Biology subjects

Cross, Z. R.

Publications and source records attributed to Cross, Z. R..

At least 19 recordsLinked to original sources

bioRxiv2026

The development of slow and fast theta oscillations in the human brain

Theta oscillations are pivotal for attention and memory, with developmental shifts in theta activity and connectivity tracking memory ability across the lifespan. Building on initial evidence that the theta band separates into slow and fast sub-bands across development within the medial temporal lobe (MTL) and the prefrontal cortex (PFC), this preregistered study (https://osf.io/gsru7) characterized the frequencies of slow (~1.5-4.5 Hz) and fast (~4.5-9.0 Hz) theta oscillations across the brain in a large developmental cohort. We analyzed intracranial EEG (iEEG) recordings from widespread brain regions in 101 children and adults (5.93-54.00 years, 63 males; n electrodes = 5691) using task-based (attention to to-be-remembered visual stimuli) and task-free (resting-state) data. We reveal distinct slow and fast theta oscillations in all regions and identify a spatial gradient in both frequency ranges, with slow theta oscillations speeding up and fast theta oscillations slowing down from posterior to anterior regions. The dissociation between slow and fast theta frequencies peaks during young adulthood, mirroring the developmental trajectory of attention and memory. In the hippocampus and PFC, attentional state (task-based, task-free) modulated age effects, and individual differences in task-based slow theta frequencies predicted individual differences in memory performance, linking the development of slow theta oscillations to the development of memory. Gray matter volume was not associated with age- or task-related differences in theta frequencies, suggesting that the development of theta oscillations is independent of regional brain structure. This study establishes developmental trajectories of slow and fast theta oscillations in localized brain regions and links the maturation of hippocampal and PFC slow theta oscillations to the development of attention and memory.

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bioRxiv2026

Opposing effects of slow and fast theta synchrony on working memory in the human hippocampal-orbitofrontal network

Working memory (WM) enables us to maintain and manipulate information over time, but how the brain organizes sequential information locally and across networks remains unclear. Recent work suggests that slow and fast theta oscillations serve different roles in memory, yet their distinct contributions to sequential WM are unknown. Based on evidence that the hippocampus (HC) and orbitofrontal cortex (OFC) support sequential WM and that slower theta cycles provide optimal temporal windows for organizing items in WM, we predicted that these regions would coordinate via slow theta dynamics. We analyzed intracranial EEG from the HC, OFC, and amygdala (AMY) in 21 neurosurgical patients (7 female, 13-54 years of age; M {+/-} SD, 30 {+/-} 11.2 years) performing a delayed match-to-sample WM task. We assessed phase locking between regions, phase-amplitude coupling within regions, and neuronal phase coding for slow (~1-4.5 Hz) and fast (~4.5-8 Hz) theta oscillations. We found significant slow and fast theta synchrony between all regions, but identical anatomical pathways produced opposing behavioral effects depending on oscillatory frequency, particularly during higher cognitive demand. Slow theta synchrony was associated with faster response times (RTs), while fast theta synchrony between HC and OFC hindered both accuracy and RTs. Unexpectedly, AMY modulated RT through demand-dependent slow theta synchrony, where AMY-OFC synchrony predicted faster RTs during maintenance and HC-AMY synchrony predicted faster RTs during higher cognitive demand. Sustained coupling between slow theta oscillations and high-frequency broadband activity within each region suggests that local organization coincides with beneficial network behavioral effects. These results establish a frequency-opponent mechanism in which theta oscillation frequencies determine whether HC-OFC circuits facilitate or impair sequential WM.

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bioRxiv2025

Effects of aperiodic neural activity on sleep-based emotional memory consolidation across the lifespan

