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Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform,Proc Natl Acad Sci U S A, 21 (111), 7867-7872.

Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform,Proc Natl Acad Sci U S A, 21 (111), 7867-7872.

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The mapping of number onto space is fundamental to measurement and mathematics. However, the mapping of young children, unschooled adults, and adults under attentional load shows strong compressive nonlinearities, thought to reflect intrinsic logarithmic encoding mechanisms, which are later “linearized” by education. Here we advance and test an alternative explanation: that the nonlinearity results from adaptive mechanisms incorporating the statistics of recent stimuli. This theory predicts that the response to the current trial should depend on the magnitude of the previous trial, whereas a static logarithmic nonlinearity predicts trialwise independence. We found a strong and highly significant relationship between numberline mapping of the current trial and the magnitude of the previous trial, in both adults and school children, with the current response influenced by up to 15% of the previous trial value. The dependency is sufficient to account for the shape of the numberline, without requiring logarithmic transform. We show that this dynamic strategy results in a reduction of reproduction error, and hence improvement in accuracy.

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Separate mechanisms for perception of numerosity and density,Psychol Sci, 1 (25), 265-270.

Separate mechanisms for perception of numerosity and density,Psychol Sci, 1 (25), 265-270.

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Despite the existence of much evidence for a number sense in humans, several researchers have questioned whether number is sensed directly or derived indirectly from texture density. Here, we provide clear evidence that numerosity and density judgments are subserved by distinct mechanisms with different psychophysical characteristics. We measured sensitivity for numerosity discrimination over a wide range of numerosities: For low densities (less than 0.25 dots/deg(2)), thresholds increased directly with numerosity, following Weber’s law; for higher densities, thresholds increased with the square root of texture density, a steady decrease in the Weber fraction. The existence of two different psychophysical systems is inconsistent with a model in which number is derived indirectly from noisy estimates of density and area; rather, it points to the existence of separate mechanisms for estimating density and number. These results provide strong confirmation for the existence of neural mechanisms that sense number directly, rather than indirectly from texture density.

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Vision: efficient adaptive coding,Curr Biol, 22 (24), R1096-1098.

Vision: efficient adaptive coding,Curr Biol, 22 (24), R1096-1098.

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Recent studies show that perception is driven not only by the stimuli currently impinging on our senses, but also by the immediate past history. The influence of recent perceptual history on the present reflects the action of efficient mechanisms that exploit temporal redundancies in natural scenes.

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Development of context-dependency in human space perception,Exp Brain Res,

Development of context-dependency in human space perception,Exp Brain Res,

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Perception is a complex process, where prior knowledge exerts a fundamental influence over what we see. The use of priors is at the basis of the well-known phenomenon of central tendency: Judgments of almost all quantities (such as length, duration, and number) tend to gravitate toward their mean magnitude. Although such context-dependency is universal in adult perceptual judgments, how it develops with age remains unknown. We asked children from 7 to 14 years of age and adults to reproduce lengths of stimuli drawn from different distributions and evaluated whether judgments were influenced by stimulus context. All participants reproduced the presented length differently depending on the context: The same stimulus was reproduced as shorter, when on average stimuli were short, and as longer, when on average stimuli were long. Interestingly, the relative importance given to the current sensory signal and to priors was almost constant during childhood. This strategy, which in adults is optimal in Bayesian terms, is apparently successful in holding the sensory noise at bay even during development. Hence, the influence of previous knowledge on perception is present already in young children, suggesting that context-dependency is established early in the developing brain.

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Buildup of spatial information over time and across eye-movements,Behavioural brain research.

Buildup of spatial information over time and across eye-movements,Behavioural brain research.

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To interact rapidly and effectively with our environment, our brain needs access to a neural represen-tation of the spatial layout of the external world. However, the construction of such a map poses majorchallenges, as the images on our retinae depend on where the eyes are looking, and shift each time wemove our eyes, head and body to explore the world. Research from many laboratories including ourown suggests that the visual system does compute spatial maps that are anchored to real-world coordi-nates. However, the construction of these maps takes time (up to 500 ms) and also attentional resources.We discuss research investigating how retinotopic reference frames are transformed into spatiotopicreference-frames, and how this transformation takes time to complete. These results have implicationsfor theories about visual space coordinates and particularly for the current debate about the existence ofspatiotopic representations.

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Impairment of auditory spatial localization in congenitally blind human subjects,Brain, Pt 1 (137), 288-293.

Impairment of auditory spatial localization in congenitally blind human subjects,Brain, Pt 1 (137), 288-293. 

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Several studies have demonstrated enhanced auditory processing in the blind, suggesting that they compensate their visual impairment in part with greater sensitivity of the other senses. However, several physiological studies show that early visual deprivation can impact negatively on auditory spatial localization. Here we report for the first time severely impaired auditory localization in the congenitally blind: thresholds for spatially bisecting three consecutive, spatially-distributed sound sources were seriously compromised, on average 4.2-fold typical thresholds, and half performing at random. In agreement with previous studies, these subjects showed no deficits on simpler auditory spatial tasks or with auditory temporal bisection, suggesting that the encoding of Euclidean auditory relationships is specifically compromised in the congenitally blind. It points to the importance of visual experience in the construction and calibration of auditory spatial maps, with implications for rehabilitation strategies for the congenitally blind.

