Alerting enhances attentional bias for salient stimuli: Evidence from a global/local processing task

Task-irrelevant valence-preferred colors boost visual search for a singleton-shape target

Some studies have suggested that emotion-associated features might influence attentional capture. However, demonstrating valence-dependent distractor interference has proven challenging, possibly due to the neglect of individuals' color-valence preferences in standard, averaged reaction-time (RT) measures. To address this, we investigated valence-driven attentional-capture using an association phase in which emotionally neutral vs. positive-feedback photographs were paired with two alternative target colors, red vs. green. This was followed by a test phase requiring participants to search for a pop-out shape target in the presence or absence of an emotion-associated color. In Experiments 1 and 2, this color could only appear in a distractor, while in Experiment 3, it appeared in the target. Analyzing the standard, averaged RT measures, we found no significant valence association or valence-modulated attentional capture. However, correlational analyses revealed a positive relationship between individual participants' color-valence preference during the association phase and their valence-based effect during the test phase. Moreover, most individuals favored red over green in the association phase, leading to marked color-related asymmetries in the average measures. Crucially, the presence of the valence-preferred color anywhere in the test display facilitated RTs. This effect persisted even when the color appeared in one of the distractors (Experiments 1 and 2), at variance with this distractor capturing attention. These findings suggest that task-irrelevant valence-preferred color signals were registered pre-attentively and boosted performance, likely by raising the general (non-spatial) alertness level. However, these signals were likely kept out of attentional-priority computation to prevent inadvertent attentional capture.

Testing the saliency-based account of phasic alertness

As an essential component of the human attention system, the effect of phasic alertness refers to the change of performance with the presence of a preceding warning signal. Weinbach and Henik (Cognition, 133 (2), 414-419, 2014) argued that phasic alertness is an adaptive mechanism that diverts attention to salient events. This mechanism enhances selective attention when the critical event is more salient than others. When selective attention to less salient details is required, phasic alertness can lead to more interference from task-irrelevant information. The experiment on which this saliency-based account of phasic alertness is based has not been replicated. In two experiments, the present study attempted to replicate the alertness-related findings of Weinbach and Henik. Although we used a similar design, the results did not reveal evidence for an interaction between phasic alertness and response congruency in the global/local processing task. Our results do not support the saliency-based account of phasic alertness. We argue that more systematic investigation is needed for this phasic alertness account.

Encoding specificity instead of online integration of real-world spatial regularities for objects in working memory

Most objects show high degrees of spatial regularity (e.g. beach umbrellas appear above, not under, beach chairs). The spatial regularities of real-world objects benefit visual working memory (VWM), but the mechanisms behind this spatial regularity effect remain unclear. The "encoding specificity" hypothesis suggests that spatial regularity will enhance the visual encoding process but will not facilitate the integration of information online during VWM maintenance. The "perception-alike" hypothesis suggests that spatial regularity will function in both visual encoding and online integration during VWM maintenance. We investigated whether VWM integrates sequentially presented real-world objects by focusing on the existence of the spatial regularity effect. Throughout five experiments, we manipulated the presentation (simultaneous vs. sequential) and regularity (with vs. without regularity) of memory arrays among pairs of real-world objects. The spatial regularity of memory objects presented simultaneously, but not sequentially, improved VWM performance. We also examined whether memory load, verbal suppression and masking, and memory array duration hindered the spatial regularity effect in sequential presentation. We found a stable absence of the spatial regularity effect, suggesting that the participants were unable to integrate real-world objects based on spatial regularities online. Our results support the encoding specificity hypothesis, wherein the spatial regularity of real-world objects can enhance the efficiency of VWM encoding, but VWM cannot exploit spatial regularity to help organize sampled sequential information into meaningful integrations.

Manipulation of Attention Affects Subitizing Performance: A Systematic Review and Meta-analysis

Subitizing is the fast and accurate enumeration of small sets. Whether attention is necessary for subitizing remains controversial considering (1) subitizing is claimed to be "pre-attentive", and (2) existing experimental methods and results are inconsistent. To determine whether manipulations to attention demonstratively affect subitizing, the current study comprises a systematic review and meta-analysis. Results from fourteen studies (22 experiments, 35 comparisons) suggest that changes to attentional demands interferes with enumeration of small sets; leading to slower response times, lower accuracy, and poorer Weber acuity (p <.010; p <.001; p <.001; respectively)-notwithstanding a potential publication bias. A unifying framework is proposed to explain the role of attention in visual enumeration, with progressively greater attentional involvement from estimation to subitizing to counting. Our findings suggest attention is integral for subitizing and highlights the need to emphasise attentional mechanisms into neurocognitive models of numerosity processing. We also discuss the possible role of attention in numerical processing difficulties (e.g., dyscalculia).

