Moving Dot Stimuli Research Articles

Threat Expectation Does Not Improve Perceptual Discrimination despite Causing Heightened Priority Processing in the Frontoparietal Network.

Threat cues have been widely shown to elicit increased sensory and attentional neural processing. However, whether this enhanced recruitment leads to measurable behavioral improvements in perception is still in question. Here, we adjudicate between two opposing theories: that threat cues do or do not enhance perceptual sensitivity. We created threat stimuli by pairing one direction of motion in a random dot kinematogram with an aversive sound. While in the MRI scanner, 46 subjects (both men and women) completed a cued (threat/safe/neutral) perceptual decision-making task where they indicated the perceived motion direction of each moving dot stimulus. We found strong evidence that threat cues did not increase perceptual sensitivity compared with safe and neutral cues. This lack of improvement in perceptual decision-making ability occurred despite the threat cue resulting in widespread increases in frontoparietal BOLD activity, as well as increased connectivity between the right insula and the frontoparietal network. These results call into question the intuitive claim that expectation automatically enhances our perception of threat and highlight the role of the frontoparietal network in prioritizing the processing of threat-related environmental cues.

Explicit effort may not influence perceptuomotor decision-making.

Many decisions that humans make are enacted by the action system. For example, humans use reach-to-grasp movements when making perceptuomotor decisions between and obtaining fruits of varying quality from a pile. Recent work suggests that the characteristics of each action alternative may influence the decision itself-there may be a bias away from making perceptuomotor alternatives associated with high effort when participants are unaware of the effort differences between responses. The present study examined if perceptuomotor decisions were influenced by explicit reaching effort differences. Neurotypical human participants were presented with random dot motion stimuli in which most dots moved in random directions and varying percentages of remaining dots moved coherently left- or rightward. Participants reported leftward motion judgements by performing leftward (or left hand) reaching movements and rightward motion judgements by performing rightward (or right hand) reaching movements. A resistance band was affixed to participants' wrists and to the table in different configurations. The configurations allowed for one movement/motion direction judgement to always require stretching of the band and, therefore, require relatively more effort. Across a set of experiments, the response context (i.e. selecting directions within a limb or selecting between limbs) and the effort difference between responses were manipulated. Overall, no experiment revealed a bias away from the perceptuomotor decision associated with high effort. Based on these results, it is concluded that, in this biomechanical context, explicit effort may not influence perceptuomotor decision-making and may point to a contextual influence of action effort on perceptuomotor decision-making.

Impairment of visual and neurologic functions associated with agrochemical use.

To determine whether exposure to occupational levels of agrochemicals is associated with a range of low- (contrast and colour) and higher-level visual functions, particularly the detection of global form and motion coherence. We compared the performance of workers exposed to occupational levels of pesticides and non-exposed individuals on visual tasks that measured colour discrimination (Farnsworth Munsell 100 and Lanthony D15 desaturated) and the contrast sensitivity function (1-16 cpd). Global form and motion detection thresholds were measured using Glass-pattern and global dot motion stimuli. Neurotoxicity symptoms and biological markers associated with pesticide exposure were quantified using the Q16 modified questionnaire and via tests for levels of acetylcholinesterase in blood and substance P from the tear film, respectively. Workers exposed to pesticides had significantly more neurotoxic symptoms than non-exposed workers. No significant difference between groups for acetylcholinesterase levels was found, but there was a significant group difference in Substance P. The exposed group also had significantly poorer contrast sensitivity, colour discrimination and higher coherence detection thresholds for global form and motion perception. Exposure to occupational levels of agrochemicals in workers with signs of neurotoxicity is associated with low and high visual perception deficits.

Noise in the brain: Transcranial random noise stimulation and perceptual noise act on a stochastic resonance-like mechanism.

