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Langlois ET, Bennequin D, de Marco G. Role of the Cerebellum in the Construction of Functional and Geometrical Spaces. CEREBELLUM (LONDON, ENGLAND) 2024:10.1007/s12311-024-01693-y. [PMID: 38625534 DOI: 10.1007/s12311-024-01693-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/10/2024] [Indexed: 04/17/2024]
Abstract
The perceptual and motor systems appear to have a set of movement primitives that exhibit certain geometric and kinematic invariances. Complex patterns and mental representations can be produced by (re)combining some simple motor elements in various ways using basic operations, transformations, and respecting a set of laws referred to as kinematic laws of motion. For example, point-to-point hand movements are characterized by straight hand paths with single-peaked-bell-shaped velocity profiles, whereas hand speed profiles for curved trajectories are often irregular and more variable, with speed valleys and inflections extrema occurring at the peak curvature. Curvature and speed are generically related by the 2/3 power law. Mathematically, such laws can be deduced from a combination of Euclidean, affine, and equi-affine geometries, whose neural correlates have been partially detected in various brain areas including the cerebellum and the basal ganglia. The cerebellum has been found to play an important role in the control of coordination, balance, posture, and timing over the past years. It is also assumed that the cerebellum computes forward internal models in relationship with specific cortical and subcortical brain regions but its motor relationship with the perceptual space is unclear. A renewed interest in the geometrical and spatial role of the cerebellum may enable a better understanding of its specific contribution to the action-perception loop and behavior's adaptation. In this sense, we complete this overview with an innovative theoretical framework that describes a possible implementation and selection by the cerebellum of geometries adhering to different mathematical laws.
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Affiliation(s)
- Eya Torkhani Langlois
- LINP2, UPL, Université Paris Nanterre, 200 avenue de la République, Nanterre, 92000, France
| | - Daniel Bennequin
- Equipe Géométrie et Dynamique, Paris-Cité, UFR de Mathématiques, Bâtiment Sophie Germain, 8 place Aurélie Nemours, Paris, 75013, France
| | - Giovanni de Marco
- LINP2, UPL, Université Paris Nanterre, 200 avenue de la République, Nanterre, 92000, France.
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2
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Torricelli F, Tomassini A, Pezzulo G, Pozzo T, Fadiga L, D'Ausilio A. Motor invariants in action execution and perception. Phys Life Rev 2023; 44:13-47. [PMID: 36462345 DOI: 10.1016/j.plrev.2022.11.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2022] [Accepted: 11/21/2022] [Indexed: 11/27/2022]
Abstract
The nervous system is sensitive to statistical regularities of the external world and forms internal models of these regularities to predict environmental dynamics. Given the inherently social nature of human behavior, being capable of building reliable predictive models of others' actions may be essential for successful interaction. While social prediction might seem to be a daunting task, the study of human motor control has accumulated ample evidence that our movements follow a series of kinematic invariants, which can be used by observers to reduce their uncertainty during social exchanges. Here, we provide an overview of the most salient regularities that shape biological motion, examine the role of these invariants in recognizing others' actions, and speculate that anchoring socially-relevant perceptual decisions to such kinematic invariants provides a key computational advantage for inferring conspecifics' goals and intentions.
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Affiliation(s)
- Francesco Torricelli
- Department of Neuroscience and Rehabilitation, University of Ferrara, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy; Center for Translational Neurophysiology of Speech and Communication, Italian Institute of Technology, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy
| | - Alice Tomassini
- Center for Translational Neurophysiology of Speech and Communication, Italian Institute of Technology, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy
| | - Giovanni Pezzulo
- Institute of Cognitive Sciences and Technologies, National Research Council, Via San Martino della Battaglia 44, 00185 Rome, Italy
| | - Thierry Pozzo
- Center for Translational Neurophysiology of Speech and Communication, Italian Institute of Technology, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy; INSERM UMR1093-CAPS, UFR des Sciences du Sport, Université Bourgogne Franche-Comté, F-21000, Dijon, France
| | - Luciano Fadiga
- Department of Neuroscience and Rehabilitation, University of Ferrara, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy; Center for Translational Neurophysiology of Speech and Communication, Italian Institute of Technology, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy
| | - Alessandro D'Ausilio
- Department of Neuroscience and Rehabilitation, University of Ferrara, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy; Center for Translational Neurophysiology of Speech and Communication, Italian Institute of Technology, Via Fossato di Mortara, 17-19, 44121 Ferrara, Italy.
