that integration of sequentially sampled evidence over time until reaching a threshold (i.e. accumulation-to-bound model) can explain these representations during a decision-making task ^5,8–16. This process of integration and termination of it, is also found to be correlated with the ramping to a stereotype activity in several areas of the brain including the cortical and subcortical structures ^2,3,17–19.

In our daily experiences, we typically gather the information required for decision-making, presented as distinct pieces of evidence ^20–22. While the classic version of the accumulation-to-bound model assumes a time independent accumulation process ^{5,23,24,24,25}, a number of models include some form of time-dependent accumulation ^15,26–29 to account for information leakage or attention modulation. Several preceding studies have tried to integrate elements of real-life contexts inherent in perceptual decision-making to the conventional paradigms of visual tasks ^6,30–33. Previous studies on the spatial integration of the visual stimuli have focused on feature fusion ³⁴, spatial statistics ³⁵ and face perception ^36–38.

To explore how the passage of time influences the accumulation of visual evidence, researchers employed temporally discrete paradigms of established perceptual decision-making tasks by introducing temporal gaps between successive pulses of stimuli ^39–41. The results have shown that the accuracy of the ultimate decision is not affected by the duration of the gap between discrete pieces of evidence and participants integrate them with no loss (i.e., perfect integration). However, the observers extracted more information from the last pulse compared to the first one (sequence dependence or recency effect). It has also been shown that prediction of perfect accumulation models underperforms participants in double pulses (i.e., better than expected accuracy). Researchers tried to explain these effects by a time dependent attention mechanism ⁴⁰, the reliability bias ⁴² or adaptive gain of the information processing ⁴³. More importantly, the observed behavioral effects deviated from the predictions made by the proposed attractor-based decision-making models ^39,44 and thus they play an important role in understanding the underlying mechanism of decision making.

While some studies replicated these behavioral effects, to our knowledge none of them considered the role of spatial and temporal integration of evidence and their interaction in the observed effects. In other words, the effects so far are observed when pulses of evidence have been presented in same spatial position. In the present study, we aimed to investigate whether the similarity of spatial position may manipulate these effects. Two pulses of Random Dots Motion (RDM) stimuli were presented in either the same or different locations at the para-foveal vision of the participants. By fitting logistic regression models, we tested whether spatial and temporal separation of evidence had any influence on the eventual decision and thus the previously observed effects. We found that when RDM pulses were presented at different locations, subjects could not perfectly integrate the whole evidence coming from each of the pulses. Moreover, we showed that the previously observed effects are spatially dependent and some of them are vanished if the pulses of discrete evidence are presented at different locations.

Seven human participants completed several blocks of single or double pulse trials presented in either periphery (top or bottom) or center of their vision. The two peripheral pulses in each trial were presented at either the same (SL) or different locations of the screen (DL). The presented stimulus in each pulse was a set of random dots moving towards right or left for 150ms. At the end of each trial, subjects reported their perceived direction by pressing the right or left arrow key (Fig. 1). In order to avoid uncertainty about the location of stimuli, in each session, the sequence of presentation was fixed and participants were informed of it in advance. We collected 11836 trials in the center, 8940 in top-top, 9151 in bottom-bottom, and 8956 in top-bottom, and 9064 trials in bottom-top conditions, that gave us 47947 trials in total.

Participants improve their decision by using information within each pulse

First, we looked at the performance of participants in the single pulse trials as a function of coherence conditioned on RDM location (Fig. 2). Despite the brief presentation of stimulus (150ms), subjects showed a graded level of performance depending on the stimulus strength and reached close to 100% performance for the coherence of 51.2%. This pattern was very similar between conditions. While participants showed a bias to the right at the center location (Blue circles and line, Eq. 2, β₀ = 0.20 ± 0.08, p = 0.01), there was no significant bias observed in other conditions (Eq. 2, SL: cyan, β₀ = -0.12 ± 0.06, p = 0.07; DL: magenta, β₀ = -0.08 ± 0.07, p = 0.24). Performance of single pulse trials in the DL (73.76%) was higher than the SL (72.02%), but this difference did not reach significance level (repeated-measures ANOVA, F = 2.10, df = 2, p = 0.16). Next, we looked at the performance in double pulse trials. When both pulses had the same coherence, in center (Fig. 3A), same (Fig. 3B), and different (Fig. 3C) locations, performance in the double pulse trials (circles) were better than the corresponding performance in the single pulse trials (colored arrows).