Sleep neurophysiology undergoes significant changes across the lifespan, which coincide with age-related differences in memory, particularly for emotional information. However, the mechanisms that underlie these effects remain poorly understood. One potential mechanism is the aperiodic component, which reflects "neural noise", differs across age, and is predictive of perceptual and cognitive processes. In this study, we investigated how intrinsic (i.e., resting-state) aperiodic neural activity modulates sleep-based emotional memory consolidation across the human lifespan. In a within-subjects, repeated measures design, forty-two participants aged 7 - 72 years (M = 26.60, SD = 17.45; 26 female) completed a learning and baseline recognition emotional memory task before a 2hr afternoon sleep opportunity and an equivalent period of wake. Recognition accuracy was also assessed post-delay. We found that aperiodic slopes follow a u-shaped trajectory across the lifespan: slopes flatten from childhood to young adulthood, before steepening thereafter, with this effect most prominent in frontal regions. Age-related differences in aperiodic slopes also explained interindividual differences in emotional memory consolidation, with less age-related flattening of slopes associated with stronger consolidation of negative stimuli post-sleep but not post-wake. Lastly, independent of aperiodic activity, age-related differences in NREM oscillatory activity predicted emotional memory consolidation. These findings suggest that the efficiency of sleep-based emotional memory consolidation is modulated by age-related differences in aperiodic neural and NREM oscillatory activities, providing novel insights into the neurophysiological mechanisms underpinning emotional memory across the lifespan.

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bioRxiv2025

Declarative Memory Through the Lens of Single-Trial Peaks in High-Frequency Power

Declarative memory depends on the coordination of local processing, indexed by high-frequency broadband (HFB) activity, with global network organization, indexed by theta oscillations. However, theta and HFB exhibit asynchronous timing, raising the question of how results of local processing are communicated throughout the network. Using intracranial EEG in patients performing a recognition memory task, we examined this coordination across the medial temporal lobe (MTL) and prefrontal cortex (PFC). HFB peak activity was earlier in the MTL than PFC. Anchoring analyses of theta phase clustering and connectivity to HFB peaks revealed strong phase clustering locked to HFB peaks in the PFC, as well as connectivity between the PFC and MTL that predicted individual memory performance. Graph analysis revealed specific connections amidst sparse network connectivity during memory success. This study demonstrates that transient brain states linked to internal physiological events support memory and refines our understanding of local and network-level process interactions. HighlightsO_LIMemory-linked theta activity is time-locked to internal brain events C_LIO_LINetwork connectivity changes dynamically during memory processing C_LIO_LISparse network connectivity supports successful memory C_LIO_LISpecific sequences of transient states may be critical for declarative memory C_LI

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bioRxiv2024

The development of aperiodic neural activity in the human brain

The neurophysiological mechanisms supporting brain maturation are fundamental to attention and memory capacity across the lifespan. Human brain regions develop at different rates, with many regions developing into the third and fourth decades of life. Here, in this preregistered study (https://osf.io/gsru7), we analyzed intracranial EEG (iEEG) recordings from widespread brain regions in a large developmental cohort. Using task-based (i.e., attention to-be-remembered visual stimuli) and task-free (resting-state) data from 101 children and adults (5.93 - 54.00 years, 63 males; n electrodes = 5691), we mapped aperiodic (1/[f]-like) activity, a proxy of neural noise, with steeper slopes indexing less noise and flatter slopes indexing more noise. We reveal that aperiodic slopes flatten with age into young adulthood in both association and sensorimotor cortices, challenging models of early sensorimotor development based on brain structure. In prefrontal cortex (PFC), attentional state modulated age effects, revealing steeper task-based than task-free slopes in adults and the opposite in children, consistent with the development of cognitive control. Age-related differences in task-based slopes also explained age-related gains in memory performance, linking the development of PFC cognitive control to the development of memory. Last, with additional structural imaging measures, we reveal that age-related differences in gray matter volume are similarly associated with aperiodic slopes in association and sensorimotor cortices. Our findings establish developmental trajectories of aperiodic activity in localized brain regions and illuminate the development of PFC control during adolescence in the development of attention and memory.

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bioRxiv2024

Predictive influences on memory encoding: investigating oscillations and the N400 event-related potential component

To effectively function in an ever-changing environment, the brain is proposed to make predictions about upcoming information. However, the association between prediction and memory formation and the role of between-subject neural variability in this relationship is unclear. To shed light on the relationship between prediction and memory, the present study reanalysed data from Jano, Chatburn, and colleagues (2024). In the original experiment, participants were exposed to naturalistic images in predictable and unpredictable four-item sequences, after which their memory was tested using an old/new paradigm. In the present analysis (N = 46), N400 amplitude and oscillatory power during learning was measured to gauge processes related to prediction error and memory encoding, respectively. This activity was compared with subsequent memory outcomes and individual alpha frequency (IAF) calculated at rest. Linear mixed-effects regressions revealed an alpha power subsequent memory effect that was not related to the amplitude of the N400, suggesting that memory encoding may occur independently of the level of prediction error. Notably, IAF influenced the relationship between theta power, N400 amplitude and subsequent memory, implying that the electrophysiological conditions for successful memory formation differ between individuals. Consequently, the degree to which prediction errors (presumably gauged via the N400) drive memory encoding could depend on inter-individual variability in intrinsic neural activity. These findings emphasise the flexible nature of memory, whilst having potential implications for prediction error-driven accounts of learning.

