Non-face Stimuli Research Articles

The neuronal signature of surprised facial expression processing under different attentional focuses: A time-domain and time-frequency study.

Previous studies have shown that high-arousal positive and negative facial expressions influence event-related potential (ERP) and time-frequency responses depending on attentional focuses. However, little is known about how relevant neural responses are influenced by surprised facial expressions, which are also high in arousal but ambiguous in valence. To address the issue, 38 participants were presented with surprised, happy, angry and neutral facial expressions. Attention was manipulated to focus on facial emotional attributes, facial non-emotional attributes, non-facial attributes, or was free to the participants. ERP results showed larger N170 responses to surprised compared to neutral facial expressions when attention focused on facial attributes and to surprised compared to angry and neutral facial expressions when attention focused on facial non-emotional attributes. Time-frequency analyses revealed reduced power of early occipital theta to surprised compared to happy and angry expressions when attention focused on facial emotions and to surprised compared to angry expressions when attention focused on non-facial stimuli. Parietal delta power was smaller for surprised facial expressions than for angry facial expressions when attention focused on facial emotions and for surprised facial expressions than for angry and neutral facial expressions when attention was directed to non-facial stimuli. These findings might suggest that neural responses to surprised facial expressions are modulated by attentional focus.

Rapid integration of face detection and task set in visually guided reaching.

The superior colliculus (SC) has been increasingly implicated in the rapid processing of evolutionarily relevant stimuli like faces, but the behavioural relevance of such processing is unclear. The SC has also been implicated in the generation of express visuomotor responses (EVR), which are very short-latency (~80 ms) bursts of muscle activity time-locked to visual target presentation. These observations led us to investigate the influence of faces on EVRs. We recorded upper limb muscle activity from healthy participants as they reached toward targets in the presence of a distractor. In some experiments, faces were used as stimuli. Across blocks of trials, we varied the instruction as to which stimulus served as the target or distractor. Doing so allowed us to assess the impact of instruction on muscle recruitment given identical visual stimuli. We found that responses were uniquely modulated in tasks involving high-contrast faces, promoting reaches toward or away from a face depending on instruction. Follow-up experiments confirmed that the phenomenon required highly salient repeated faces and was not observed to non-facial stimuli nor to faces expressing different affects. This study extends the hypothesis that the SC mediates the EVR by demonstrating that faces impact muscle recruitment at short latencies that precede cortical activity for face perception. Our results constitute direct evidence for the behavioural relevance of face detection in the brainstem, and also implicate a role for top-down cortical pre-setting of the EVR depending on task context.

Applying an eye tracking technique to gibbons: First study using scanpath measurements for visual stimuli

Compared to the abundance of research on cognition in various nonhuman primate species, studies of gibbons -- often called “the small apes” -- remain limited, despite the importance of gibbons for understanding evolutionary processes in humans and other apes. Over the past decade, eye tracking techniques have been established in chimpanzees and other nonhuman primates using the free-participation method, which requires no physical restraint of the subjects. We investigated the feasibility of using the same method to record visual scanpaths in gibbons. We attempted to measure the eye movements of three adult gibbons while they spontaneously viewed images, with no prior fixation training. Calibration was successful in all three individuals, with errors of less than one degree. In total, 24 stimuli were used, with landscape and nonhuman primate face photographs presented on one-quarter of the screen, to test the prediction that gibbons would change their viewing time depending on image category. All three gibbons viewed the images for longer than the background, and primate face images for longer than landscapes. These results are consistent with previous findings in other primate species that faces attract more attention than non-face stimuli, suggesting that this effect is common across primates. This study demonstrates the feasibility of using eye tracking with gibbons. Further studies on gibbon visual exploration and cognition may enhance our understanding of the phylogenetic origins of hominid intelligence as well as the unique evolution of gibbons.