The effect of gap duration varies based on the location of the stimuli

Looking at the results of the Eq. 4, we observed a significant difference between center and DL (Eq. 4, p < 0.01), while there was no significant difference in canter vs. same, or same vs. different comparisons (Eq. 4, p’s > 0.05). At the SL condition, we found that the gap between the two pulses had a significant effect on performance (Fig. 3B & E, Eq. 3: β₃ = -0.24 ± 0.11, p = 0.03). This effect was not observed for central (Fig. 3A & D, β₃ = 0.1 ± 0.14, p = 0.47), or DL conditions (Fig. 3C & F, β₃ = -0.13 ± 0.11, p = 0.24). In other words, while gap ($\:{{\beta\:}}_{3}$ in Eq. 3) had a significant effect on performance in the same condition (i.e., top-top and bottom-bottom), it did not reach significance level in center and different conditions.

Dissimilarity in the location of pulses reverses the better-than-expected effect

In order to test the hypothesis of location dependency of the better-than-expected effect, we compared the performance of participants with the expected performance computed by perfect integrator in different conditions of the experiment. The perfect integrator estimates the performance of double pulses based on the performance of the single pulses, assuming a perfect integration of evidence (Eq. 6). Our results suggest that while subjects had a performance at the level of perfect integrator in the center condition (Fig. 3A, Eq. 5: β = 0.03 ± 0.04, p = 0.80), they outperformed the expected accuracy at the SL (Fig. 3B, Eq. 5: β = 0.07 ± 0.03, p = 0.008), and underperformed in the DL condition (Fig. 3C, Eq. 5: β = -0.17 ± 0.03, p < 0.001). This pattern was the same when we rerun the analysis for double pulse trials with unequal coherences (Fig. 3D-F, Eq. 5: center: β = -0.01 ± 0.03, p = 0.35, SL: β = 0.14 ± 0.02, p < 0.001, DL: β = -0.16 ± 0.02, p < 0.001).

Sequence dependency effect is location dependent

As shown in previous work of Kiani et. al., and Tohidi-Moghaddam et. al., better-than-expected performance is the result of sequence dependency effect (i.e. extracting more information from the second pulse compared to the first pulse). As mentioned above, our results also showed this effect in the SL (i.e., top-top and bottom-bottom) but not in the DL condition (i.e., top-bottom and bottom-top, Fig. 4). To test if sequence dependency of the performance is also observed here, we divided the double-pulse trials based on the sequence of weak and strong coherences (e.g., 3.2–6.4% vs. 6.4–3.2%, Fig. 4). At the SL condition, we found that performance was significantly higher when the second pulse was stronger (Fig. 4B, 3.2–6.4 = 66.33%, 6.4–3.2 = 62.36%, p = 0.013; 3.2–12.8 = 75.65%, 12.8–3.2 = 72.36%, p = 0.024; 6.4–12.8 = 78.12%, 12.8–6.4 = 75.01%, p = 0.028, Wilcoxon Rank Sum). We observed the same pattern of results for the central location (Fig. 4A, 3.2–6.4 = 66.16%, 6.4–3.2 = 65.09%; 3.2–12.8 = 79.05%, 12.8–3.2 = 76.53%; 6.4–12.8 = 81.01%, 12.8–6.4 = 78.13%), though the difference did not reach significance level (p’s > 0.05). For the DL condition, we observed that the first pulse had a stronger effect on performance (Fig. 4C, 3.2–6.4 = 63.86%, 6.4–3.2 = 64.82%; 3.2–12.8 = 71.18%, 12.8–3.2 = 71.48%; 6.4–12.8 = 76.71%, 12.8–6.4 = 77.10%), but these differences did not reach significance level either (p’s > 0.05).

Due to the stochasticity in the RDM stimulus, an analysis of motion energy on each pulse can give us a better understanding of the effect of the pulse sequence on performance. This analysis was done on a portion of 30058 trials of the data with gap durations bigger than 0ms. Results from motion energy analysis on the data of central location confirmed the stronger influence of the second pulse on the accuracy of subjects (Fig. 5, top row, Eq. 11: β₃ = -0.07, p = 0.04; Eq. 12, β₄ = 0.17, p = 0.001). However, it seems that in the same and different locations, both pulses contribute almost equally to the performance (same: Eq. 11: β₃ = 0.004, p = 0.88; Eq. 12: β₄ = -0.01, p = 0.75; different: Eq. 11: β₃ = -0.02, p = 0.44; Eq. 12: β₄ = 0.03, p = 0.43).