Stochastic resonance (SR) is a phenomenon in which a certain amount of random noise added to a weak subthreshold stimulus can enhance signal detectability. It is unknown how external noise interacts with neural noise in producing an SR-like phenomenon and whether this interaction results in a modulation of either network efficiency or the efficiency of single neurons. Using random dot motion stimuli and noninvasive brain stimulation, we attempted to unveil the specific mechanism of action of the SR-like phenomenon in motion perception, if present. We aimed to determine whether signal integration efficiency changes with external noise (random dot numerosity) and how electrical transcranial random noise stimulation (tRNS) can affect the peak performance. The participants performed a coherent motion detection task in which the random dot numerosity varied, whereas the signal-to-noise ratio (SNR) remained constant. We applied placebo or tRNS with an amplitude of either 1 or 2mA during task execution. We found peaks in participants' performance both in the case of placebo stimulation and in the case of 1-mA tRNS. In the latter case (i.e., with an additional noise source), the peak emerged at lower random dot numerosity levels than when no additional noise was added (placebo). No clear peak was observed with 2-mA tRNS. An equivalent noise (EN) analysis confirmed that SR arises from a modulation of the network efficiency underlying motion signal integration. These results indicate a joint contribution of external and neural noise (modulated by tRNS) in eliciting an SR-like phenomenon.

Behavior in a visual search task with moving dot stimuli.

Understanding the neuronal mechanisms underlying the processing of visual attention requires a well-designed behavioral task that allows investigators to clearly describe the behavioral effects of attention. Here, we introduce a behavioral paradigm in which one, two or four moving dot stimuli are used in a visual search paradigm that includes two additional attentional conditions. Two animals were trained to make a saccade to a target (a dot patch with net rightward motion) and hold central fixation if no target was present. To implement covert visual attention, we included trials in which a 100% valid spatial cue appeared and trials in which the color of the fixation point indicated, with 100% validity, which of four colored dot patches the animals should attend to. We analyzed the behavior in terms of reaction times and signal detection theory metrics d-prime (representing sensitivity) and criteria. In both animals, we found that reaction times were greater for larger set-sizes and that the introduction of an attentional cue reduced the reaction times substantially. We also found that both animals showed increases in criteria, but no change in sensitivity, as set-size increased and the attentional cues led to an increase in sensitivity, with only some change in criteria. Our results illustrate how the animals perform this task and imply that both animals chose similar strategies. Importantly, this will allow future neurophysiological studies to probe not only the effects of attention, but will give the possibility of seeing whether different neural mechanisms drive changes in criteria and d-prime.

Stimulus-Specific Visual Working Memory Representations in Human Cerebellar Lobule VIIb/VIIIa.

fMRI research has revealed that cerebellar lobule VIIb/VIIIa exhibits load-dependent activity that increases with the number of items held in visual working memory (VWM). However, it remains unclear whether these cerebellar responses reflect processes specific to VWM or more general visual attentional mechanisms. To investigate this question, we examined whether cerebellar activity during the delay period of a VWM task is selective for stimuli held in working memory. A sample of male and female human subjects performed a VWM continuous report task in which they were retroactively cued to remember the direction of motion of moving dot stimuli. Cerebellar lobule VIIb/VIIIa delay-period activation accurately decoded the direction of the remembered stimulus, as did frontal and parietal regions of the dorsal attention network. Arguing against a motor explanation, no other cerebellar area exhibited stimulus specificity, including the oculomotor vermis, a key area associated with eye movement control. Finer-scale analysis revealed that the medial portion of lobule VIIb and to a lesser degree the lateral most portion of lobules VIIb and VIIIa, which exhibit robust resting state connectivity with frontal and parietal regions of the dorsal attention network, encoded the identity of the remembered stimulus, while intermediate portions of lobule VIIb/VIIIa did not. These findings of stimulus-specific coding of VWM within lobule VIIb/VIIIa indicate for the first time that the distributed network responsible for the encoding and maintenance of mnemonic representations extends to the cerebellum.SIGNIFICANCE STATEMENT There is considerable debate concerning where in the brain the contents of visual working memory (VWM) are stored. To date, this literature has primarily focused on the role of regions located within cerebral cortex. There is growing evidence for cerebellar involvement in higher-order cognitive functions including working memory. While the cerebellum has been previously shown to be recruited by VWM paradigms, it is unclear whether any portion of cerebellum actively encodes and maintains mnemonic representations. The present study demonstrates that cerebellar lobule VIIb/VIIIa activity patterns are selective for remembered stimuli and that this selectivity persists in the absence of perceptual input. These findings provide novel evidence for the participation of cerebellar structures in the persistent storage of visual information.

