The influences of intracortical inhibition on simple cell RFs can be
investigated at various levels, ranging from the most detailed,
where one deals with a large number of ``real'' neurons and with the fidelity
of connections, up to the most abstract ones, where one deals with
functional counterparts. An analytical study demands to
sacrifice the degree of detail to the advantage of the formalization of
cortical computation; thus, we transformed the anatomical description into
a functional one, by means of the concept of * mean anatomy*
[68]. This means averaging the multiplicity of forms of cytoarchitecture and the richness of
synaptic chemical reactions to achieve a continuous
medium where electrical variables express macroscopic properties.
Further, assuming the linearity of simple cell responses
[27,70], and let that, in the visual cortex, inhibitory synapses operate primarily in the linear mode
[7,31,36,38], such macroscopic variables and their effects on the spatial structure of simple cell RFs can be studied within a
linear framework which deals with linear spatial filter functions and linear
couplings (cf. system theory of homogeneous layers
[134,135]). In this context, a location on the cortical plane represents a population of
cells, whose behavior will be modeled by a single cell that represents the
average response of the neurons belonging to that population. Similarly,
connections represent interactions among populations and they will be described
by a linear, spatial coupling function representing the spreading of the synaptic
net influence of that population on its neighborhood, as mediated by local
axon and dendritic fields.
Limitations of the linear approach will be discussed in Section 4.

- General Assumptions
- Superposition Assumption
- Long-Range Clustered Inhibitory Kernel
- The Resultant Receptive Fields