Modelling spatiotemporal properties of directionally sensitive multi-input single-output systems

Area of Science:

• Systems Engineering
• Mathematical Physics
• Neuroscience

Background:

• Directionally tuned linear systems exhibit input-output dynamics dependent on spatial input orientation.
• Input-output behavior is modeled using vector transfer functions characterizing system polarization.
• System matrix eigenvectors and eigenvalues define these polarization directions.

Purpose of the Study:

• To analyze the spatial tuning behavior of linear systems based on their vector transfer functions.
• To differentiate between unidirectional and bidirectional vector transfer functions.
• To explore the distinct processing characteristics of neuronal systems with these different transfer functions.

Main Methods:

• Calculating eigenvectors and eigenvalues of the system matrix derived from harmonic stimulation.
• Analyzing the quadratic form associated with the system matrix to determine spatial tuning.
• Comparing the input-output behavior of systems with unidirectional versus bidirectional vector transfer functions.

Main Results:

• Linear systems can possess either one (unidirectional) or two (bidirectional) vector transfer functions, never three.
• Bidirectional vector transfer functions arise from specific system matrix properties.
• Neuronal systems with bidirectional vector transfer functions exhibit plane-specific information processing.

Conclusions:

• The number of vector transfer functions (one or two) dictates the system's spatial tuning.
• Bidirectional vector transfer functions in neuronal systems lead to unique, plane-specific information processing.
• Understanding these vector transfer functions is key to characterizing complex system dynamics.