Phasic Alertness and Multisensory Integration Contribute to Visual Awareness of Weak Visual Targets in Audio-Visual Stimulation under Continuous Flash Suppression

Multisensory stimulation is associated with behavioural benefits, including faster processing speed, higher detection accuracy, and increased subjective awareness. These effects are most likely explained by multisensory integration, alertness, or a combination of the two. To examine changes in subjective awareness under multisensory stimulation, we conducted three experiments in which we used Continuous Flash Suppression to mask subthreshold visual targets for healthy observers. Using the Perceptual Awareness Scale, participants reported their level of awareness of the visual target on a trial-by-trial basis. The first experiment had an audio-visual Redundant Signal Effect paradigm, in which we found faster reaction times in the audio-visual condition compared to responses to auditory or visual signals alone. In two following experiments, we separated the auditory and visual signals, first spatially (experiment 2) and then temporally (experiment 3), to test whether the behavioural benefits in our multisensory stimulation paradigm could best be explained by multisensory integration or increased phasic alerting. Based on the findings, we conclude that the largest contributing factor to increased awareness of visual stimuli accompanied by auditory tones is a rise in phasic alertness and a reduction in temporal uncertainty with a small but significant contribution of multisensory integration.

Brain changes associated with impaired attention function in chronic pain

Attention function is thought to be important in chronic pain, with the pathology of chronic pain closely associated with cognitive-emotional components. However, there have been few neuroimaging studies of the relationship between attention function and chronic pain. We used the method of functional connectivity analysis for resting-state fMRI (rs-fMRI) data and the Attention Network Test-Revision (ANT-R) to clarify the attention-related pathology of chronic pain. We performed rs-fMRI and ANT-R on a group of 26 chronic pain (somatoform pain disorder) patients and 28 age-matched healthy controls. A significant group difference in validity effects, a component of ANT-R, emerged (F_1,46 = 5.91, p = 0.019), and the chronic pain group exhibited slower reaction times. Decreased brain connectivity of the left insula and left frontal regions was confirmed in chronic pain patients (p^FWE < 0.05), and connectivity was negatively correlated with validity effects (r = -0.29, permutation test p = 0.033). Further, decreased functional connectivity strength of the right insula and left temporal gyrus in the chronic pain group were confirmed (p^FWE < 0.05). We conclude that poor control of attention function results from deficits of functional connectivity in the left insula and left frontal regions in chronic pain.

Comparing saccadic and manual responses in the attention network test

Attention is proposed to be a system of multiple functional networks, including alertness, orienting and executive control. A popular experimental paradigm for testing these networks and their interactions within a single design is the Attentional Networks Test (ANT) (Fan et al., 2002). The role of the oculomotor system in these various networks, however, has not been tested despite the strong link between attention and eye movements. We modified the executive control component of the manual response ANT version (ANTm) that allows testing the networks' involvement with oculomotor responses. Specifically, we used a central target to signal pro or anti-saccades that allows us to match the saccadic response compatibility of the original ANTm. We conducted three experiments to compare interactions of the networks between the traditional ANTm that used a flanker task response, our new ANTs with saccadic responses signalled with a fixation arrow, and a manual response version with the response arrow at fixation (ANTf). Results for all three experiments showed typical main effects of all three attention networks, but we observed differences in their interactions. The ANTm showed only an interaction of alerting enhancing the orienting; ANTs showed a congruency by orienting interaction with the orienting effect only observed for pro-saccades. The ANTf showed both alerting by orienting, and orienting by congruency. Although the saccadic response did differ from the original ANTm, key differences were also highlighted by the switch from peripheral to central target. Overall the proposed ANTf is a valid tool to test main effects of attentional networks. Further investigation of interaction differences between manual and oculomotor systems is required.

