Multifractal structure of microscopic eye–head coordination

Abstract Fixational eye movements contribute to visual processing. The information encoded in them is crucial for signals coming from fovea since it connects visual information with brain activity. We recorded microsaccades and tiny head movements at high resolution, with a sampling rate of 300 Hz. Microsaccades are likely influenced by heads’s motion. Multifractal analysis shows that both movements are multiplicative processes of different origins, thereby reflecting the presence of different strategies. Microsaccades draw steps from a broad distribution of probability values, which likely indicates the way that the eyes use to maximize information, and satisfies a stretched exponential distribution. On the other hand, tiny head movements are described well by a lognormal distribution. Both movements, eye and head, are initially correlated and de-coherence of the two takes place for times greater than 29.2 seconds.

[1]  Wei‐Xing Zhou,et al.  Direct determination approach for the multifractal detrending moving average analysis. , 2017, Physical review. E.

[2]  M. Rolfs Microsaccades: Small steps on a long way , 2009, Vision Research.

[3]  Peter Herman,et al.  Real-time fractal signal processing in the time domain , 2013 .

[4]  Daniel Mirman,et al.  Interactions dominate the dynamics of visual cognition , 2010, Cognition.

[5]  Damian G. Stephen,et al.  Fractal fluctuations in gaze speed visual search , 2011, Attention, perception & psychophysics.

[6]  Ralf Engbert,et al.  Microsaccades uncover the orientation of covert attention , 2003, Vision Research.

[7]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[8]  Wei‐Xing Zhou Multifractal detrended cross-correlation analysis for two nonstationary signals. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Martina Poletti,et al.  Microscopic Eye Movements Compensate for Nonhomogeneous Vision within the Fovea , 2013, Current Biology.

[10]  H. Stanley,et al.  Quantifying cross-correlations using local and global detrending approaches , 2009 .

[11]  Boris Podobnik,et al.  Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  M. Rucci,et al.  Microsaccades Precisely Relocate Gaze in a High Visual Acuity Task , 2010, Nature Neuroscience.

[13]  J. G. Contreras,et al.  Performance of multifractal detrended fluctuation analysis on short time series. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Ziad M. Hafed,et al.  Neuronal Response Gain Enhancement prior to Microsaccades , 2015, Current Biology.

[15]  Xoana G. Troncoso,et al.  Microsaccades Counteract Visual Fading during Fixation , 2005, Neuron.

[16]  J. Doyne Farmer,et al.  A Rosetta stone for connectionism , 1990 .

[17]  Luc Van Gool,et al.  Speeded-Up Robust Features (SURF) , 2008, Comput. Vis. Image Underst..

[18]  Nikos K. Logothetis,et al.  Microsaccades differentially modulate neural activity in the striate and extrastriate visual cortex , 1998, Experimental Brain Research.

[19]  Daniel Mirman,et al.  Gaze fluctuations are not additively decomposable: Reply to Bogartz and Staub , 2013, Cognition.

[20]  M. Ausloos Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[22]  S. Martinez-Conde,et al.  The impact of microsaccades on vision: towards a unified theory of saccadic function , 2013, Nature Reviews Neuroscience.

[23]  Frigyes Samuel Racz,et al.  Multifractal dynamics of resting-state functional connectivity in the prefrontal cortex , 2018, Physiological measurement.

[24]  Mark W. Greenlee,et al.  Event-related Functional Mri of Cortical Activity Evoked by Microsaccades, Small Visually-guided Saccades, and Eyeblinks in Human Visual Cortex , 2022 .

[25]  G. Barnes,et al.  Extraction of visual motion information for the control of eye and head movement during head-free pursuit , 2011, Experimental Brain Research.

[26]  Ziad M. Hafed Mechanisms for generating and compensating for the smallest possible saccades , 2011, The European journal of neuroscience.

[27]  Peter Mukli,et al.  Multifractal formalism by enforcing the universal behavior of scaling functions , 2015 .

[28]  Xoana G. Troncoso,et al.  Microsaccadic Efficacy and Contribution to Foveal and Peripheral Vision , 2012, The Journal of Neuroscience.

[29]  Zhi-Qiang Jiang,et al.  Multifractal detrending moving-average cross-correlation analysis. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Ladislav Kristoufek,et al.  Multifractal height cross-correlation analysis: A new method for analyzing long-range cross-correlations , 2011, 1201.3473.

[31]  P. Varotsos,et al.  Long-range correlations in the electric signals that precede rupture: further investigations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  J. Victor,et al.  Temporal Encoding of Spatial Information during Active Visual Fixation , 2012, Current Biology.

[33]  S. Martinez-Conde Fixational eye movements in normal and pathological vision. , 2006, Progress in brain research.

[34]  Ralf Engbert,et al.  Modeling the control of fixational eye movements with neurophysiological delays. , 2007, Physical review letters.

[35]  Eileen Kowler,et al.  The eye on the needle , 2010, Nature Neuroscience.

[36]  Reinhold Kliegl,et al.  Microsaccades Are Coupled to Heartbeat , 2016, The Journal of Neuroscience.

[37]  I. Nelken,et al.  Transient Induced Gamma-Band Response in EEG as a Manifestation of Miniature Saccades , 2008, Neuron.

[38]  Ziad M. Hafed,et al.  A Neural Mechanism for Microsaccade Generation in the Primate Superior Colliculus , 2009, Science.

[39]  L. P. O'Keefe,et al.  The influence of fixational eye movements on the response of neurons in area MT of the macaque , 1998, Visual Neuroscience.

[40]  Ladislav Kristoufek,et al.  On Hurst exponent estimation under heavy-tailed distributions , 2010, 1201.4786.

[41]  Martina Poletti,et al.  Head-Eye Coordination at a Microscopic Scale , 2015, Current Biology.

[42]  Bruce J. West,et al.  Colloquium: Fractional calculus view of complexity: A tutorial , 2014 .