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3
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Steel KA, Robbins RA, Nijhuis P. Trainability of novel person recognition based on brief exposure to form and motion cues. Front Psychol 2022; 13:933723. [PMID: 36248463 PMCID: PMC9554208 DOI: 10.3389/fpsyg.2022.933723] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2022] [Accepted: 08/29/2022] [Indexed: 11/17/2022] Open
Abstract
Fast and accurate recognition of teammates is crucial in contexts as varied as fast-moving sports, the military, and law enforcement engagements; misrecognition can result in lost scoring opportunities in sport or friendly fire in combat contexts. Initial studies on teammate recognition in sport suggests that athletes are adept at this perceptual ability but still susceptible to errors. The purpose of the current proof-of-concept study was to explore the trainability of teammate recognition from very brief exposure to vision of the whole-body form and motion of a previously unknown individual. Participants were divided into three groups: a 4-week training group who were also the actors for the test and training footage, a 2-week training group, and a no-training group. Findings revealed significant differences between the training groups and their improvement from the pre-to post-test on Response Accuracy and Movement Time. The current study found the best performance in the 4-week Training group. The biggest improvement was found in the 2-week training group, whilst no significant improvement was made in the Control group. These results suggest that training was effective, but also indicate that having initially performed the movements as actors may have led to improvements in baseline testing and ultimately the best results, thus physical performance of skills combined with video-based training may reduce the amount of time needed to improve teammate identification.
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Affiliation(s)
- Kylie Ann Steel
- School of Health Science, Western Sydney University, Penrith, NSW, Australia
- The MARCS Institute for Brain, Behaviour and Development, Western Sydney University, Penrith, NSW, Australia
- *Correspondence: Kylie Ann Steel, ;
| | - Rachel A. Robbins
- Research School of Psychology, College of Health and Medicine, Australian National University, Canberra, ACT, Australia
| | - Patti Nijhuis
- The MARCS Institute for Brain, Behaviour and Development, Western Sydney University, Penrith, NSW, Australia
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de’Sperati C, Granato M, Moretti M. If You Are Old, Videos Look Slow. The Paradoxical Effect of Age-Related Motor Decline on the Kinematic Interpretation of Visual Scenes. Front Hum Neurosci 2022; 15:783090. [PMID: 35069153 PMCID: PMC8766849 DOI: 10.3389/fnhum.2021.783090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2021] [Accepted: 12/02/2021] [Indexed: 11/13/2022] Open
Abstract
Perception and action are tightly coupled. However, there is still little recognition of how individual motor constraints impact perception in everyday life. Here we asked whether and how the motor slowing that accompanies aging influences the sense of visual speed. Ninety-four participants aged between 18 and 90 judged the natural speed of video clips reproducing real human or physical motion (SoS, Sense-of-Speed adjustment task). They also performed a finger tapping task and a visual search task, which estimated their motor speed and visuospatial attention speed, respectively. Remarkably, aged people judged videos to be too slow (speed underestimation), as compared to younger people: the Point of Subjective Equality (PSE), which estimated the speed bias in the SoS task, was +4% in young adults (<40), +12% in old adults (40–70) and +16% in elders. On average, PSE increased with age at a rate of 0.2% per year, with perceptual precision, adjustment rate, and completion time progressively worsening. Crucially, low motor speed, but not low attentional speed, turned out to be the key predictor of video speed underestimation. These findings suggest the existence of a counterintuitive compensatory coupling between action and perception in judging dynamic scenes, an effect that becomes particularly germane during aging.
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Affiliation(s)
- Claudio de’Sperati
- Laboratory of Action, Perception and Cognition, School of Psychology, Vita-Salute San Raffaele University, Milan, Italy
- *Correspondence: Claudio de’Sperati
| | - Marco Granato
- Laboratory of Action, Perception and Cognition, School of Psychology, Vita-Salute San Raffaele University, Milan, Italy
- Department of Computer Sciences, University of Milan, Milan, Italy
| | - Michela Moretti
- Laboratory of Action, Perception and Cognition, School of Psychology, Vita-Salute San Raffaele University, Milan, Italy
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5
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Rossi F, Montanaro E, de'Sperati C. Speed Biases With Real-Life Video Clips. Front Integr Neurosci 2018; 12:11. [PMID: 29615875 PMCID: PMC5864902 DOI: 10.3389/fnint.2018.00011] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2017] [Accepted: 02/28/2018] [Indexed: 11/13/2022] Open
Abstract
We live almost literally immersed in an artificial visual world, especially motion pictures. In this exploratory study, we asked whether the best speed for reproducing a video is its original, shooting speed. By using adjustment and double staircase methods, we examined speed biases in viewing real-life video clips in three experiments, and assessed their robustness by manipulating visual and auditory factors. With the tested stimuli (short clips of human motion, mixed human-physical motion, physical motion and ego-motion), speed underestimation was the rule rather than the exception, although it depended largely on clip content, ranging on average from 2% (ego-motion) to 32% (physical motion). Manipulating display size or adding arbitrary soundtracks did not modify these speed biases. Estimated speed was not correlated with estimated duration of these same video clips. These results indicate that the sense of speed for real-life video clips can be systematically biased, independently of the impression of elapsed time. Measuring subjective visual tempo may integrate traditional methods that assess time perception: speed biases may be exploited to develop a simple, objective test of reality flow, to be used for example in clinical and developmental contexts. From the perspective of video media, measuring speed biases may help to optimize video reproduction speed and validate "natural" video compression techniques based on sub-threshold temporal squeezing.