Making a decision in the real world usually requires collecting information from various sources that are often presented in different parts of our visual field. In our study, with the goal of getting closer to the real-world conditions, we examined both time and space dimensions simultaneously. Participants were asked to discriminate the direction of motion of two pulses of RDM displayed in the center or periphery of their visual field, and at the same or different locations of the screen. We observed that performance in the center of vision was generally better than peripheral conditions, which is not unexpected as previous work has shown that spatial resolution decreases with eccentricity ^45–48. More interestingly, there seemed to be differences in the process of evidence accumulation in different conditions such that participants performed better than expected (from a perfect integrator) when both pieces of information were presented at a same location of periphery and worse than expected when presented at different locations. The sequential effect of the second pulse on the performance also depended on the location of the presentation of the stimuli. Previous studies that showed subjects integrate information at the perfect level, or better than perfect integrator, all presented stimuli at the center ^39–41,49. As far as we know, our study is the first one that systematically investigated the effects of location of evidence on subject’s performance.

Considering the temporal dimension and in line with previous works ^39,40, we observed that the gap duration did not show a significant effect on the performance of the subjects in the center condition. We observed the same pattern of results for the different location. However, for the SL condition, the gap between pulses had a significant effect on subjects’ performance (p-value = 0.03). Previous work that studied decision making with discrete stimuli ^39–41,49 showed that when both stimuli were presented at the center of vision, the second piece of information had a stronger effect on choice than the first one. We replicated those findings at the center of vision and extended them to the same peripheral location. When we presented our stimuli at different locations, we found that the stronger effect of the second pulse was not there anymore.

The perfect integrator model is calculated based on the performance of the single pulse trials in each condition. The single pulse figure is slightly higher for the different condition in comparison to the same peripheral condition (Fig. 2). Even though this improvement did not reach the significance level, the resulted values for the perfect integrator of the different condition seem to be larger than the ones regarding the same condition. Therefore, the worse than perfect integration in the different condition could be in part due to the higher performance in the single pulse trials. On the other hand, the DL condition appears to necessitate shifting spatial attention between the two pulses, a process taking approximately 150ms ⁵⁰. This becomes particularly pronounced at the 0ms gap, where participants have no time between successive stimuli, potentially causing them to miss information from the latter part of the first pulse and the initial part of the second pulse. Thus, the information from the pulses does not seem to be fully attended and hence, we do not reach a perfect integration.

Comparison of the accuracy in weak-strong and strong-weak trials showed a pattern of the stronger effect of the second pulse in the same conditions, both in fovea and periphery, but the effect was significant only in the peripheral condition (Fig. 4). On the other hand, the motion energy analysis showed the sequential effect to be significant merely in the central condition (Fig. 5). Considering the exclusion of the gap of 0ms in the motion energy analysis, we decided to separate the plots presented in Fig. 4 based on the gap duration between two pulses (Fig. 6). Interestingly, we observed that the privileged effect of the second pulse at the center and same conditions was limited to the 0ms gap, and as the gap duration increased, the significant effect of the second pulse on subject’s performance decreased. These results suggest the role of continuity in the stream of evidence on the perception of the second piece of the information. When we break this continuity in time, or space, both pulses contribute to the same degree to the final decision.

The effect of the second pulse observed in 0ms gap duration of central and same conditions could be due to some manifestation of recency or confirmation bias ^43,51–54. Considering the higher performance in the 0ms gap, in comparison to other gaps, shows that subjects gathered more information from the second pulse. One reason could be that viewing the first pulse increases the sensitivity to the observed data in either the low-level visual circuits or evidence integration in higher levels of decision-making system. This increase in sensitivity could be what decays during the gap duration, leading to absence of the sequential effect and a lower performance in the gap durations longer than 0ms. Additionally, giving a break in the process of accumulation of the data could make the observer treat the pulses as distinct pieces of information, leading to a categorical judgment of the first pulse, which lessens the sensitivity to the newer information ^34,55,56. Previous studies have also shown the effect of attention and top-down procedures leading to a flexibility in making perceptual decisions in a changing environment ^57–60.