Shared neural codes of recognition memory

Recognition memory research has identified several electrophysiological indicators of successful memory retrieval, known as old-new effects. These effects have been observed in different sensory domains using various stimulus types, but little attention has been given to their similarity or distinctiveness and the underlying processes they may share. Here, a data-driven approach was taken to investigate the temporal evolution of shared information content between different memory conditions using openly available EEG data from healthy human participants of both sexes, taken from six experiments. A test dataset involving personally highly familiar and unfamiliar faces was used. The results show that neural signals of recognition memory for face stimuli were highly generalized starting from around 200 ms following stimulus onset. When training was performed on non-face datasets, an early (around 200–300 ms) to late (post-400 ms) differentiation was observed over most regions of interest. Successful cross-classification for non-face stimuli (music and object/scene associations) was most pronounced in late period. Additionally, a striking dissociation was observed between familiar and remembered objects, with shared signals present only in the late window for correctly remembered objects, while cross-classification for familiar objects was successful in the early period as well. These findings suggest that late neural signals of memory retrieval generalize across sensory modalities and stimulus types, and the dissociation between familiar and remembered objects may provide insight into the underlying processes.

Effect of inverted faces as visual stimuli on the performance of the hybrid SSVEP + P300 brain computer interface

IntroductionThis study proposes a hybrid brain-computer interface (BCI) system that simultaneously evokes steady-state visual evoked potentials (SSVEP) and event-related potentials (P300). The goal of this study was to improve the performance of the current hybrid SSVEP + P300 BCI systems by incorporating inverted faces into visual stimuli. MethodsIn this study, upright and inverted faces were added to visual stimulus to elicit stronger cortical responses in a hybrid SSVEP + P300 BCI. We also considered triggering the P300 signals with facial stimuli and the SSVEP signals with non-facial stimuli. We have tested four paradigms: the upright face paradigm (UF), the inverted face paradigm (IF), the upright face and flicker paradigm (UFF), and the inverted face and flicker paradigm (IFF). Results and ConclusionsThe results showed that the IFF paradigm evoked more robust cortical responses, which led to enhanced system accuracy and ITR. The IFF paradigm had an average accuracy of 96.6% and a system communication rate of 26.45 bits per second. The UFF paradigm is the best candidate for BCI applications among other paradigms because it provides maximum comfort while maintaining a reasonable ITR.

The use of happy faces as visual stimuli improves the performance of the hybrid SSVEP+P300 brain computer interface

BackgroundThis study illustrates a hybrid brain-computer interface (BCI) in which steady-state visual evoked potentials (SSVEP) and event-related potentials (P300) are evoked simultaneously. The goal of this study was to improve the performance of the current hybrid SSVEP+P300 BCI systems by incorporating a happy face into visual stimuli. New methodIn this study, happy and sad faces were added to a visual stimulus to induce stronger cortical signals in a hybrid SSVEP+P300 BCI. Additionally, we developed a paradigm in which SSVEP responses were triggered by non-face stimuli, whereas P300 responses were triggered by face stimuli. We tested four paradigms: happy face paradigm (HF), sad face paradigm (SF), happy face and flicker paradigm (HFF), and sad face and flicker paradigm (SFF). Results and conclusionsThe results demonstrated that the HFF paradigm elicited more robust cortical responses, which resulted in enhanced system accuracy and information transfer rate (ITR). The HFF paradigm has a system communication rate of 25.9 bits per second and an average accuracy of 96.1%. Compared with other paradigms, the HFF paradigm is the best choice for BCI applications because it has the highest ITR and maximum level of comfort.

The time course of stimulus-specific perceptual learning.

Practice on perceptual tasks can lead to long-lasting, stimulus-specific improvements. Rapid stimulus-specific learning, assessed 24hours after practice, has been found with just 105 practice trials in a face identification task. However, a much longer time course for stimulus-specific learning has been found in other tasks. Here, we examined 1) whether rapid stimulus-specific learning occurs for unfamiliar, non-face stimuli in a texture identification task; 2) the effects of varying practice across a range from just 21 trials up to 840 trials; and 3) if rapid, stimulus-specific learning persists over a 1-week, as well as a 1-day, interval. Observers performed a texture identification task in two sessions separated by one day (Experiment 1) or 1 week (Experiment 2). Observers received varying amounts of practice (21, 63, 105, or 840 training trials) in session 1 and completed 840 trials in session 2. In session 2, one-half of the observers in each group performed the task with the same textures as in session 1, and one-half switched to novel textures (same vs.novel conditions). In both experiments we found that stimulus-specific learning - defined as the difference in response accuracy in the same and novel conditions - increased as a linear function of the log number of session 1 training trials and was statistically significant after approximately 100 training trials. The effects of stimulus novelty did not differ across experiments. These results support the idea that stimulus-specific learning in our task arises gradually and continuously through practice, perhaps concurrently with general learning.