Performance on a visual search task using random dot motion stimuli

The priority map hypothesis posits that visual attention is allocated according to the priority of objects in the visual scene. We and others have suggested that activity in priority maps during visual search might explain behavior based on the accumulation of evidence at each stimulus location (Purcell et al, 2012; Arcizet et al, 2018; Servant et al, 2019), however these studies have utilized simple stimuli that require little temporal integration of information. In this study, we use random dot stimuli in visual search to quantify how the accumulation of evidence changes under distinctive conditions within visual search. Two adult animals were trained on a visual search task in which 1, 2 or 4 random moving dot stimuli were presented. One subject indicated the presence of a target (a stimulus with rightwards motion) by making a saccade to the target. The other subject indicated the presence of a target by releasing one of two bars. The number of stimuli and the coherence of the stimuli were changed on each trial, such that all stimuli had the same coherence. Targets were present on 50% of trials for set size 1, 66% of trials for set size 2, 80% of trials for set size 4 in the saccade task and 66% of trials for set size 4 in the bar release task. In a subset of trials with a set size of 4, we also had a spatial cue condition and a feature-based cue condition. We found a decrease in performance, hit rate, and correct rejections for the greater set sizes. In the spatial cue and feature-based cue conditions, we found an increase in hit rates and decrease in reaction times. These behavioral data show that our task should allow us to measure the neural accumulation of evidence in a visual search task.

Perceptual learning of motion direction discrimination: Location specificity and the uncertain roles of dorsal and ventral areas

One interesting observation of perceptual learning is the asymmetric transfer between stimuli at different external noise levels: learning at zero/low noise can transfer significantly to the same stimulus at high noise, but not vice versa. The mechanisms underlying this asymmetric transfer have been investigated by psychophysical, neurophysiological, brain imaging, and computational modeling studies. One study (PNAS 113 (2016) 5724–5729) reported that rTMS stimulations of dorsal and ventral areas impair motion direction discrimination of moving dot stimuli at 40% coherent (“noisy”) and 100% coherent (zero-noise) levels, respectively. However, after direction training at 100% coherence, only rTMS stimulation of the ventral cortex is effective, disturbing direction discrimination at both coherence levels. These results were interpreted as learning-induced changes of functional specializations of visual areas. We have concerns with the behavioral data of this study. First, contrary to the report of highly location-specific motion direction learning, our replicating experiment showed substantial learning transfer (e.g., transfer/learning ratio = 81.9%. vs 14.8% at 100% coherence). Second and more importantly, we found complete transfer of direction learning from 40% to 100% coherence, a critical baseline that is missing in this study. The transfer effect suggests that similar brain mechanisms underlie motion direction processing at two coherence levels. Therefore, this study’s conclusions regarding the roles of dorsal and ventral areas in motion direction processing at two coherence levels, as well as the effects of perceptual learning, are not supported by proper experimental evidence. It remains unexplained why distinct impacts of dorsal and ventral rTMS stimulations on motion direction discrimination were observed.

Neural dynamics underlying coherent motion perception in children and adults

Motion sensitivity increases during childhood, but little is known about the neural correlates. Most studies investigating children’s evoked responses have not dissociated direction-specific and non-direction-specific responses. To isolate direction-specific responses, we presented coherently moving dot stimuli preceded by incoherent motion, to 6- to 7-year-olds (n = 34), 8- to 10-year-olds (n = 34), 10- to 12-year-olds (n = 34) and adults (n = 20). Participants reported the coherent motion direction while high-density EEG was recorded. Using a data-driven approach, we identified two stimulus-locked EEG components with distinct topographies: an early component with an occipital topography likely reflecting sensory encoding and a later, sustained positive component over centro-parietal electrodes that we attribute to decision-related processes. The component waveforms showed clear age-related differences. In the early, occipital component, all groups showed a negativity peaking at ˜300 ms, like the previously reported coherent-motion N2. However, the children, unlike adults, showed an additional positive peak at ˜200 ms, suggesting differential stimulus encoding. The later positivity in the centro-parietal component rose more steeply for adults than for the youngest children, likely reflecting age-related speeding of decision-making. We conclude that children’s protracted development of coherent motion sensitivity is associated with maturation of both early sensory and later decision-related processes.

