The construction of a simultaneous functional order in nervous systems. II. Computing geometrical structures

Area of Science:

• Neuroscience
• Computational Neuroscience
• Network Theory

Background:

• Previous work established functional order in neural nets using signal covariances.
• This order represents modalities as concatenated lattice districts.
• Anatomical order is external, while functional order is internal to the system.

Purpose of the Study:

• To link the functional order of neural nets to the geometry of their detector arrays.
• To develop an algorithm for constructing an abstract geometrical complex from functional order.
• To demonstrate how this complex reflects underlying geometry and stimulus pattern topology.

Main Methods:

• Utilizing signal covariances and coincidences within neural nets.
• Developing an algorithm to build an abstract geometrical complex from functional order.
• Analyzing the algebraic structure and homology of the constructed complex.

Main Results:

• The functional order of a neural net can be algorithmically translated into an abstract geometrical complex.
• The complex's algebraic structure mirrors the detector array's topology and geometry.
• Activated subcomplexes correspond to stimulus-activated detector array segments.

Conclusions:

• The neural system can objectively represent the geometry of its detector array and the topology of stimulus patterns.
• Functional order provides an internal, system-available representation of external structure.
• This framework bridges signal processing, network topology, and geometric representation in neural systems.