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Affiliation(s)
- Federica Rossi
- Laboratory of Action, Perception and Cognition, Faculty of Psychology, Vita-Salute San Raffaele University, Milan, Italy
| | - Elisa Montanaro
- Department of Neuroscience Rita Levi Montalcini, University of Turin, Turin, Italy
| | - Claudio de'Sperati
- Laboratory of Action, Perception and Cognition, Faculty of Psychology, Vita-Salute San Raffaele University, Milan, Italy.,Experimental Psychology Unit, Division of Neuroscience, San Raffaele Scientific Institute, Milan, Italy
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Covert enaction at work: Recording the continuous movements of visuospatial attention to visible or imagined targets by means of Steady-State Visual Evoked Potentials (SSVEPs). Cortex 2015; 74:31-52. [PMID: 26615517 DOI: 10.1016/j.cortex.2015.10.008] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2014] [Revised: 06/19/2015] [Accepted: 10/19/2015] [Indexed: 01/23/2023]
Abstract
Whereas overt visuospatial attention is customarily measured with eye tracking, covert attention is assessed by various methods. Here we exploited Steady-State Visual Evoked Potentials (SSVEPs) - the oscillatory responses of the visual cortex to incoming flickering stimuli - to record the movements of covert visuospatial attention in a way operatively similar to eye tracking (attention tracking), which allowed us to compare motion observation and motion extrapolation with and without eye movements. Observers fixated a central dot and covertly tracked a target oscillating horizontally and sinusoidally. In the background, the left and the right halves of the screen flickered at two different frequencies, generating two SSVEPs in occipital regions whose size varied reciprocally as observers attended to the moving target. The two signals were combined into a single quantity that was modulated at the target frequency in a quasi-sinusoidal way, often clearly visible in single trials. The modulation continued almost unchanged when the target was switched off and observers mentally extrapolated its motion in imagery, and also when observers pointed their finger at the moving target during covert tracking, or imagined doing so. The amplitude of modulation during covert tracking was ∼25-30% of that measured when observers followed the target with their eyes. We used 4 electrodes in parieto-occipital areas, but similar results were achieved with a single electrode in Oz. In a second experiment we tested ramp and step motion. During overt tracking, SSVEPs were remarkably accurate, showing both saccadic-like and smooth pursuit-like modulations of cortical responsiveness, although during covert tracking the modulation deteriorated. Covert tracking was better with sinusoidal motion than ramp motion, and better with moving targets than stationary ones. The clear modulation of cortical responsiveness recorded during both overt and covert tracking, identical for motion observation and motion extrapolation, suggests to include covert attention movements in enactive theories of mental imagery.
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Dayan E, Inzelberg R, Flash T. Altered perceptual sensitivity to kinematic invariants in Parkinson's disease. PLoS One 2012; 7:e30369. [PMID: 22363430 PMCID: PMC3281839 DOI: 10.1371/journal.pone.0030369] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2011] [Accepted: 12/19/2011] [Indexed: 11/19/2022] Open
Abstract
Ample evidence exists for coupling between action and perception in neurologically healthy individuals, yet the precise nature of the internal representations shared between these domains remains unclear. One experimentally derived view is that the invariant properties and constraints characterizing movement generation are also manifested during motion perception. One prominent motor invariant is the "two-third power law," describing the strong relation between the kinematics of motion and the geometrical features of the path followed by the hand during planar drawing movements. The two-thirds power law not only characterizes various movement generation tasks but also seems to constrain visual perception of motion. The present study aimed to assess whether motor invariants, such as the two thirds power law also constrain motion perception in patients with Parkinson's disease (PD). Patients with PD and age-matched controls were asked to observe the movement of a light spot rotating on an elliptical path and to modify its velocity until it appeared to move most uniformly. As in previous reports controls tended to choose those movements close to obeying the two-thirds power law as most uniform. Patients with PD displayed a more variable behavior, choosing on average, movements closer but not equal to a constant velocity. Our results thus demonstrate impairments in how the two-thirds power law constrains motion perception in patients with PD, where this relationship between velocity and curvature appears to be preserved but scaled down. Recent hypotheses on the role of the basal ganglia in motor timing may explain these irregularities. Alternatively, these impairments in perception of movement may reflect similar deficits in motor production.