Confirmation Bias through Selective Overweighting of Choice-Consistent Evidence

People's assessments of the state of the world often deviate systematically from the information available to them [1]. Such biases can originate from people's own decisions: committing to a categorical proposition, or a course of action, biases subsequent judgment and decision-making. This phenomenon, called confirmation bias [2], has been explained as suppression of post-decisional dissonance [3, 4]. Here, we provide insights into the underlying mechanism. It is commonly held that decisions result from the accumulation of samples of evidence informing about the state of the world [5-8]. We hypothesized that choices bias the accumulation process by selectively altering the weighting (gain) of subsequent evidence, akin to selective attention. We developed a novel psychophysical task to test this idea. Participants viewed two successive random dot motion stimuli and made two motion-direction judgments: a categorical discrimination after the first stimulus and a continuous estimation of the overall direction across both stimuli after the second stimulus. Participants' sensitivity for the second stimulus was selectively enhanced when that stimulus was consistent with the initial choice (compared to both, first stimuli and choice-inconsistent second stimuli). A model entailing choice-dependent selective gain modulation explained this effect better than several alternative mechanisms. Choice-dependent gain modulation was also established in another task entailing averaging of numerical values instead of motion directions. We conclude that intermittent choices direct selective attention during the evaluation of subsequent evidence, possibly due to decision-related feedback in the brain [9]. Our results point to a recurrent interplay between decision-making and selective attention.

Activation, Inhibition, or Something Else: An Exploratory Study on Response Priming Using Moving Dots as Primes in Middle-Aged and Old Adults.

Response priming refers to the finding that a prime stimulus preceding a target stimulus influences the response to the following target stimulus. With young subjects, using moving dot stimuli as primes indicated faster responses to compatible targets (i.e., prime and target are associated with the same response) with short stimulus onset asynchronies (SOAs). In contrast, with longer SOAs, participants responded faster to incompatible targets. In the present study, we extended the evidence by comparing middle-aged (50–65 years) and old (66–87 years) adults. With two different motion types, the result found in young participants was replicated in the middle-aged adults. In contrast, old adults showed large positive compatibility effects with the short SOA but neither activation nor inhibition effects with the longer SOA. We discuss our findings in light of several theoretical accounts (i.e., inhibitory deficit, deautomatization, evaluation window account, attention, rapid decay).

Novel method of extracting motion from natural movies

BackgroundThe visual system in primates can be segregated into motion and shape pathways. Interaction occurs at multiple stages along these pathways. Processing of shape-from-motion and biological motion is considered to be a higher-order integration process involving motion and shape information. However, relatively limited types of stimuli have been used in previous studies on these integration processes. New methodWe propose a new algorithm to extract object motion information from natural movies and to move random dots in accordance with the information. The object motion information is extracted by estimating the dynamics of local normal vectors of the image intensity projected onto the x-y plane of the movie. ResultsAn electrophysiological experiment on two adult common marmoset monkeys (Callithrix jacchus) showed that the natural and random dot movies generated with this new algorithm yielded comparable neural responses in the middle temporal visual area. Comparison with existing methodsIn principle, this algorithm provided random dot motion stimuli containing shape information for arbitrary natural movies. This new method is expected to expand the neurophysiological and psychophysical experimental protocols to elucidate the integration processing of motion and shape information in biological systems. ConclusionsThe novel algorithm proposed here was effective in extracting object motion information from natural movies and provided new motion stimuli to investigate higher-order motion information processing.

Smooth pursuit detection in binocular eye-tracking data with automatic video-based performance evaluation.

An increasing number of researchers record binocular eye-tracking signals from participants viewing moving stimuli, but the majority of event-detection algorithms are monocular and do not consider smooth pursuit movements. The purposes of the present study are to develop an algorithm that discriminates between fixations and smooth pursuit movements in binocular eye-tracking signals and to evaluate its performance using an automated video-based strategy. The proposed algorithm uses a clustering approach that takes both spatial and temporal aspects of the binocular eye-tracking signal into account, and is evaluated using a novel video-based evaluation strategy based on automatically detected moving objects in the video stimuli. The binocular algorithm detects 98% of fixations in image stimuli compared to 95% when only one eye is used, while for video stimuli, both the binocular and monocular algorithms detect around 40% of smooth pursuit movements. The present article shows that using binocular information for discrimination of fixations and smooth pursuit movements is advantageous in static stimuli, without impairing the algorithm's ability to detect smooth pursuit movements in video and moving-dot stimuli. With an automated evaluation strategy, time-consuming manual annotations are avoided and a larger amount of data can be used in the evaluation process.