A hierarchy of visual processing deficits in body dysmorphic disorder: a conceptual review and empirical investigation

ABSTRACT Objective Abnormal visual processing has been proposed as a mechanism underlying excessive focus on minor appearance flaws in body dysmorphic disorder (BDD). Existing BDD research has not differentiated the various stages of face processing (featural, first-order configural, holistic and second-order configural) that are required for higher-order processes such as emotion recognition. This study investigated a hierarchical visual processing model to examine the nature of abnormalities in face processing in BDD. Method Thirty BDD participants and 27 healthy controls completed the Navon task, a featural and configural face processing task and a facial emotion labelling task. Results BDD participants performed similarly to controls when processing global and local non-face stimuli on the Navon task, when detecting subtle changes in the features and spacing of a target face, and when labelling emotional faces. However, BDD participants displayed poorer performance when viewing inverted faces, indicating difficulties in configural processing. Conclusions The findings only partially support prior work. However, synthesis of results with previous findings indicates that heterogenous task methodologies may contribute to inconsistent findings. Recommendations are provided regarding the task parameters that appear most sensitive to abnormalities in BDD.

Infants' individuation of human faces across race and identity.

Young infants' face perception capabilities quickly tune to the features of their primary caregiver. The current study examines whether infants distinguish faces in a more conceptual manner using a manual-search, violation of expectation task that has previously been used to test kind-based individuation. We tested how well infants between 11 and 27months of age individuated faces that varied by superordinate category (human vs. non-human in Experiment 1) subordinate category (individual identity in Experiment 2) or by race (White vs. Black, Experiments 1 & 2). We assessed individuation by quantifying the difference in infants' duration of reaching within an empty box between trials when the box was unexpectedly empty and expectedly empty. We found evidence of individuation across all ages and conditions, but with within-infant variation. On average, infants individuated face from non-face stimuli (Experiment 1), individual face identities (Experiment 2), and White versus Black faces (Experiments 1 & 2). These findings suggest that 1- to 2-year-old infants use distinct human face features to represent individuals across time and space. We discuss this evidence for race-based individuation and related complexities of face identity in terms of implications for conceptual development for faces in the first years of life.

Your place or mine? The neural dynamics of personally familiar scene recognition suggests category independent familiarity encoding.

Recognizing a stimulus as familiar is an important capacity in our everyday life. Recent investigation of visual processes has led to important insights into the nature of the neural representations of familiarity for human faces. Still, little is known about how familiarity affects the neural dynamics of non-face stimulus processing. Here we report the results of an EEG study, examining the representational dynamics of personally familiar scenes. Participants viewed highly variable images of their own apartments and unfamiliar ones, as well as personally familiar and unfamiliar faces. Multivariate pattern analyses were used to examine the time course of differential processing of familiar and unfamiliar stimuli. Time-resolved classification revealed that familiarity is decodable from the EEG data similarly for scenes and faces. The temporal dynamics showed delayed onsets and peaks for scenes as compared to faces. Familiarity information, starting at 200ms, generalized across stimulus categories and led to a robust familiarity effect. In addition, familiarity enhanced category representations in early (250-300ms) and later (>400ms) processing stages. Our results extend previous face familiarity results to another stimulus category and suggest that familiarity as a construct can be understood as a general, stimulus-independent processing step during recognition.

Relationship between autonomic arousal and attention orienting in children and adolescents with ADHD, autism and co-occurring ADHD and autism