Responses to Navon tasks differ across development and between tasks with differing attentional demands

Navon hierarchical stimuli are designed to measure responses to the global level (grouped local elements, e.g. a forest) and the local level (individuated local elements, e.g. trees) of a visual scene. Cross-sectional evidence suggests that there are developmental changes in global and local processing. We examined global and local processing in 135 typically developing children in Year 1 (aged 5-6 year), Year 3 (aged 7-8 years), and Year 5 (aged 9-10 years). Participants completed a range of Navon tasks, each with different attentional demands. The design of the Navon stimuli remained constant across the tasks, ensuring that any task-related differences were not due to stimulus characteristics. Sixty children from Years 1 and 3 repeated the testing session two years later. Linear mixed model analyses combined longitudinal and cross-sectional data to assess developmental changes and the influence of attentional task demands on responses. The results revealed differing patterns of global and local processing responses according to Year group and attentional task demands. We found some evidence of developmental change in responses from a relatively more local advantage to a relatively more global advantage, which is consistent with the literature. However, the age at which this transition occurred varied across the tasks. We conclude that responses to hierarchical Navon stimuli are modulated by attentional task characteristics which mask any underlying global or local processing advantage.

Auditory local-global temporal processing: evidence for perceptual reorganization with musical expertise

The way the visual system processes different scales of spatial information has been widely studied, highlighting the dominant role of global over local processing. Recent studies addressing how the auditory system deals with local–global temporal information suggest a comparable processing scheme, but little is known about how this organization is modulated by long-term musical training, in particular regarding musical sequences. Here, we investigate how non-musicians and expert musicians detect local and global pitch changes in short hierarchical tone sequences structured across temporally-segregated triplets made of musical intervals (local scale) forming a melodic contour (global scale) varying either in one direction (monotonic) or both (non-monotonic). Our data reveal a clearly distinct organization between both groups. Non-musicians show global advantage (enhanced performance to detect global over local modifications) and global-to-local interference effects (interference of global over local processing) only for monotonic sequences, while musicians exhibit the reversed pattern for non-monotonic sequences. These results suggest that the local–global processing scheme depends on the complexity of the melodic contour, and that long-term musical training induces a prominent perceptual reorganization that reshapes its initial global dominance to favour local information processing. This latter result supports the theory of “analytic” processing acquisition in musicians.

Strength of Ventral Tegmental Area Connections With Left Caudate Nucleus Is Related to Conflict Monitoring

Successful learning requires the control of attention to monitor performance and compare actual versus expected outcomes. Neural activity in the ventral tegmental area (VTA) has been linked to attention control in animals. However, it is unknown whether the strength of VTA connections is related to conflict monitoring in humans. To study the relationship between VTA connections and conflict monitoring, we acquired diffusion tensor imaging (DTI) data on 50 second language learners who we have previously studied. We performed probabilistic tractography to document VTA connections with the dorsal striatum and the anterior cingulate cortex (ACC), and administered the Flanker task in which subjects were required to monitor and report conflicts in visual stimuli. Reaction times (RTs) indexed students’ conflict monitoring. Probabilistic tractography revealed distinct neural connections between the VTA and the dorsal striatum and ACC. Correlational analyses between tractography and flanker RTs revealed that the strength of VTA connections with the left caudate nucleus was negatively correlated with RTs recorded in the presence of conflicts. This provides the first evidence to suggest that VTA connections with the left caudate nucleus are related to conflict monitoring in humans.

Audiovisual integration capacity modulates as a function of illusory visual contours, visual display circumference, and sound type

Research into the capacity of audiovisual integration has previously assessed whether capacity is strictly limited to a single item, or whether it can exceed one item under certain environmental conditions. More recently, investigations have turned to examining the effects of various stimulus factors on capacity. Across two experiments, we looked at a number of factors that were expected to play a modulatory role on capacity. Experiment 1 deployed a manipulation of illusory polygons, revealing an increase in audiovisual capacity, even in an absence of visual connections. This demonstrates that exceeding the capacity of 1 does not only represent a functional increase in the binding of a singular, complex visual object, but that it can also represent binding of multiple simpler objects. Findings also support the hypothesis that capacity modulates quantitatively, but not qualitatively, with respect to speed of presentation. Experiment 2 examined the effects of different sound types (sine tones or white noise) and of different spatial visual field sizes on the capacity of audiovisual integration. The results indicate that capacity is maximized when stimuli are presented in a smaller circle (7.5°) if alongside a sine tone, and when presented in a larger circle (18.5°) alongside white noise. These results suggest that audiovisual integration capacity is dependent on the combination of sound type and visual spatial field size. The combination of these results reveal additional phenomenological features of the capacity of audiovisual integration, and provides impetus for further research into applications of the findings.