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Musical training generalises across modalities and reveals efficient and adaptive mechanisms for reproducing temporal intervals,Acta Psychol (Amst), (147), 25-33.

Musical training generalises across modalities and reveals efficient and adaptive mechanisms for reproducing temporal intervals,Acta Psychol (Amst), (147), 25-33.

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Expert musicians are able to time their actions accurately and consistently during a musical performance. We investigated how musical expertise influences the ability to reproduce auditory intervals and how this generalises across different techniques and sensory modalities. We first compared various reproduction strategies and interval length, to examine the effects in general and to optimise experimental conditions for testing the effect of music, and found that the effects were robust and consistent across different paradigms. Focussing on a ‘ready-set-go’ paradigm subjects reproduced time intervals drawn from distributions varying in total length (176, 352 or 704 ms) or in the number of discrete intervals within the total length (3, 5, 11 or 21 discrete intervals). Overall, Musicians performed more veridical than Non-Musicians, and all subjects reproduced auditory-defined intervals more accurately than visually-defined intervals. However, Non-Musicians, particularly with visual stimuli, consistently exhibited a substantial and systematic regression towards the mean interval. When subjects judged intervals from distributions of longer total length they tended to regress more towards the mean, while the ability to discriminate between discrete intervals within the distribution had little influence on subject error. These results are consistent with a Bayesian model that minimizes reproduction errors by incorporating a central tendency prior weighted by the subject’s own temporal precision relative to the current distribution of intervals. Finally a strong correlation was observed between all durations of formal musical training and total reproduction errors in both modalities (accounting for 30% of the variance). Taken together these results demonstrate that formal musical training improves temporal reproduction, and that this improvement transfers from audition to vision. They further demonstrate the flexibility of sensorimotor mechanisms in adapting to different task conditions to minimise temporal estimation errors.

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The visual component to saccadic compression,J Vis, 12 (14).

The visual component to saccadic compression,J Vis, 12 (14).

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Visual objects presented around the time of saccadic eye movements are strongly mislocalized towards the saccadic target, a phenomenon known as “saccadic compression.” Here we show that perisaccadic compression is modulated by the presence of a visual saccadic target. When subjects saccaded to the center of the screen with no visible target, perisaccadic localization was more veridical than when tested with a target. Presenting a saccadic target sometime before saccade initiation was sufficient to induce mislocalization. When we systematically varied the onset of the saccade target, we found that it had to be presented around 100 ms before saccade execution to cause strong mislocalization: saccadic targets presented after this time caused progressively less mislocalization. When subjects made a saccade to screen center with a reference object placed at various positions, mislocalization was focused towards the position of the reference object. The results suggest that saccadic compression is a signature of a mechanism attempting to match objects seen before the saccade with those seen after.

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A generalized sense of number, Proc R Soc B (2014).

A generalized sense of number, Proc R Soc B (2014).

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Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique ofadaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.

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Children do not recalibrate motor-sensory temporal order after exposure to delayed sensory feedback,Dev Sci.

Children do not recalibrate motor-sensory temporal order after exposure to delayed sensory feedback,Dev Sci.

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Prolonged adaptation to delayed sensory feedback to a simple motor act (such as pressing a key) causes recalibration of sensory-motor synchronization, so instantaneous feedback appears to precede the motor act that caused it (Stetson, Cui, Montague & Eagleman, 2006). We investigated whether similar recalibration occurs in school-age children. Although plasticity may be expected to be even greater in children than in adults, we found no evidence of recalibration in children aged 8-11 years. Subjects adapted to delayed feedback for 100 trials, intermittently pressing a key that caused a tone to sound after a 200 ms delay. During the test phase, subjects responded to a visual cue by pressing a key, which triggered a tone to be played at variable intervals before or after the keypress. Subjects judged whether the tone preceded or followed the keypress, yielding psychometric functions estimating the delay when they perceived the tone to be synchronous with the action. The psychometric functions also gave an estimate of the precision of the temporal order judgment. In agreement with previous studies, adaptation caused a shift in perceived synchrony in adults, so the keypress appeared to trail behind the auditory feedback, implying sensory-motor recalibration. However, school children of 8 to 11 years showed no measureable adaptation of perceived simultaneity, even after adaptation with 500 ms lags. Importantly, precision in the simultaneity task also improved with age, and this developmental trend correlated strongly with the magnitude of recalibration. This suggests that lack of recalibration of sensory-motor simultaneity after adaptation in school-age children is related to their poor precision in temporal order judgments. To test this idea we measured recalibration in adult subjects with auditory noise added to the stimuli (which hampered temporal precision). Under these conditions, recalibration was greatly reduced, with the magnitude of recalibration strongly correlating with temporal precision.