IntroductionAttention-Deficit/Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD) may be characterized by different profiles of visual attention orienting. However, there are also many inconsistent findings emerging from the literature, probably due to the fact that the potential effect of autonomic arousal (which has been proposed to be dysregulated in these conditions) on oculomotor performance has not been investigated before. Moreover, it is not known how visual attention orienting is affected by the co-occurrence of ADHD and autism in people with a double diagnosis. Methods99 children/adolescents with or without ADHD and/or autism (age 10.79 ± 2.05 years, 65% boys) completed an adapted version of the gap-overlap task (with baseline and overlap trials only). The social salience and modality of stimuli were manipulated between trials. Eye movements and pupil size were recorded. We compared saccadic reaction times (SRTs) between diagnostic groups and investigated if a trial-by-trial association existed between pre-saccadic pupil size and SRTs. ResultsFaster orienting (shorter SRT) was found for baseline compared to overlap trials, faces compared to non-face stimuli and–more evidently in children without ADHD and/or autism–for multi-modal compared to uni-modal stimuli. We also found a linear negative association between pre-saccadic pupil size and SRTs, in autistic participants (without ADHD), and a quadratic association in children with ADHD (without autism), for which SRTs were slower when intra-individual pre-saccadic pupil size was smallest or largest. ConclusionOur findings are in line with previous literature and indicate a possible effect of dysregulated autonomic arousal on oculomotor mechanisms in autism and ADHD, which should be further investigated in future research studies with larger samples, to reliably investigate possible differences between children with single and dual diagnoses.

Holistic processing is modulated by the probability that parts contain task-congruent information.

Holistic processing of face and non-face stimuli has been framed as a perceptual strategy, with classic hallmarks of holistic processing, such as the composite effect, reflecting a failure of selective attention, which is a consequence of this strategy. Further, evidence that holistic processing is impacted by training different patterns of attentional prioritization suggest that it may be a result of learned attention to the whole, which renders it difficult to attend to only part of a stimulus. If so, holistic processing should be modulated by the same factors that shape attentional selection, such as the probability that distracting or task-relevant information will be present. In contrast, other accounts suggest that it is the match to an internal face template that triggers specialized holistic processing mechanisms. Here we probed these accounts by manipulating the probability, across different testing sessions, that the task-irrelevant face part in the composite face task will contain task-congruent or -incongruent information. Attentional accounts of holistic processing predict that when the probability that the task-irrelevant part contains congruent information is low (25%), holistic processing should be attenuated compared to when this probability is high (75%). In contrast, template-based accounts of holistic face processing predict that it will be unaffected by manipulation given the integrity of the faces remains intact. Experiment 1 found evidence consistent with attentional accounts of holistic face processing and Experiment 2 extends these findings to holistic processing of non-face stimuli. These findings are broadly consistent with learned attention accounts of holistic processing.

Testing EEG functional connectivity between sensorimotor and face processing visual regions in individuals with congenital facial palsy.

Moebius syndrome (MBS) is characterized by the congenital absence or underdevelopment of cranial nerves VII and VI, leading to facial palsy and impaired lateral eye movements. As a result, MBS individuals cannot produce facial expressions and did not develop motor programs for facial expressions. In the latest model of sensorimotor simulation, an iterative communication between somatosensory, motor/premotor cortices, and visual regions has been proposed, which should allow more efficient discriminations among subtle facial expressions. Accordingly, individuals with congenital facial motor disability, specifically with MBS, should exhibit atypical communication within this network. Here, we aimed to test this facet of the sensorimotor simulation models. We estimated the functional connectivity between the visual cortices for face processing and the sensorimotor cortices in healthy and MBS individuals. To this aim, we studied the strength of beta band functional connectivity between these two systems using high-density EEG, combined with a change detection task with facial expressions (and a control condition involving non-face stimuli). The results supported our hypothesis such that when discriminating subtle facial expressions, participants affected by congenital facial palsy (compared to healthy controls) showed reduced connectivity strength between sensorimotor regions and visual regions for face processing. This effect was absent for the condition with non-face stimuli. These findings support sensorimotor simulation models and the communication between sensorimotor and visual areas during subtle facial expression processing.

Assessing the perception of face pareidolia in children (Homo sapiens), rhesus monkeys (Macaca mulatta), and capuchin monkeys (Sapajus apella).

Face pareidolia is the misperception of a face in an inanimate object and is a common feature of the face detection system in humans. Whereas there are many similarities in how humans and nonhuman animals such as monkeys perceive and respond to faces, it is still unclear whether other species also perceive certain nonface stimuli as faces. We presented a novel computerized task to capuchin monkeys (Sapajus apella), rhesus monkeys (Macaca mulatta), and preschool-aged children (Homo sapiens). This task trained subjects to choose faces over nonface images, and then presented pareidolia images with nonface images. All species selected faces most often on trials that included face images. However, only children selected pareidolia images at levels above chance. These results indicate that while children report perceiving face pareidolia, monkeys do not. These species differences could be due to human-unique experiences that result in an increased aptitude for anthropomorphizing objects with face-like patterns. It could also be due to monkeys showing a greater reliance on stimulus features rather than global, holistically organized cues that faces provide. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Effects of aging on face processing: An ERP study of the own-age bias with neutral and emotional faces

