Dataset Information

Field patterns: a new mathematical object.

ABSTRACT: Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns. Alternatively one can view a collection as a multi-component potential, with as many components as the number of field patterns. Presumably, if one added a tiny nonlinear term to the wave equation one would then see interactions between these field patterns in the multi-dimensional space that one can consider them to live, or between the different field components of the multi-component potential if one views them that way. As a result of [Formula: see text]-symmetry many of the complex eigenvalues of an appropriately defined transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. There are also modes that blow up exponentially with time.

SUBMITTER: Milton GW

PROVIDER: S-EPMC5332618 | biostudies-literature | 2017 Feb

REPOSITORIES: biostudies-literature

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Field patterns: a new mathematical object.

Milton Graeme W GW Mattei Ornella O

Proceedings. Mathematical, physical, and engineering sciences 20170201 2198

Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but ...[more]

PMID: 28293143

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Project description:Color is special among basic visual features in that it can form a defining part of objects that are engrained in our memory. Whereas most neuroimaging research on human color vision has focused on responses related to external stimulation, the present study investigated how sensory-driven color vision is linked to subjective color perception induced by object imagery. We recorded fMRI activity in male and female volunteers during viewing of abstract color stimuli that were red, green, or yellow in half of the runs. In the other half we asked them to produce mental images of colored, meaningful objects (such as tomato, grapes, banana) corresponding to the same three color categories. Although physically presented color could be decoded from all retinotopically mapped visual areas, only hV4 allowed predicting colors of imagined objects when classifiers were trained on responses to physical colors. Importantly, only neural signal in hV4 was predictive of behavioral performance in the color judgment task on a trial-by-trial basis. The commonality between neural representations of sensory-driven and imagined object color and the behavioral link to neural representations in hV4 identifies area hV4 as a perceptual hub linking externally triggered color vision with color in self-generated object imagery.SIGNIFICANCE STATEMENT Humans experience color not only when visually exploring the outside world, but also in the absence of visual input, for example when remembering, dreaming, and during imagery. It is not known where neural codes for sensory-driven and internally generated hue converge. In the current study we evoked matching subjective color percepts, one driven by physically presented color stimuli, the other by internally generated color imagery. This allowed us to identify area hV4 as the only site where neural codes of corresponding subjective color perception converged regardless of its origin. Color codes in hV4 also predicted behavioral performance in an imagery task, suggesting it forms a perceptual hub for color perception.

Dataset Information

Field patterns: a new mathematical object.

Publications

Field patterns: a new mathematical object.

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