More research is needed to see how the brain integrates discrete pieces of information over space and time with a wider set of stimuli and conditions. Specifically, our study did not encompass different location conditions involving pulses from center and periphery in order to mitigate the distinct effects attributed to each visual area. While incorporating more complex scenarios would enhance our comprehension, the limitation on the number of conditions compelled us to focus on the most informative scenarios. The significance of peripheral vision in daily navigation and directing attention towards important or potentially threatening events is well-established ^61,62. In our study, stimuli were presented at an eccentricity of 5 visual degrees from the fovea. Considering previous research indicating a decline in visual feature acuity with increases in the eccentricity ^46,48,50, it is reasonable to explore the impact of larger eccentricities in a setting similar to ours. We also believe that utilizing neuro-imaging techniques such as EEG and fMRI in the discrete stimulus could lead to a better understanding of the underlying mechanisms and to clarify on the role of attention in the accumulation of this type of the incoming information.

To make a decision in real life, it is not common to receive pieces of information from the same location. In most natural condition, given the object, head and body movements, we need to accumulate information reaching us from different places. Our results indicate that individuals incorporate discontinuous information in a distinct manner compared to its continuous form and thus, the discrete nature of evidence affects the integration process of information.

Participants

Nine human subjects (5 female, 23–43 years old), with normal or corrected-to-normal vision, were included in this study. The participants were chosen by convenience sampling and all of them filled an informed consent form before their attendance. Subjects had a rigorous training procedure before the main experiment to reach a predefined level of accuracy and reaction time (see below). Two of the female subjects failed to reach the required minimum performance in the first training phase and were excluded from the study, thus all the reported results are driven from a set of seven participants. This research received approval from the Ethics Committee of Allameh Tabataba’i University (ID: IR.ATU.REC.1401.022) and was conducted in accordance with the Declaration of Helsinki.

Stimulus

In this study, we used a Random Dots Motion paradigm (RDM) in which participants were asked to decide the net motion direction of a set of dots moving left or right with coherence varying between trials (0, 3.2, 6.4, 12.8, 25.6 or 51.2%). The more coherent the dot motion, the higher the probability of giving a correct answer. Detailed information on RDM properties were as follows: dot density of 16.7 dots/deg²/s, dot size of 3 × 3 pixels (0.075°), velocity of 5°/s, and aperture size of 5°. The stimulus consisted of white dots moving against a black background, located in one of three locations: the center, above (top), or below (bottom) the fixation point, at the eccentricity of 5°. In each block of 120 trials, having fixed the aperture location, each set of dots was displayed on the screen for one frame (16.7ms) whose position got updated every three frames, i.e. the position of dots in the first frame was updated in the fourth frame and so on, as previously has been done ^7,63.

Task design

Each trial begun by presenting a red fixation point (0.2° diameter) at the center of the screen. After subjects fixated the fixation point and pressed the space bar, two white targets (0. 65° diameter) were presented on the right and left sides of the screen (10° eccentricity). After a random delay (500-800ms, truncated exponential distribution), the motion stimulus was presented at a circular aperture at the center, top or bottom location, depending on the block condition.

In each block, we had two types of stimulus presentation; ‘single-pulse’ in which a single pulse of motion was shown for 150ms (0-51.2%); and ‘double-pulse’ trials in which two pulses of motion (each 150ms) were shown successively. The coherence of each patch of dots could be 3.2, 6.4 or 12.8%. Both pulses had the same net direction and participants knew this fact in advance. The interval between the two pulses was randomly chosen from 0, 480 and 1080ms intervals. Each block consisted of 108 double-pulse and 12 single pulse trials. Subjects were instructed to give their answer as accurately as possible after the offset of the fixation point (go cue). Subjects received visual feedback based on the accuracy of their responses, with a green circle indicating a correct response and a red circle representing an incorrect answer.

Task procedure

Stimuli were presented on a 24˝ LED monitor (screen resolution: 1920 × 1080, refresh rate: 60 Hz) at a distance of 60cm in a dark room. To make sure whether subjects’ gaze remained on the fixation point, we monitored the position of the left eye throughout the experiment (EyeLink 1000, SR Link, Canada). To stabilize the subject’s head, a chin rest and a forehead bar were used. The task was implemented in MATLAB using Psychtoolbox-3 ⁶⁴. In the main experiment, each subject completed 1,100-2,900 trials (120 trials per block) for each condition. We had three main conditions including the center location (CL): two pulses presented at the center; the same location (SL): both pulses were presented at top or bottom; the different location (DL): the first pulse was presented at the top the second one at the bottom or vice versa.