Older adults systematically show an enhanced N170 amplitude during the visualization of facial expressions of emotion. The present study aimed to replicate this finding, further investigating if this effect is specific to facial stimuli, present in other neural correlates of face processing, and modulated by own-age faces. To this purpose, younger (n=25; Mage=28.36), middle-aged (n=23; Mage=48.74), and older adults (n=25; Mage=67.36) performed two face/emotion identification tasks during an EEG recording. The results showed that groups did not differ regarding P100 amplitude, but older adults had increased N170 amplitude for both facial and non-facial stimuli. The event-related potentials analysed were not modulated by an own-age bias, but older faces elicited larger N170 in the Emotion Identification Task for all groups. This increased amplitude may reflect a higher ambiguity of older faces due to age-related changes in their physical features, which may elicit higher neural resources to decode. Regarding P250, older faces elicited decreased amplitudes than younger faces, which may reflect a reduced processing of the emotional content of older faces. This interpretation is consistent with the lower accuracy obtained for this category of stimuli across groups. These results have important social implications and suggest that aging may hamper the neural processing of facial expressions of emotion, especially for own-age peers.

An improved model for the use of facial stimulation in hybrid SSVEP+P300 brain-computer interfaces

Purpose: This research proposes a hybrid BCI that integrates Steady State Visual Evoked Potentials (SSVEP) and Event Related Potentials (P300) simultaneously. We included human facial structure into a visual stimulus to elicit stronger cortical responses in a hybrid SSVEP+P300 BCI. We also discussed the possibilities of triggering one potential with facial stimuli and another with non-facial stimuli. Methods: To elicit SSVEP and P300 responses, non-face and neutral-face stimulus paradigms are presented. We also tested the neutral-face and flicker paradigm, in which non-face stimuli would elicit SSVEP and neutral-face stimuli would elicit P300. Results: The results showed that the latter paradigm evoked more robust cortical potentials, leading to enhanced system accuracy and ITR. The neutral-face and flicker paradigm has an average accuracy of 91.62%, with an average system communication rate of 22.04 bits per second. Conclusions: The author talked about visual stimulus characteristics that might change the way that multiple brain potentials are activated simultaneously and how that affects the individual potentials.

Maturational trajectory of fusiform gyrus neural activity when viewing faces: From 4 months to 4 years old.

Infant and young child electrophysiology studies have provided information regarding the maturation of face-encoding neural processes. A limitation of previous research is that very few studies have examined face-encoding processes in children 12–48 months of age, a developmental period characterized by rapid changes in the ability to encode facial information. The present study sought to fill this gap in the literature via a longitudinal study examining the maturation of a primary node in the face-encoding network—the left and right fusiform gyrus (FFG). Whole-brain magnetoencephalography (MEG) data were obtained from 25 infants with typical development at 4–12 months, and with follow-up MEG exams every ∼12 months until 3–4 years old. Children were presented with color images of Face stimuli and visual noise images (matched on spatial frequency, color distribution, and outer contour) that served as Non-Face stimuli. Using distributed source modeling, left and right face-sensitive FFG evoked waveforms were obtained from each child at each visit, with face-sensitive activity identified via examining the difference between the Non-Face and Face FFG timecourses. Before 24 months of age (Visits 1 and 2) the face-sensitive FFG M290 response was the dominant response, observed in the left and right FFG ∼250–450 ms post-stimulus. By 3–4 years old (Visit 4), the left and right face-sensitive FFG response occurred at a latency consistent with a face-sensitive M170 response ∼100–250 ms post-stimulus. Face-sensitive left and right FFG peak latencies decreased as a function of age (with age explaining greater than 70% of the variance in face-sensitive FFG latency), and with an adult-like FFG latency observed at 3–4 years old. Study findings thus showed face-sensitive FFG maturational changes across the first 4 years of life. Whereas a face-sensitive M290 response was observed under 2 years of age, by 3–4 years old, an adult-like face-sensitive M170 response was observed bilaterally. Future studies evaluating the maturation of face-sensitive FFG activity in infants at risk for neurodevelopmental disorders are of interest, with the present findings suggesting age-specific face-sensitive neural markers of a priori interest.

