func (GoldenBasis) GlobalCoherence(x []float64) float64 · RingDiffusionStep performs dS_i/dt

Read the equation

This relation defines RingDiffusionStep performs dS_i/dt in the source section “func (GoldenBasis) GlobalCoherence(x []float64) float64 · RingDiffusionStep performs dS_i/dt”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read RingDiffusionStep performs dS_i/dt as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

	sum := 0.0
	for _, xi := range x {
		sum += 1.0 / (1.0 + math.Abs(xi-1.0))
	}
	return sum / float64(len(x))
}

// RingDiffusionStep performs dS_i/dt = λ(S_{i+1} + S_{i-1} - 2S_i)
func (GoldenBasis) RingDiffusionStep(S []float64, lambda, dt float64) {
	N := len(S)
	dS := make([]float64, N)

	for i := 0; i < N; i++ {
		prev := (i - 1 + N) % N
		next := (i + 1) % N
		dS[i] = lambda * (S[next] + S[prev] - 2.0*S[i])
	}

RingDiffusionStep performs dS_i/dt = λ(S_{i+1} + S_{i-1} - 2S_i)

Related builds