Training

All of the subjects participated in a procedure of extensive training which included two distinct phases. The first phase of training consisted of at least two sessions in which three blocks of 120 trials of RDM stimulus was displayed for a fixed duration of one second. The process was repeated for all the locations of stimulus presentation (center, top and bottom) separately, until the subject reached an average performance of 85% in a session. Finishing successfully the phase one, subjects would enter the second phase in which the presentation of stimulus in each trial continued until subject’s choice (i.e., free response). The maximum duration of viewing the stimulus on each trial was set to five seconds. By reaching an average performance of 85% in a session and in all the conditions, a subject would be ready to start the main experiment. Before starting the main task, all subjects passed several training sessions (on average, each subject performed 19 blocks to be trained in all conditions) to attain high performance levels (i.e., 85%).

Data analysis

Having the binary nature of the outcomes (either true or false), in order to assess the impact of different parameters of the stimulus in this experiment, we used multiple logistic regression models. Logit[P] stands for log$\:\left(\frac{p}{1-p}\right)$ and β_i implies fitted coefficients. The fitting method was maximum likelihood under a binomial error model (i.e., a GLM).

The probability of a correct choice for single pulse trials was estimated as:

$\:\text{L}\text{o}\text{g}\text{i}\text{t}\:\left[{P}_{correct}\right]={{\beta\:}}_{0}+{{\beta\:}}_{1}\text{C}$ (Eq. 1)

where C was the motion coherence.

A modified version of Eq. 1 was applied to check for right/left bias:

$\:\text{L}\text{o}\text{g}\text{i}\text{t}\:\left[{\text{P}}_{\text{r}\text{i}\text{g}\text{h}\text{t}}\right]={{\beta\:}}_{0}+{{\beta\:}}_{1}{\text{C}}_{\pm\:}$ (Eq. 2)

Where C₊ corresponds to rightward motion and C₋ to leftward motion.

To find the impact of time gap between the two pulses in double-pulse trials we used:

$\:\text{L}\text{o}\text{g}\text{i}\text{t}\:\left[{\text{P}}_{\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}}\right]={{\beta\:}}_{0}+{{\beta\:}}_{1}{\text{C}}_{1}+{{\beta\:}}_{2}{\text{C}}_{2}+{{{\beta\:}}_{3}\text{T}+{\beta\:}}_{4}{\text{C}}_{1}\text{T}+{{\beta\:}}_{5}{\text{C}}_{2}\text{T}$ (Eq. 3)

where T indicates the gap duration, and C₁ and C₂ indicate coherence in the first and second pulse, respectively.

To see whether location of the dots patch had any contribution to the probability of giving a correct answer, we defined another equation, where L indicates the location of the dots patch including three categories of ‘center’ (L = 0), ‘same’ (L = 1) and ‘different’ (L = -1):

In the next step, we fitted a logistic regression model to compare the expected accuracy of a perfect integrator with the observed accuracy:

$\:\text{L}\text{o}\text{g}\text{i}\text{t}\:\left[{\text{P}}_{\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}}\right]=\text{L}\text{o}\text{g}\text{i}\text{t}\left[{\text{P}}_{\text{e}}\right]+{\beta\:}$ (Eq. 5)

where P_e is the expected probability derived from a perfect integrator. If β ends up with a positive value, then observed accuracy is higher than expected. P_e was calculated as:

$\:{\text{P}}_{\text{e}}=1-\phi\:(0,{e}_{1}+{e}_{2},\sqrt{2})$ (Eq. 6)

where $\:\phi\:$ is the normal cumulative distribution function, calculated as:

$\:\phi\:\left(s,\mu\:,\sigma\:\right)=\:{\int\:}_{-\infty\:}^{s}N\left(v,\:\mu\:,\sigma\:\right)dv$ (Eq. 7)

where $\:N\left(v,\:\mu\:,\sigma\:\right)$ is the normal probability density function with mean of (µ) and standard deviation of (σ).

Also, e₁ and e₂ are pieces of evidence from the two pulses. The distribution of the evidence is calculated from the probability of correct answers from single-pulse trials:

$\:{e}_{i}={\phi\:}^{-1}\left({P}_{i},0,\:1\right)\:,\:i=1,\:2$ (Eq. 8)

where P_i is the probability of correct response of single-pulse trials based on Eq. 1, and $\:{\phi\:}^{-1}$ is the inverse of the normal cumulative distribution function from Eq. 7.