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bioRxiv2024

Augmenting complex and dynamic performance through mindfulness-based cognitive training: an investigation of on-task EEG dynamics.

Mindfulness-based cognitive training exhibits great propensity for improving cognitive performance across a range of contexts. However, the neurophysiological basis of these cognitive enhancements has remained relatively unclear. Previous studies have widely examined EEG during mindfulness practice - or made comparisons with long-term meditators and controls - but have failed to capture how EEG dynamics in subsequent cognitive testing scenarios might be altered as a function of mindfulness-based interventions. The current study therefore aimed to assess a variety of EEG dynamics (oscillatory, aperiodic, and event-related) during engagement in a dynamic and complex cognitive task, following a mindfulness-based cognitive training regime. Participants (n = 40, age range = 18 - 38) attended the lab on two separate occasions (pre- and post-a web-based one-week mindfulness intervention), where EEG was recorded during engagement in the Target Motion Analyst (TMA) task. Previous analysis of the same participants demonstrated that greater adherence to the mindfulness-based cognitive training was associated with improved performance on the TMA task (Dziego, Bornkessel-Schlesewsky, Schlesewsky et al., 2024). Here, we capitalise on these previous findings to assess whether adherence is paralleled by measurable differences in on-task EEG dynamics. Linear mixed-effects modelling demonstrated that, while main effects were observed across session, adherence to cognitive training was not directly associated with alpha power, theta power or 1/f parameters. Challenges also arose when computing event-related potentials (ERPs), illustrating the difficulties of using this technique in more complex testing environments. While these results are challenging to place within the context of previous EEG studies on meditation and cognitive performance, our findings highlight the complexities in understanding the cognitive benefits of mindfulness-based training interventions through EEG dynamics observed during subsequent cognitive testing.

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bioRxiv2023

Individual alpha frequency modulates prediction error-driven memory encoding

Prediction and memory are strongly intertwined, with predictions relying on memory retrieval, whilst also influencing memory encoding. However, it is unclear how predictability influences explicit memory performance, and how individual neural factors may modulate this relationship. The current study sought to investigate the effect of predictability on memory processing with an analysis of the N400 event-related potential in a context extending beyond language. Participants (N = 48, females = 33) completed a study-test paradigm where they first viewed predictable and unpredictable four-item ABCD sequences of outdoor scene images, whilst their brain activity was recorded using electroencephalography (EEG). Subsequently, their memory for the images was tested, and N400 patterns during learning were compared with memory outcomes. Behavioural results revealed better memory for images in predictable sequences in contrast to unpredictable sequences. Memory was also strongest for predictable images in the B position, suggesting that when processing longer sequences, the brain may prioritise the data deemed most informative. Strikingly, greater N400 amplitudes during learning were associated with enhanced memory at test for individuals with low versus high individual alpha frequencies (IAFs). In light of the relationship between the N400 and stimulus predictability, this finding may imply that predictive processing differs between individuals to influence the extent of memory encoding. Finally, exploratory analyses provided evidence for a later positivity that was predictive of subsequent memory performance. Ultimately, the results highlight the complex and interconnected relationship between predictive processing and memory, whilst shedding light on the accumulation of predictions across longer sequences.

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bioRxiv2023

Augmenting complex and dynamic performance through mindfulness-based cognitive training: an evaluation of training adherence, trait mindfulness, personality and resting-state EEG.