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Affiliation(s)
- Eran Dayan
- Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel.
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8
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Pellizzer G, Zesiger P. Hypothesis regarding the transformation of the intended direction of movement during the production of graphic trajectories: a study of drawing movements in 8- to 12-year-old children. Cortex 2008; 45:356-67. [PMID: 18653177 DOI: 10.1016/j.cortex.2008.04.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2007] [Revised: 10/23/2007] [Accepted: 04/05/2008] [Indexed: 11/18/2022]
Abstract
Children from 8 to 12 years of age drew figure-eights and ellipses at a self-chosen tempo on a digitizing tablet. Global aspects (perimeter and average speed) and local aspects (relation between instantaneous speed and curvature) of performance were analyzed across age groups and types of figures. We tested the predictions of the transformation model, which is based on the hypothesis that changing the intended direction of movement is a time-consuming process that affects the evolution in time of the movement trajectory, and compared how well it fitted the data relative to the power law. We found that the relation between speed and curvature was typically better described by the transformation model than by the power law. However, the power law provided a better description when ellipses were drawn at a fast speed. The analyses of the parameters of the transformation model indicate that processing speed increased linearly with age. In addition, the results suggest that the effects of the spring-like properties of the arm were noticeable when ellipses were drawn at a fast speed. This study indicates that both biomechanical properties and central processes have an effect on the kinematics of continuous movements and particularly on the relation between speed and curvature. However, their relative importance varies with the type of figure and average movement speed. In conclusion, the results support the hypothesis that a time-consuming process of transformation of the intended direction of movement is operating during the production of continuous movements and that this process increases in speed between 8 to 12 years of age.
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Affiliation(s)
- Giuseppe Pellizzer
- Brain Sciences Center, Veterans Affairs Medical Center, Minneapolis, MN, USA.
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9
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Dayan E, Casile A, Levit-Binnun N, Giese MA, Hendler T, Flash T. Neural representations of kinematic laws of motion: evidence for action-perception coupling. Proc Natl Acad Sci U S A 2007; 104:20582-7. [PMID: 18079289 PMCID: PMC2154474 DOI: 10.1073/pnas.0710033104] [Citation(s) in RCA: 102] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2007] [Indexed: 11/18/2022] Open
Abstract
Behavioral and modeling studies have established that curved and drawing human hand movements obey the 2/3 power law, which dictates a strong coupling between movement curvature and velocity. Human motion perception seems to reflect this constraint. The functional MRI study reported here demonstrates that the brain's response to this law of motion is much stronger and more widespread than to other types of motion. Compliance with this law is reflected in the activation of a large network of brain areas subserving motor production, visual motion processing, and action observation functions. Hence, these results strongly support the notion of similar neural coding for motion perception and production. These findings suggest that cortical motion representations are optimally tuned to the kinematic and geometrical invariants characterizing biological actions.