To see the effect of pulse sequences on the probability of correct responses we used:

$\:\text{L}\text{o}\text{g}\text{i}\text{t}\:\left[{P}_{correct}\right]={{\beta\:}}_{0}+{\:{\beta\:}}_{1}\left[{C}_{1}+{C}_{2}\right]+{\:{\beta\:}}_{2}\left[{C}_{2}-{C}_{1}\right]$ (Eq. 9)

where C₁ and C₂ are motion strength of the first and second pulse, respectively.

Furthermore, to see the interaction between two pulses (whether the stronger pulse 1 increases or decreases the effect of the second pulse), we used:

$\:\text{L}\text{o}\text{g}\text{i}\text{t}\:\left[{\text{P}}_{\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}}\right]={{\beta\:}}_{0}+{\:{\beta\:}}_{1}{\text{C}}_{1}+{\:{\beta\:}}_{2}{\text{C}}_{2}+{\:{\beta\:}}_{3}{\text{C}}_{1}{\text{C}}_{2}$ (Eq. 10)

Motion energy analysis

Since there are fluctuations in the RDM stimulus and direction of dots varies in each generated frame, no two pulses carry the same amount of information regarding a direction of motion. To overcome this issue, we calculated motion energy for each pulse of every trial. To analyze the amount of motion energy in favor of the intended direction on each trial, we used two pairs of quadrature spatiotemporal filters ^41,65,66. Each pair was selective to either right or left. The filters were convolved with the three-dimensional pattern of RDM stimulus and then squared and summed. The result was summated across space to give the motion energy estimate as a function of time. Finally, the net motion energy in each direction was calculated as the difference between motion energies of opponent directions.

To test for the larger effect of the second pulse on the performance, we fit the following linear regression model:

$\:\text{M}={{\beta\:}}_{0}+{\:{\beta\:}}_{1}\text{C}+{\:{\beta\:}}_{2}\text{E}+{\:{\beta\:}}_{3}\text{E}\text{S}$ (Eq. 11)

$$\:\text{E}=\left\{\begin{array}{c}0,\:\:correct\:response\\\:1,\:\:\:\:\:\:error\:response\end{array}\right.\:,\:\text{S}=\left\{\begin{array}{c}0,\:\:\:\:\:\:\:\:\:\:first\:pulse\\\:1,\:\:\:\:\:\:second\:pulse\end{array}\right.$$

Where C is the coherence of the pulse, E indicates if the response of subject was correct or wrong, S stands for the pulse sequence and M is the motion energy of that pulse. M is calculated as the summation of motion energy across a window of 200ms starting 50ms after the onset of stimulus. Since the motion energy for zero gap intervals overlapped with each other, they were omitted.

In order to compare the effect of motion energy of each of the pulses on the performance, a logistic regression model was used:

in which $\:{M}_{1}$and $\:{M}_{2}$ are the motion energy of the first and second pulses, respectively. For trials with equal coherence, the term $\:{\:{\beta\:}}_{2}{\text{C}}_{2}$ was dropped. The null hypothesis is that both pulses have the same effect ($\:{{\beta\:}}_{4}=0$).

Acknowledgements

We are thankful to the participants who devoted their time to take part in our experiment.

Author Contributions

R.E., S.Z. and M.S. conceived and developed the main idea of the project. S.M. collected and analyzed the behavioral data. S.M. and M.S. wrote the manuscript. All authors discussed the results and approved the final version of the manuscript.

Declaration of Competing Interests

The authors declare no potential conflicts of interests.

Data Availability

The datasets generated and analyzed during the current study are available in the Mendeley Data repository, https://data.mendeley.com/preview/9wk8p43z6j?a=ec44d207-4186-448c-92da-0cb2a107a64a.

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Better than expected performance effect depends on the spatial location of visual stimulus

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Version 1

Abstract

Figures

Introduction

Results

Participants improve their decision by using information within each pulse

The effect of gap duration varies based on the location of the stimuli

Dissimilarity in the location of pulses reverses the better-than-expected effect

Sequence dependency effect is location dependent

Discussion

Methods

Participants

Stimulus

Task design

Task procedure

Training

Data analysis

Motion energy analysis

Declarations

Data Availability

References

Additional Declarations

Status:

Version 1