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. 2015 Aug 26;11(8):e1004422. doi: 10.1371/journal.pcbi.1004422

Fig 8. Relationship between periodic patterning and receptive field refinement.

Fig 8

A. Example of RF refinement obtained by numerically solving Eq 6. Vertical teal lines denote the arbor function boundary. B. Refinement phase space for RFs as a function of wave speed and STDP time constants. Colored regions: areas of phase space in which RFs maintain a single field that is refined to smaller sizes; blue: RF 0 = 0.8 mm; purple: RF 0 = 0.44 mm. Shading indicates the total change in RF size as a percentage of RF 0. Region α corresponds to higher spatial frequencies in which RFs split into subfields. Region β corresponds to lower spatial frequencies in which RFs expand. Overlaid are the iso-frequency contours of Fig 3. Solid contours correspond to spatial frequencies with integer exponents of 10 (lower left to upper right: 10 cyc./mm, 1 cyc./mm and 0.1 cyc./mm). C. Incremental changes in wave speed can continually refine RFs while maintaining a single subfield structure. Shown is the development of a RF, averaged over 16 trials, during which the wave speed is first set to 4 mm/s and then decreases to 2.5 mm/s, after which the RF decreases in size. Increasing the wave speed back to 4 mm/s returns the RF to its previous refined size. Purple trace: plot of the mean number of synapses with strength > 0.5 as an indicator of RF size. D. Refinement phase space using a symmetric STDP rule, for which RF 0 matches that for the blue region in B. Numbers next to the iso-frequency contours indicate their spatial frequency in cycles/mm. E. Refinement phase spaces, using the asymmetric STDP rule, for different biases towards synaptic weakening. Left: A = 0.50, which corresponds to dΔtK(Δt)=0. Centre and right: A = 0.55 and 0.60, respectively, which correspond to dΔtK(Δt)>0. Red circles lie at the same v and τ + coordinates, to compare the effect of different A values on RF refinement. The refinement phase space moves to lower spatial frequencies as A increases.