55,713 research outputs found
Transformation of stimulus correlations by the retina
Redundancies and correlations in the responses of sensory neurons seem to
waste neural resources but can carry cues about structured stimuli and may help
the brain to correct for response errors. To assess how the retina negotiates
this tradeoff, we measured simultaneous responses from populations of ganglion
cells presented with natural and artificial stimuli that varied greatly in
correlation structure. We found that pairwise correlations in the retinal
output remained similar across stimuli with widely different spatio-temporal
correlations including white noise and natural movies. Meanwhile, purely
spatial correlations tended to increase correlations in the retinal response.
Responding to more correlated stimuli, ganglion cells had faster temporal
kernels and tended to have stronger surrounds. These properties of individual
cells, along with gain changes that opposed changes in effective contrast at
the ganglion cell input, largely explained the similarity of pairwise
correlations across stimuli where receptive field measurements were possible.Comment: author list corrected in metadat
Grassmann Variables and Pseudoclassical Nuclear Magnetic Resonance
The concept of a propagator is useful and is a well-known object in diffusion
NMR experiments. Here, we investigate the related concept; the propagator for
the magnetisation or the Green's function of the Torrey-Bloch equations. The
magnetisation propagator is constructed by defining functions such as the
Hamiltonian and Lagrangian and using these to define a path integral. It is
shown that the equations of motion derived from the Lagrangian produce
complex-valued trajectories (classical paths) and it is conjectured that the
end-points of these trajectories are real-valued. The complex nature of the
trajectories also suggests that the spin degrees of freedom are also encoded
into the trajectories and this idea is explored by explicitly modeling the spin
or precessing magnetisation by anticommuting Grassmann variables. A
pseudoclassical Lagrangian is constructed by combining the diffusive (bosonic)
Lagrangian with the Grassmann (fermionic) Lagrangian, and performing the path
integral over the Grassmann variables recovers the original Lagrangian that was
used in the construction of the propagator for the magnetisation. The
trajectories of the pseudoclassical model also provide some insight into the
nature of the end-points.Comment: 25 page
Boundary-Induced Pattern Formation from Temporal Oscillation: Spatial Map Analysis
Boundary-induced pattern formation from a spatially uniform state is
investigated using one-dimensional reaction-diffusion equations. The temporal
oscillation is successively transformed into a spatially periodic pattern,
triggered by diffusion from the fixed boundary. We introduced a spatial map,
whose temporal sequence, under selection criteria from multiple stationary
solutions, can completely reproduce the emergent pattern, by replacing the time
with space. The relationship of the pattern wavelength with the period of
oscillation is also obtained. The generality of the pattern selection process
and algorithm is discussed with possible relevance to biological morphogenesis.Comment: 17page
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