Sensorimotor Decision Making in the Zebrafish Tectum

An animal's survival depends on its ability to correctly evaluate sensory stimuli and select appropriate behavioral responses. When confronted with ambiguous stimuli, the brain is faced with the task of selecting one action while suppressing others. Although conceptually simple, the site and substrate of this elementary form of decision making is still largely unknown. Zebrafish larvae respond to a moving dot stimulus in either of two ways: a small object (potential prey) evokes approach, whereas a large object (potential predator) is avoided. The classification of object size relies on processing in the optic tectum. We genetically identified a population of cells, largely comprised of glutamatergic tectal interneurons with non-stratified morphologies, that are specifically required for approach toward small objects. When these neurons are ablated, we found that the behavioral response is shifted; small objects now tend to elicit avoidance. Conversely, optogenetic facilitation of neuronal responses with channelrhodopsin (ChR2) enhances approaches to small objects. Calcium imaging in head-fixed larvae shows that a large proportion of these neurons are tuned to small sizes. Their receptive fields are shaped by input from retinal ganglion cells (RGCs) that are selective for prey identity. We propose a model in which valence-based decisions arise, at a fundamental level, from competition between dedicated sensorimotor pathways in the tectum.

Evidence and Counterevidence in Motion Perception.

Sensory neurons gather evidence in favor of the specific stimuli to which they are tuned, but they could improve their sensitivity by also taking counterevidence into account. The Bours-Lankheet model for motion detection uses counterevidence that relies on a specific combination of the ON and OFF channels in the early visual system. Specifically, the model detects pairs of flashes that occur separated in space and time. If the flashes have the same contrast polarity, they are interpreted as evidence in favor of the corresponding motion. But if they have opposite contrasts, they are interpreted as evidence against it. This mechanism provides an explanation for reverse-phi (the perceived reversal of an apparent motion stimulus due to periodic contrast-inversions) that is a conceptual departure from the standard explanations of the effect. Here, we investigate this counterevidence mechanism by measuring directional tuning curves of neurons in the primary visual and middle temporal cortex areas of awake, behaving macaques using constant-contrast and inverting-contrast moving dot stimuli. Our electrophysiological data support the Bours-Lankheet model and suggest that the counterevidence computation occurs at an early stage of neural processing not captured by the standard models.

The role of selective attention during visual search using random dot motion stimuli.

Finding objects among distractors is an essential everyday skill, which is often tested with visual search tasks using static items in the display. Although these kinds of displays are ideal for studying search behavior, the neural encoding of the visual stimuli can occur rapidly, which limits the analysis that can be done on the accumulation of evidence. Searching for a target among multiple random dot motion (RDM) stimuli should allow us to study the effect of attention on the accumulation of information during visual search. We trained an animal to make a saccade to a RDM stimulus with motion in a particular direction (the target). The animal began the task by fixating a central square. After a short delay, it changed to a dotted hollow square and one, two or four RDM stimuli appeared equally spaced in the periphery for 700 ms. The animal was rewarded for looking at the target, if present, or for maintaining fixation if the target was absent from the display. In the spread attention condition, all the dots in the RDM stimuli were the same color. In the focused attention condition, the color of the fixation square and the dotted hollow square matched the color of the dots in one RDM stimulus, which was a 100% valid cue. We varied the coherence of the RDM stimuli for each condition from 65 to 100% (100 ms limited lifetime). At the lower coherences, there were strong effects of set size and attention condition on both performance and reaction time. Our data show that using a RDM visual search task allows us to clearly illustrate the role of attention in the accumulation of perceptual evidence, which increases response accuracy and shortens reaction time. Meeting abstract presented at VSS 2015

Does perceptual confidence facilitate cognitive control?