Prioritised self-referential processing is modulated by emotional arousal

Stimuli related to the self are processed more efficiently in a variety of cognitive tasks. Recent studies have shown that this self-referential processing bias is modulated by emotion. However, a clear understanding of how emotional valence and arousal affect self-referential processing is still lacking. With a label-shape matching task, Experiment 1 measured a self-prioritisation effect in four different mood states. The results revealed stronger self-prioritisation effects in moods with higher arousal levels and a reliable correlation between the self-prioritisation effect and the arousal level reported by the participants; however, the effect of emotional valence was not statistically reliable. Experiment 2 further showed that alerting cues, known to raise arousal level, effectively increased the self-prioritisation effect in the same label-shape matching task. Experiment 3 clarified that alerting cues do not affect reward processing in a similar label-shape matching task, suggesting that arousal may selectively modulate self-referential processing. These observations provide clear evidence that emotional arousal modulates self-referential processing.

How Infants' Arousal Influences Their Visual Search

The influence of arousal on visual attention was examined in 6.5-month-old infants (N = 42) in the context of a visual search task. Phasic increases in arousal were induced with brief sounds and measured with pupil dilation. Evidence was found for an inverted U-shaped relation between pupil dilation amplitude and visual orienting, with highest likelihood of a target fixation at intermediate levels of arousal. Effects were similar for facial stimuli and simple objects. Together, these results contribute to our understanding of the relation between arousal and attention in infancy. The study also demonstrates that infants have a bias to orient to human eyes, even when presented in isolation.

Exploring the Limitations of the Shielding Function of Categorization Rules in Task-Switching

Applying categorization rules narrows attention toward the relevant features of a target and helps participants to ignore the irrelevant features of the target. This is called the shielding function of categorization rules. Here we explored the limitation of the shielding function in two task-switching experiments. In Experiment 1, we assigned each target a single digital numeral as an additional feature in addition to conventional bivalent features as in the previous task-switching experiments with bivalent tasks. In the first two stages of Experiment 1, half of the participants learned the numeral-response associations and the other half used an alternative numeral-categorization rule to infer the response. Without participants applying conventional task-switching rules, the switching costs disappeared. Moreover, when participants performed tasks by numeral-response associations the bivalent features interfered with response retrieval and caused response-congruency effects, whereas when participants applied the numeral-categorization rule, the bivalent features were shielded away and thereby the response-congruency effects disappeared. In the third stage, in which all participants applied task-switching rules by discriminating between bivalent features (i.e., filling and orientations), we found task-switching costs and response-congruency effects. In Experiment 2, new bivalent features produced stronger interference compared to Experiment 1. As a consequence, participants in both the association group and the numeral-categorization rule group showed significant response-congruency effects in the first two stages, where task-switching rules were not introduced. It follows that the shielding function of categorization rules has limits—strong interference from bivalent features can break down the shielding function. In addition, participants in the association group showed task-switching costs without being informed about the task-switching rules. We propose that strong proactive interference can produce task-switching costs even without the use of task-switching rules.

The gist and details of sex differences in cognition and the brain: How parallels in sex differences across domains are shaped by the locus coeruleus and catecholamine systems

Across three different domains, there are similar sex differences in how men and women process information. There tends to be a male advantage in attending to and remembering the gist (essential central information of a scene or situation), but a female advantage in attending to and remembering the details (non-essential peripheral information of a scene or situation). This is seen in emotional memory, where emotion enhances gist memory more for males than for females, but enhances detail memory more for females than for males. It also occurs in spatial memory, where men tend to notice and remember the gist of where they or objects are in space, allowing them to more flexibly manipulate themselves or objects within that space, whereas women tend to recall the details of the space around them, allowing them to accurately remember the locations of objects. Finally, such sex differences have also been noted in perception of stimuli such that men attend to global aspects of stimuli (such as a large letter E) more than women, whereas women attend more to the local aspects (such as the many smaller letter Ts making up the E). We review the parallel sex differences seen across these domains in this paper and how they relate to the different brain systems involved in each of these task domains. In addition, we discuss how sex differences in evolutionary pressures and in the locus coeruleus and norepinephrine system may account for why parallel sex differences occur across these different task domains.