Face specific inversion effects provide evidence for two subtypes of developmental prosopagnosia

Many studies have attempted to identify the perceptual underpinnings of developmental prosopagnosia (DP). The majority have focused on whether holistic and configural processing mechanisms are impaired in DP. However, previous work suggests that there is substantial heterogeneity in holistic and configural processing within the DP population; further, there is disagreement as to whether any deficits are face-specific or reflect a broader perceptual deficit. This study used a data-driven approach to examine whether there are systematic patterns of variability in DP that reflect different underpinning perceptual deficits. A group of individuals with DP (N = 37) completed a cognitive battery measuring holistic/configural and featural processing in faces and non-face objects. A two-stage cluster analysis on data from the Cambridge Face Perception Test identified two subgroups of DPs. Across several tasks, the first subgroup (N = 21) showed typical patterns of holistic/configural processing (measured via inversion effects); the second (N = 16) was characterised by reduced or abolished inversion effects compared to age-matched control participants (N = 91). The subgroups did not differ on tasks measuring upright face matching, object matching, non-face holistic processing, or composite effects. These findings indicate two separable pathways to face recognition impairment, one characterised by impaired configural processing and the other potentially by impaired featural processing. Comparisons to control participants provide some preliminary evidence that the deficit in featural processing may extend to some non-face stimuli. Our results demonstrate the utility of examining both the variability between and consistency across individuals with DP as a means of illuminating our understanding of face recognition in typical and atypical populations.

A Multinomial Processing Tree Model of the 2-back Working Memory Task.

The -back task is a widely used behavioral task for measuring working memory and the ability to inhibit interfering information. We develop a novel model of the commonly used 2-back task using the cognitive psychometric framework provided by Multinomial Processing Trees. Our model involves three parameters: a memory parameter, corresponding to how well an individual encodes and updates sequence information about presented stimuli; a decision parameter corresponding to how well participants execute choices based on information stored in memory; and a base-rate parameter corresponding to bias for responding "yes" or "no". We test the parameter recovery properties of the model using existing 2-back experimental designs, and demonstrate the application of the model to two previous data sets: one from social psychology involving faces corresponding to different races (Stelter and Degner, British Journal of Psychology 109:777-798, 2018), and one from cognitive neuroscience involving more than 1000 participants from the Human Connectome Project (Van Essen et al., Neuroimage 80:62-79, 2013). We demonstrate that the model can be used to infer interpretable individual-level parameters. We develop a hierarchical extension of the model to test differences between stimulus conditions, comparing faces of different races, and comparing face to non-face stimuli. We also develop a multivariate regression extension to examine the relationship between the model parameters and individual performance on standardized cognitive measures including the List Sorting and Flanker tasks. We conclude by discussing how our model can be used to dissociate underlying cognitive processes such as encoding failures, inhibition failures, and binding failures.

Seeing faces where there are none: Pareidolia correlates with age but not autism traits

Previous research has found that individuals with autism spectrum disorder experience difficulties when visually processing face stimuli compared to developmentally typical individuals. Whether, in the typically-developing population, face detection depends on autism-like traits (ALTs) is less clear. In this report, we aimed to develop an experimental design that is more sensitive to any individual differences in face detection than previous reports. We employed pareidolia, that is, cases where non-face stimuli are perceived to be faces, assuming this is more difficult than detection of ‘real’ faces, decreasing changes of ceiling performance. We also show multiple faces per trial, allowing for a more graded assessment of face detection ability. Participants were 263 individuals aged between 18 and 82 years of age. Pareidolia was investigated in two online experiments, with different types of stimuli: objects that could be perceived as faces (i.e., embedded faces task) and Mooney faces (Mooney face task). In the latter condition, we also investigated the face inversion effect. We found that neither detection ability or the inversion effect depended on ALTs. We did find a dependence of age for both measures, and a complex dependence on gender for Mooney faces. Our data suggest that face detection (and specifically pareidolia) does not depend on ALTs, but does depend on the age of the observer. The dependence on age appears to be different between the two experiments, suggesting that the underlying mechanisms necessary for face detection in our two experiments mature and decline at different rates.