Our visual perception is typically accompanied by a sense of subjective confidence. Since perceptual confidence is related to prefrontal activity, higher perceptual confidence may enhance cognitive control functions. To examine this interaction, we developed a novel method to selectively manipulate perceptual confidence while keeping stimulus discrimination accuracy constant. In a behavioral experiment, grating stimuli with different orientations were presented as go/no-go signals. Surprisingly, the results showed that confidence in visual discrimination of the signals on its own did not facilitate response inhibition, since when participants were presented with stimuli that yielded higher confidence, they were no better at performing a go/no-go task. These results were replicated with different (dot motion) stimuli, ruling out alternative explanations based on stimulus idiosyncrasy. In a different experiment, when the grating stimuli were presented as cues for task set preparation, we found that higher perceptual confidence also did not enhance task set preparation efficiency. This result was again replicated with dot motion stimuli. Since confidence may relate to perceptual awareness (Peirce & Jastrow, 1885), our findings may put current dominant theories in question, since these theories often suppose the critical involvement of consciousness in cognitive control. As a proof of concept, our method may also provide a new and powerful way to examine other functions of consciousness in future studies.

Eye dominance alternations in binocular rivalry do not require visual awareness.

Binocular rivalry provides a valuable means to study how sensory processing gives rise to subjective experiences because it involves a changing percept without any change in the visual stimulus. An important question, however, is whether visual awareness is necessary for binocular rivalry to emerge. To address this question, we presented conflicting random dot motion stimuli in the two eyes at luminance contrasts around perceptual threshold. We asked subjects to report continuously, via button presses, if they noticed any kind of motion in the display (be it coherent or not) and indicate which direction of motion they thought was dominant at any given instant even if they were unaware of any motion in the display. We biased the competition between the two dichoptic stimuli by changing the motion coherence in one eye while keeping it fixed in the other to test if this induced predictable changes in rivalry dynamics. We also probed the strength of the interocular suppression. Our data show that binocular rivalry continues even if subjects claim complete absence of visual motion awareness. This remarkable dissociation between visually guided behavior and visual awareness resembles the dissociation seen in other phenomena, such as blindsight and visual masking. Fluctuations in awareness that did occur were temporally linked to the dominance switches in a manner that is consistent with adaptation reciprocal-inhibition models of binocular rivalry.

Behavioral consequences of perceptual decision-making in oculomotor brain structures

Neurons in several oculomotor brain areas (such as the lateral intraparietal area and superior colliculus) carry a multitude of signals. Even within a single task, individual neurons may exhibit responses related to visual/sensory events, decision formation, and saccade execution. Little is known about whether these signals interact and if such interactions have functional consequences. To test for interactions between decision-making and saccade execution signals, we used a behavioral dual-task paradigm that measured saccade reaction time (SRT) to a decision-irrelevant target while observers conducted a motion direction discrimination task. Observers (n=5) judged the direction (leftward versus rightward) of a random dot motion stimulus (of variable coherence; speed: 5 °/s). At the offset of the dots, a target appeared either left or right side of the fixation point (displaced by 20°). Observers were instructed to make an eye movement to the target as quickly as possible. After the eye movement, the direction of preceding dot motion was reported with a button press. We tested whether the SRT to the target was affected by the direction and strength of motion stimuli presented during the direction-discrimination task. Indeed, SRTs were faster on congruent trials (when the direction of motion was same as the saccade direction) compared to incongruent trials (F1,4=26.23, p<0.01). Furthermore, SRTs progressively decreased with increased coherence (F4,16=5.45, p<0.05). Thus, simple visually-guided saccades were affected by the ongoing buildup of activity related to decision formation, in a manner that was direction-selective and parametrically affected by motion strength. Our results are not due to the mere presence of motion stimuli because the dependencies on coherence and directional congruency were eliminated in a single-task (saccade only) control experiment. Revealing such interactions between decision making and saccade executions suggests that these two types of signals cannot be completely demixed in neural circuitry. Meeting abstract presented at VSS 2014

Discrimination of fixations and smooth pursuit movements in high-speed eye-tracking data.

A novel three-stage algorithm for detection of fixations and smooth pursuit movements in high-speed eye-tracking data is proposed. In the first stage, a segmentation based on the directionality of the data is performed. In the second stage, four spatial features are computed from the data in each segment. Finally, data are classified into fixations and smooth pursuit movements based on a combination of the spatial features and the properties of neighboring segments. The algorithm is evaluated under the assumption that the intersaccadic intervals represent fixations in data recorded when viewing images, and mainly smooth pursuit movements in data recorded when viewing moving dots. The results show that the algorithm is able to detect 94.3% of the fixations for image stimuli, compared to a previous algorithm with 80.4% detected fixations. For moving dot stimuli the proposed algorithm detects 86.7% smooth pursuit movements compared to 68.0% for the previous algorithm.