Do alerting signals increase the size of the attentional focus?

Previous research has shown that the presentation of an auditory alerting signal before a visual target increases the interference from flanking distractors. Recently, it has been suggested that this increase in interference may be due to an expansion of the spatial focus of attention. In five experiments, this hypothesis was tested by using a probe technique dedicated to measuring variations in the size of the attentional focus: In the majority of trials, participants performed a letter discrimination task in which their attention was focused on a central target letter. In a randomly intermixed probe task, the size of the attentional focus was measured by letting participants respond to a probe occurring at varying positions. In all experiments, reaction time (RT) to the probe increased from the most central to more lateral probe positions. This V-shaped probe-RT function, however, was not flattened by the presentation of an alerting signal. Overall, this pattern of results is inconsistent with the hypothesis that alerting signals increase the attentional focus. Instead, it is consistent with nonspatial accounts that attribute the increase in interference to an alerting effect on perceptual processing, which then leads to a detrimental effect at the level of response selection.

Lost in Time and Space: States of High Arousal Disrupt Implicit Acquisition of Spatial and Sequential Context Information

Biased cognition during high arousal states is a relevant phenomenon in a variety of topics: from the development of post-traumatic stress disorders or stress-triggered addictive behaviors to forensic considerations regarding crimes of passion. Recent evidence indicates that arousal modulates the engagement of a hippocampus-based "cognitive" system in favor of a striatum-based "habit" system in learning and memory, promoting a switch from flexible, contextualized to more rigid, reflexive responses. Existing findings appear inconsistent, therefore it is unclear whether and which type of context processing is disrupted by enhanced arousal. In this behavioral study, we investigated such arousal-triggered cognitive-state shifts in human subjects. We validated an arousal induction procedure (three experimental conditions: violent scene, erotic scene, neutral control scene) using pupillometry (Preliminary Experiment, n = 13) and randomly administered this method to healthy young adults to examine whether high arousal states affect performance in two core domains of contextual processing, the acquisition of spatial (spatial discrimination paradigm; Experiment 1, n = 66) and sequence information (learned irrelevance paradigm; Experiment 2, n = 84). In both paradigms, spatial location and sequences were encoded incidentally and both displacements when retrieving spatial position as well as the predictability of the target by a cue in sequence learning changed stepwise. Results showed that both implicit spatial and sequence learning were disrupted during high arousal states, regardless of valence. Compared to the control group, participants in the arousal conditions showed impaired discrimination of spatial positions and abolished learning of associative sequences. Furthermore, Bayesian analyses revealed evidence against the null models. In line with recent models of stress effects on cognition, both experiments provide evidence for decreased engagement of flexible, cognitive systems supporting encoding of context information in active cognition during acute arousal, promoting reduced sensitivity for contextual details. We argue that arousal fosters cognitive adaptation towards less demanding, more present-oriented information processing, which prioritizes a current behavioral response set at the cost of contextual cues. This transient state of behavioral perseverance might reduce reliance on context information in unpredictable environments and thus represent an adaptive response in certain situations.

Exposure to arousal-inducing sounds facilitates visual search

Exposure to affective stimuli could enhance perception and facilitate attention via increasing alertness, vigilance, and by decreasing attentional thresholds. However, evidence on the impact of affective sounds on perception and attention is scant. Here, a novel aspect of affective facilitation of attention is studied: whether arousal induced by task-irrelevant auditory stimuli could modulate attention in a visual search. In two experiments, participants performed a visual search task with and without auditory-cues that preceded the search. Participants were faster in locating high-salient targets compared to low-salient targets. Critically, search times and search slopes decreased with increasing auditory-induced arousal while searching for low-salient targets. Taken together, these findings suggest that arousal induced by sounds can facilitate attention in a subsequent visual search. This novel finding provides support for the alerting function of the auditory system by showing an auditory-phasic alerting effect in visual attention. The results also indicate that stimulus arousal modulates the alerting effect. Attention and perception are our everyday tools to navigate our surrounding world and the current findings showing that affective sounds could influence visual attention provide evidence that we make use of affective information during perceptual processing.

