Network Symmetry and Binocular Rivalry Experiments

The Journal of Mathematical Neuroscience

Table 1 Isotypic components corresponding to representations where ρ acts as −1 in the four-dot networks

Experiment	Symmetries	V	Subspace	Kernel
Conventional 4-dot	$D_{4} \oplus Z_{2} (ρ)$	$V_{1}^{+}$	$(\begin{array}{c} x & x & x & x \\ - x & - x & - x & - x \end{array})$	$D_{4}$
		$V_{1}^{-}$	$(\begin{array}{c} x & - x & x & - x \\ - x & x & - x & x \end{array})$	$D_{4}$
		$V_{2}^{-}$	$(\begin{array}{c} x & y & - x & - y \\ - x & - y & x & y \end{array})$	1
Scrambled diagonal	$D_{4} \oplus Z_{2} (ρ)$	$V_{1}^{+}$	$(\begin{array}{c} x & - x & x & - x \\ - x & x & - x & x \end{array})$	$D_{4}$
		$V_{1}^{-}$	$(\begin{array}{c} x & x & x & x \\ - x & - x & - x & - x \end{array})$	$D_{4}$
		$V_{2}^{-}$	$(\begin{array}{c} x & y & - x & - y \\ - x & - y & x & y \end{array})$	1
Scrambled adjacent	$D_{2} (κ, τ) \oplus Z_{2} (ρ)$	$V_{1}$	$(\begin{array}{c} x & x & x & x \\ - x & - x & - x & - x \end{array})$	$D_{2}$
		$V_{2}$	$(\begin{array}{c} x & x & - x & - x \\ - x & - x & x & x \end{array})$	$Z_{2} (κ)$
		$V_{3}$	$(\begin{array}{c} x & - x & - x & x \\ - x & x & x & - x \end{array})$	$Z_{2} (τ)$
		$V_{4}$	$(\begin{array}{c} x & - x & x & - x \\ - x & x & - x & x \end{array})$	$Z_{2} (κ τ)$
Scrambled unbalanced	$Z_{2} (σ) \oplus Z_{2} (ρ)$	$V_{1}$	$(\begin{array}{c} x & y & x & z \\ - x & - y & - x & - z \end{array})$	$Z_{2} (σ)$
Scrambled unbalanced	$Z_{2} (σ) \oplus Z_{2} (ρ)$	$V_{2}$	$(\begin{array}{c} x & 0 & - x & 0 \\ - x & 0 & x & 0 \end{array})$	$Z_{2} (σ ρ)$