Human performance applications of mindfulness-based training have demonstrated its utility in enhancing cognitive functioning. Previous studies have illustrated how these interventions can improve performance on traditional cognitive tests, however, little investigation has explored the extent to which mindfulness-based training can optimise performance in more dynamic and complex contexts. Further, from a neuroscientific perspective, the underlying mechanisms responsible for performance enhancements remain largely undescribed. With this in mind, the following study aimed to investigate how a short-term mindfulness intervention (one week) augments performance on a dynamic and complex task (target motion analyst task; TMA) in young, healthy adults (n = 40, age range = 18 - 38). Linear mixed effect modelling revealed that increased adherence to the mindfulness-based training regime (ranging from 0-21 sessions) was associated with improved performance in the second testing session of the TMA task, controlling for baseline performance. Further analyses of resting-state electroencephalographic (EEG) metrics and additional individual factors demonstrated enhancements associated with training adherence remained relatively consistent across varying levels of participants resting-state EEG metrics, personality measures (i.e., trait mindfulness, neuroticism, conscientiousness), self-reported enjoyment and timing of intervention adherence. Our results thus indicate that mindfulness-based cognitive training leads to performance enhancements in distantly related tasks, irrespective of several individual differences. We also revealed nuances in the magnitude of cognitive enhancements contingent on the timing of adherence, regardless of total volume of training. Overall, our findings suggest that mindfulness-based training could be used in a myriad of settings to elicit transferable performance enhancements.

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bioRxiv2022

Individual differences in information processing predict sleep-based memory consolidation of complex rules

Memory is critical for many cognitive functions, from remembering facts, to learning complex environmental rules. While memory encoding occurs during wake, memory consolidation is associated with sleep-related neural activity. Further, research suggests that individual differences in alpha frequency during wake ([~] 7 - 13 Hz) modulate memory processes, with higher individual alpha frequency (IAF) associated with greater memory performance. However, the relationship between wake-related EEG individual differences, such as IAF, and sleep-related neural correlates of memory consolidation has been largely unexplored, particularly in a complex rule-based memory context. Here, we aimed to investigate whether wake-derived IAF and sleep neurophysiology interact to influence rule learning in a sample of 35 healthy adults (16 males; mean age = 25.4, range: 18 - 40). Participants learned rules of a modified miniature language prior to either 8hrs of sleep or wake, after which they were tested on their knowledge of the rules in a grammaticality judgement task. Results indicate that sleep neurophysiology and wake-derived IAF do not interact but modulate memory for complex linguistic rules separately. Phase-amplitude coupling between slow oscillations and spindles during non-rapid eye-movement (NREM) sleep also promoted memory for rules that were analogous to the canonical English word order. As an exploratory analysis, we found that rapid eye-movement (REM) sleep theta power at posterior regions interacts with IAF to predict rule learning and proportion of time in REM sleep predicts rule learning differentially depending on grammatical rule type. Taken together, the current study provides behavioural and electrophysiological evidence for a complex role of NREM and REM sleep neurophysiology and wake-derived IAF in the consolidation of rule-based information.

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bioRxiv2022

Resting-state aperiodic neural activity as a novel objective marker of daytime somnolence

Study ObjectivesCurrent assessment of excessive daytime somnolence (EDS) requires subjective measurements such as the Epworth Sleepiness Scale (ESS), and/or resource intensive sleep laboratory investigations. Recent work 1,2 has called for more non-performance-based measures of EDS. One promising non-performance-based measure of EDS is the aperiodic component of electroencephalography (EEG). Aperiodic (non-oscillatory) activity reflects excitation/inhibition ratios of neural populations and is altered in various states of consciousness, and thus may be a potential biomarker of hypersomnolence. MethodsWe retrospectively analysed EEG data from patients who underwent a Multiple Sleep Latency Test (MSLT) and determined whether aperiodic neural activity is predictive of EDS. Participants having undergone laboratory polysomnogram and next day MSLT were grouped into MSLT+ (n = 26) and MSLT- (n = 33) groups (mean sleep latency of < 8min and > 10min, respectively) and compared against a non-clinical (Control) group of participants (n = 26). ResultsWhile the MSLT+ and MSLT- groups did not differ in their aperiodic activity, the Control group had a significantly flatter slope and larger offset compared to both MSLT+ and MSLT- groups. Logistic regression machine learning predicted group status (i.e., symptomatic, non-symptomatic) with 90% accuracy based on the aperiodic slope while controlling for age. Slow oscillation-spindle coupling was also significantly stronger in the Control group relative to MSLT+ and MSLT- groups. ConclusionsOur results provide first evidence that aperiodic neural dynamics and sleep-based cross-frequency coupling is predictive of EDS, thereby providing a novel avenue for basic and applied research in the study of sleepiness.