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Affiliation(s)
- Eran Dayan
- Departments of *Computer Science and Applied Mathematics
- Neurobiology, and
- Functional Brain Imaging Unit, Wohl Institute for Advanced Imaging, Tel Aviv Sourasky Medical Center, Tel Aviv 64361, Israel
| | - Antonino Casile
- Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research, University Clinic, 72076 Tübingen, Germany
| | - Nava Levit-Binnun
- Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Martin A. Giese
- Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research, University Clinic, 72076 Tübingen, Germany
- School of Psychology, Bangor University, Gwynedd LL57 2AS, United Kingdom; and
| | - Talma Hendler
- Functional Brain Imaging Unit, Wohl Institute for Advanced Imaging, Tel Aviv Sourasky Medical Center, Tel Aviv 64361, Israel
- **Faculty of Medicine, Tel Aviv University, Tel Aviv 69978, Israel
| | - Tamar Flash
- Departments of *Computer Science and Applied Mathematics
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Levit-Binnun N, Schechtman E, Flash T. On the similarities between the perception and production of elliptical trajectories. Exp Brain Res 2006; 172:533-55. [PMID: 16501963 DOI: 10.1007/s00221-006-0355-4] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2005] [Accepted: 12/29/2005] [Indexed: 10/25/2022]
Abstract
In an earlier study, Viviani and Stucchi (J Exp Psychol Hum Percept Perform 18:603-623, 1992) have introduced a visual illusion, whereby it was shown that when subjects are asked to determine what movement of a light spot, when tracing an elliptical trajectory, appears to be most uniform, they tend to choose movements that are close to obeying the 2/3 power law (Lacquaniti et al. Acta Psychol 54:115-130, 1983) rather than constant speed movements, even though the actual changes in velocity could exceed 200%. Here we have extended the study of this illusion by directly testing the effect of the shape (eccentricity) and size (perimeter) of the elliptical trajectory, the duration of the tracing of the ellipse and the effect of fixation on the subjects' decision regarding movement uniformity. We found that the ellipse's eccentricity and tracing out speed of the elliptical trajectory significantly affect the subjects' decisions, although the effect of eccentricity seems to be stronger than that of speed. Our findings also indicated that fixation significantly affects the subject's decision for ellipses that are more eccentric. Surprisingly, the ellipse's perimeter had a much smaller effect on the subjects' decisions, although changes in the ellipse's perimeter should have the same effect on the average velocity as changes in the time it takes to trace out the ellipse. This suggested the possibility that the subjects based their decision regarding movement uniformity on other velocity variables in addition to tangential velocity. Computer simulations we have performed have led us to conclude that the subjects' perception of movement uniformity may also be based on assessing the variations in angular velocity and possibly also in affine velocity. Our behavioral and simulation studies thus suggest that the motion perception system is quite responsive to variations in the velocity along an elliptical trajectory but in a way that depends on the path's curvature. Furthermore, the movement is judged to be more uniform when there are minimal differences in angular, tangential and perhaps also in affine velocities, along the trajectory. Our results suggest the existence of similar underlying constraints that affect both the motion perception and production systems when the movements are associated with very large velocities or large changes in velocity along more curved portions of the trajectory. Our observations therefore provide further insight into the possibility that these constraints are either imposed by the underlying neuronal dynamics, the internal architecture of the cortical neural populations or the variables used in the coding of both sensory and motor information regarding movement.
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Affiliation(s)
- Nava Levit-Binnun
- Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, POB 26, Rehovot, 76100, Israel
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Actis-Grosso R, Stucchi N. Shifting the start: backward mislocation of the initial position of a motion. J Exp Psychol Hum Percept Perform 2003; 29:675-91. [PMID: 12848333 DOI: 10.1037/0096-1523.29.3.675] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Participants asked to judge the final position of a moving target typically indicate a position shifted forward. In the 6 experiments reported here, participants were asked to indicate both the starting position (SP) and the vanishing position (VP) at the onset and offset of a moving target. Results confirmed the forward displacement of the VP and showed a backward displacement of the SP. To test whether perceptual estimation was influenced by curvature of the trajectory, curvilinear motions were also used. Results showed that apparent displacements are along the geometrical tangents to the SP and VP. Relationships between the results and other findings such as the flash-lag effect the representational momentum, and the Fröhlich effect are discussed.
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12
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The relationship between curvature and velocity in two-dimensional smooth pursuit eye movements. J Neurosci 1997. [PMID: 9133411 DOI: 10.1523/jneurosci.17-10-03932.1997] [Citation(s) in RCA: 84] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Curvature and tangential velocity of voluntary hand movements are constrained by an empirical relation known as the Two-Thirds Power Law. It has been argued that the law reflects the working of central control mechanisms, but it is not known whether these mechanisms are specific to the hand or shared also by other types of movement. Three experiments tested whether the power law applies to the smooth pursuit movements of the eye, which are controlled by distinct neural motor structures and a peculiar set of muscles. The first experiment showed that smooth pursuit of elliptic targets with various curvature-velocity relationships was most accurate when targets were compatible with the Two-Thirds Power Law. Tracking errors in all other cases reflected the fact that, irrespective of target kinematics, eye movements tended to comply with the law. Using only compatible targets, the second experiment demonstrated that kinematics per se cannot account for the pattern of pursuit errors. The third experiment showed that two-dimensional performance cannot be fully predicted on the basis of the performance observed when the horizontal and vertical components of the targets used in the first condition were tracked separately. We conclude that the Two-Thirds Power Law, in its various manifestations, reflects neural mechanisms common to otherwise distinct control modules.
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