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Different dynamics induced by a human nose vs. plain stripes. (a) Contrast filtered image of a nose on a background of black-white stripes. (b) Snapshot of phase distribution. The stripes induce plane waves, while the nose pattern induces spiral waves. (c) Frequency map. The nose ’pops out’ due to high frequency at spiral centres.
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We are investigating possible functional roles for spiral wave activity in visual cortex. Our initial findings suggest that spiral wave formation can be useful for visual salience analysis, in particular for mediating attention to human body features. Exploiting travelling wave dynamics for visual processing offers many advantages, including templa...
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... centres are characterised by high frequency, low amplitude oscillations. Figure 1 gives an example of the different dynamics in- duced by a nose and plain black and white stripes. The image is first contrast filtered with a centre surround ker- nel, then imprinted pixelwise as a phase perturbation of the corresponding oscillator (each oscillator in the sensory surface maps to one pixel of the input stimulus). ...Citations
... In fact, spiral wave also plays active role in coordinating oscillation phases over a population of neurons and binding sensory information or dynamical temporal storage in working memory. Some interesting works about the development and selection of spiral wave in network of neurons have been reported [53][54][55][56][57][58][59]. For an example, Schiff [53] observed that oscillatory episodes from isotropic preparations in the middle layers of a mammalian cortex, which can display irregular and chaotic spatiotemporal wave activity. ...
... For an example, Schiff [53] observed that oscillatory episodes from isotropic preparations in the middle layers of a mammalian cortex, which can display irregular and chaotic spatiotemporal wave activity. For example, Wilkinson and Metta [55] studied the possible functional roles for spiral wave activity in visual cortex. Ma et al. [59] detected the effect of ion channel block on the transition of spiral wave in the small-world network of Hodgkin-Huxley neurons. ...
The development of spiral wave in the regular network of Hindmarsh–Rose neurons with nearest-neighbor connection is investigated under no-flux and/or periodical boundary condition, respectively. At first, specific initial values are selected to detect the formation of spiral wave, it is found that the developed state is controlled by the bifurcation ss, which controls the electric activity of neuron from spiking to burst behavior, and different developed states are observed. Furthermore, the formation of ordered wave induced by the defect block in the network of neurons is also investigated. In the numerical studies, the first step is to generate target-like wave by imposing a discrepant forcing current (not periodical signal) on a local region, the second step is to produce an artificial defect by setting the variables in a local area to zero. The supposed defect is used to block the propagation of target wave in the network, and the condition for spiral wave emergence is investigated in a numerical way. It indicates that the existence of defect in the media accounts for the emergence of spiral wave though most of the previous works used to simulate the development of spiral wave by using specific initial values. A statistical factor of synchronization in the two-dimensional space is defined to detect the appearance and robustness of spiral wave in the network of neurons. It is confirmed that the contour profile of the developed pattern is dependent on the intensity of coupling and defects block.
... In fact, spiral wave also plays active role in coordinating oscillation phases over a population of neurons and binding sensory information or dynamical temporal storage in working memory. Some interesting works about the development and selection of spiral wave in network of neurons have been reported [53][54][55][56][57][58][59]. For an example, Schiff [53] observed that oscillatory episodes from isotropic preparations in the middle layers of a mammalian cortex, which can display irregular and chaotic spatiotemporal wave activity. ...
... For an example, Schiff [53] observed that oscillatory episodes from isotropic preparations in the middle layers of a mammalian cortex, which can display irregular and chaotic spatiotemporal wave activity. For example, Wilkinson and Metta [55] studied the possible functional roles for spiral wave activity in visual cortex. Ma et al. [59] detected the effect of ion channel block on the transition of spiral wave in the small-world network of Hodgkin-Huxley neurons. ...
Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales.