Cognitive control, dynamic salience, and the imperative toward computational accounts of neuromodulatory function

We draw attention to studies indicating that phasic arousal increases interference effects in tasks necessitating the recruitment of cognitive control. We suggest that arousal-biased competition models such as GANE (glutamate amplifies noradrenergic effects) may be able to explain these findings by taking into account dynamic, within-trial changes in the relative salience of task-relevant and task-irrelevant features. However, testing this hypothesis requires a computational model.

Sex differences in the Kimchi-Palmer task revisited: Global reaction times, but not number of global choices differ between adult men and women

Research, directly assessing sex-dependent differences in global versus local processing is sparse, but predominantly suggesting that men show a stronger global processing bias than women. Utilizing the Kimchi-Palmer task however, sex differences in the number of global choices can only be found in children, but not in adults. In the current study 52 men and 46 women completed a computerized version of the Kimchi Palmer task, in order to investigate whether sex-differences in global-local processing in the Kimchi-Palmer task are reflected in choice reaction times rather than choices per se. While no sex differences were found in the number of global choices, we found that especially women are faster in making local choices than men, while men are faster in making global choices than women. We did not find support for the assumption that this sex difference was modulated by menstrual cycle phase of women, since the difference between reaction times to global and local choices was consistent across the menstrual cycle of women. Accordingly there was no relationship between progesterone and global-local processing in the Kimchi-Palmer task. However, like in studies utilizing the Navon task, testosterone was positively related to the number of global choices in both men and women. To our knowledge, this is the first study including reaction times as outcome measure in a Kimchi Palmer paradigm and also the first study demonstrating sex differences in the Kimchi Palmer task in adults.

Scalable Semisupervised Functional Neurocartography Reveals Canonical Neurons in Behavioral Networks

Large-scale data collection efforts to map the brain are underway at multiple spatial and temporal scales, but all face fundamental problems posed by high-dimensional data and intersubject variability. Even seemingly simple problems, such as identifying a neuron/brain region across animals/subjects, become exponentially more difficult in high dimensions, such as recognizing dozens of neurons/brain regions simultaneously. We present a framework and tools for functional neurocartography-the large-scale mapping of neural activity during behavioral states. Using a voltage-sensitive dye (VSD), we imaged the multifunctional responses of hundreds of leech neurons during several behaviors to identify and functionally map homologous neurons. We extracted simple features from each of these behaviors and combined them with anatomical features to create a rich medium-dimensional feature space. This enabled us to use machine learning techniques and visualizations to characterize and account for intersubject variability, piece together a canonical atlas of neural activity, and identify two behavioral networks. We identified 39 neurons (18 pairs, 3 unpaired) as part of a canonical swim network and 17 neurons (8 pairs, 1 unpaired) involved in a partially overlapping preparatory network. All neurons in the preparatory network rapidly depolarized at the onsets of each behavior, suggesting that it is part of a dedicated rapid-response network. This network is likely mediated by the S cell, and we referenced VSD recordings to an activity atlas to identify multiple cells of interest simultaneously in real time for further experiments. We targeted and electrophysiologically verified several neurons in the swim network and further showed that the S cell is presynaptic to multiple neurons in the preparatory network. This study illustrates the basic framework to map neural activity in high dimensions with large-scale recordings and how to extract the rich information necessary to perform analyses in light of intersubject variability.

Zooming into creativity: individual differences in attentional global-local biases are linked to creative thinking

While recent studies have investigated how processes underlying human creativity are affected by particular visual-attentional states, we tested the impact of more stable attention-related preferences. These were assessed by means of Navon’s global-local task, in which participants respond to the global or local features of large letters constructed from smaller letters. Three standard measures were derived from this task: the sizes of the global precedence effect, the global interference effect (i.e., the impact of incongruent letters at the global level on local processing), and the local interference effect (i.e., the impact of incongruent letters at the local level on global processing). These measures were correlated with performance in a convergent-thinking creativity task (the Remote Associates Task), a divergent-thinking creativity task (the Alternate Uses Task), and a measure of fluid intelligence (Raven’s matrices). Flexibility in divergent thinking was predicted by the local interference effect while convergent thinking was predicted by intelligence only. We conclude that a stronger attentional bias to visual information about the “bigger picture” promotes cognitive flexibility in searching for multiple solutions.