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bioRxiv2022

Electrophysiological indices of individual differences in adult language learning

Individual differences in second language (L2) learning can offer insights into the neurobiological bases of learning aptitude. One neurophysiological marker of inter-individual differences in cognition is the individual alpha frequency (IAF), a trait-like measure correlated with cognition. Further, the N400 is an electrophysiological marker indexing stimulus irregularity and has been used to study L2 learning; however, its relationship with IAF and L2 learning remains unknown. To examine the relation between IAF and L2 learning (indexed by N400 amplitude), we report data from a modified miniature language learning study. After a vocabulary learning period, participants (N = 38, Mage = 25.3, SD = 7.13) judged the grammaticality of classifier-noun pairs, with mixed-effects modelling revealing lower IAF individuals were better than higher IAF individuals at grammaticality judgements. N400 amplitude also reduced across the experiment in low relative to high IAF individuals, indicating the relationship between IAF and language learning is more complex than initially postulated.

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bioRxiv2022

Neural and cognitive correlates of performance in dynamic multi-modal settings

The endeavour to understand human cognition has largely relied upon investigation of task-related brain activity. However, resting-state brain activity can also offer insights into individual information processing and performance capabilities. Previous research has identified electroencephalographic resting-state characteristics (most prominently: the individual alpha frequency; IAF) that predict cognitive function. However, it has largely overlooked a second component of electrophysiological signals: aperiodic 1/f activity. The current study examined how both oscillatory and aperiodic resting-state EEG measures, alongside traditional cognitive tests, can predict performance in a dynamic and complex, semi-naturalistic cognitive task. Participants resting-state EEG was recorded prior to engaging in a Target Motion Analysis (TMA) task in a simulated submarine control room environment (CRUSE), which required participants to integrate dynamically changing information over time. We demonstrated that the relationship between IAF and cognitive performance extends from simple cognitive tasks (e.g., digit span) to complex, dynamic measures of information processing. Further, our results showed that individual 1/f parameters (slope and intercept) differentially predicted performance across practice and testing sessions, whereby flatter slopes were associated with improved performance during learning, while higher intercepts were linked to better performance during testing. In addition to the EEG predictors, we demonstrate a link between cognitive skills most closely related to the TMA task (i.e., spatial imagery) and subsequent performance. Overall, the current study highlights (1) how resting-state metrics - both oscillatory and aperiodic - have the potential to index higher-order cognitive capacity, while (2) emphasising the importance of examining these electrophysiological components within more dynamic settings and over time.

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bioRxiv2021

Theta activity during encoding interacts with NREM sleep oscillations to predict memory generalization

Relatively little is known regarding the interaction between encoding-related neural activity and sleep-based memory consolidation. One suggestion is that a function of encoding-related theta power may be to tag memories for subsequent processing during sleep. This study aimed to extend previous work on the relationships between sleep spindles, slow oscillation-spindle coupling and task-related theta activity with a combined Deese-Roediger-McDermott (DRM) and nap paradigm. This allowed us to examine the influence of task- and sleep-related oscillatory activity on the recognition of both encoded list words and associative theme words. Thirty-three participants (29 females, mean age = 23.2 years) learned and recognised DRM lists separated by either a 2hr wake or sleep period. Mixed-effects modelling revealed the sleep condition endorsed more associative theme words and fewer list words in comparison to the wake group. Encoding-related theta power was also found to influence sleep spindle density, and this interaction was predictive of memory outcomes. The influence of encoding-related theta was specific to sleep spindle density, and did not appear to influence the strength of slow oscillation-spindle coupling as it relates to memory outcomes. The finding of interactions between wakeful and sleep oscillatory-related activity in promoting memory and learning has important implications for theoretical models of sleep-based memory consolidation.

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bioRxiv2021

Neural Mechanisms of Learning are Critically Dependent on Sleep

Sleep supports memory consolidation as well as next-day learning. The influential Active Systems account of offline consolidation suggests that sleep-associated memory processing paves the way for new learning, but empirical evidence in support of this idea is scarce. Using a within-subjects (N = 30), crossover design, we assessed behavioural and electrophysiological indices of episodic encoding after a night of sleep or total sleep deprivation in healthy adults (aged 18-25 years), and investigated whether behavioural performance was predicted by the overnight consolidation of episodic associations formed the previous day. Sleep supported memory consolidation and next-day learning, as compared to sleep deprivation. However, the magnitude of this sleep-associated consolidation benefit did not significantly predict the ability to form novel memories after sleep. Interestingly, sleep deprivation prompted a qualitative change in the neural signature of encoding: whereas 12-20 Hz beta desynchronization - an established marker of successful encoding - was observed after sleep, sleep deprivation disrupted beta desynchrony during successful learning. Taken together, these findings suggest that effective learning depends on sleep, but not necessarily sleep-associated consolidation.

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bioRxiv2021

Neural signatures of teamwork: Evidence from real-world military training

Effective teams are essential for optimally functioning societies. However, little is known regarding the neural basis of two or more individuals engaging cooperatively in real-world tasks, such as in operational training environments. In this exploratory study, we recruited forty individuals paired as twenty dyads and recorded dual-EEG at rest and during realistic training scenarios of increasing complexity using virtual simulation systems. We estimated markers of intrinsic brain activity (i.e., individual alpha frequency and aperiodic activity), as well as task-related theta and alpha oscillations. Using nonlinear modelling and a logistic regression machine learning model, we found that resting-state EEG predicts performance and can also reliably differentiate between members within a dyad. Task-related theta and alpha activity during easy training tasks predicted later performance on complex training to a greater extent than prior behaviour. These findings complement laboratory-based research on both oscillatory and aperiodic activity in higher-order cognition and provide evidence that theta and alpha activity play a critical role in complex task performance in team environments.

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bioRxiv2021

Resting-state aperiodic neural dynamics predict individual differences in visuomotor performance and learning

An emerging body of work has demonstrated that resting-state non-oscillatory, or aperiodic, 1/f neural activity is a functional and behaviorally relevant marker of cognitive function capacity. In the motor domain, previous work has only applied 1/f analyses to description of action coordination and performance. The value of aperiodic resting-state neural dynamics as a marker of individual visuomotor performance capacity remains unknown. Accordingly, the aim of this work was to investigate if individual 1/f intercept and slope parameters of aperiodic resting-state neural activity predict reaction time and perceptual sensitivity in an immersive virtual reality marksmanship task. The marksmanship task required speeded selection of target stimuli and avoidance of non-target stimuli selection. Motor and perceptual demands were incrementally increased across task blocks and participants performed the task across three training sessions spanning one week. When motor demands were high, steeper individual 1/f slope predicted shorter reaction time. This relationship did not change with practice. Increased 1/f intercept and a steeper 1/f slope were associated with higher perceptual sensitivity, measured as d. However, this association was only observed under the highest levels of perceptual demand and only in the initial exposure to these conditions. Individuals with a lower 1/f intercept and a shallower 1/f slope demonstrated the greatest gains in perceptual sensitivity from task practice. These findings demonstrate that individual differences in motor and perceptual performance can be accounted for with resting-state aperiodic neural dynamics. The 1/f aperiodic parameters are most informative in predicting visuomotor performance under complex and demanding task conditions. In addition to predicting capacity for high visuomotor performance with a novel task, 1/f aperiodic parameters might also be useful in predicting which individuals might derive the most improvements from practice.

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bioRxiv2020

Oscillatory and aperiodic neural activity jointly predict grammar learning

Memory formation involves the synchronous firing of neurons in task-relevant networks, with recent models postulating that a decrease in low frequency oscillatory activity underlies successful memory encoding and retrieval. However, to date, this relationship has been investigated primarily with face and image stimuli; considerably less is known about the oscillatory correlates of complex rule learning, as in language. Further, recent work has shown that non-oscillatory (1/f) activity is functionally relevant to cognition, yet its interaction with oscillatory activity during complex rule learning remains unknown. Using spectral decomposition and power-law exponent estimation of human EEG data (17 females, 18 males), we show for the first time that 1/f and oscillatory activity jointly influence the learning of word order rules of a miniature artificial language system. Flexible word order rules were associated with a steeper 1/f slope, while fixed word order rules were associated with a shallower slope. We also show that increased theta and alpha power predicts fixed relative to flexible word order rule learning and behavioural performance. Together, these results suggest that 1/f activity plays an important role in higher-order cognition, including language processing, and that grammar learning is modulated by different word order permutations, which manifest in distinct oscillatory profiles.

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