Stochastic Resonance demo — gain/dopamine × noise × threshold

A tiny, self-contained browser demo that shows why adding moderate broadband noise can improve detection/recall in a nonlinear, thresholded system — and why lower dopaminergic gain shifts the optimum to higher noise. This is a toy illustration of the Moderate Brain Arousal (MBA) idea applied to ADHD.

Open index.html in any modern browser. No build. No dependencies.

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Quick start

1. Put these files in a folder:
   • index.html - the interactive demo
   • style.css - stylesheet
   • README.md - this file
2. Double click index.html or run a static server, e.g. python -m http.server and open http://localhost:8000.

You can also host this on GitHub Pages by placing index.html at the repository root.

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What you are seeing

• Model: a simple threshold detector with dopaminergic gain g, threshold θ, internal noise σ_int, and external noise σ_ext that couples in with strength α.
• Signal path: x = s + n_int + α·n_ext → y = σ(g·x − θ), σ is a logistic.
• The plot shows balanced accuracy as a function of σ_ext. For subthreshold s, accuracy follows an inverted‑U vs noise (stochastic resonance). Lower gain needs more noise to reach the sweet spot and often peaks lower.

Equations shown in the UI

• Hit rate: H = 1 − Φ((θ − g·s)/(g·σ))
• False alarm: F = 1 − Φ(θ/(g·σ))
• Balanced accuracy: 0.5 · (H + (1 − F))
• Effective noise: σ = sqrt(σ_int^2 + (α·σ_ext)^2)

This is a deliberately minimal, static model that illustrates intuition, not a claim about full neural dynamics.

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Why noise can help (intuitive theory)

• Stochastic resonance: in nonlinear systems with thresholds, a small amount of noise helps weak signals cross effective boundaries, improving detection. Too much noise swamps the code. Result: an inverted‑U performance curve.
• Gain modulation: dopamine is often modeled as neural gain. Lower dopamine → lower gain. In an SR system, lower gain right‑shifts the optimal noise level, which is exactly what is observed in ADHD cohorts.
• Continuous broadband noise works because it adds energy without structured content that would capture attention. Intermittent or meaningful sounds tend to harm performance.

For background and data, see:

• Söderlund, Sikström (2007). Listen to the noise: noise is beneficial for cognitive performance in ADHD, Journal of Child Psychology and Psychiatry, 48(8), 840–847. doi:10.1111/j.1469-7610.2007.01749.x. This paper introduces the ADHD finding and links it to stochastic resonance and dopamine-modulated gain.
• Moss, Ward, Sannita (2004). Stochastic resonance and sensory information processing: a tutorial and review of applications, Clinical Neurophysiology, 115, 267–281.

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Controls cheat sheet

• s: stimulus amplitude. Keep it subthreshold relative to θ/g to see the SR hump.
• θ: threshold. Higher θ makes detection harder.
• σ_int: internal noise floor.
• α: coupling from external noise to effective internal noise.
• σ_ext,max: x‑axis range. Widen this if your peak is off the right edge.
• g_A, g_B: two gains to compare (e.g., “low‑DA/ADHD” vs “control”).

Buttons:

• Reset restores defaults.
• Export PNG saves the current plot image.

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Repo structure

sr-gain-noise-demo/
├─ index.html        # the interactive demo
├─ style.css         # stylesheet: look and feel. 
├─ README.md         # this file
└─ LICENSE           # MIT License. 

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Credits

• Concept and demo code: Oskar Paulander (based on the MBA intuition and SR toy model).
• Theory and empirical grounding:
  • G. Söderlund, S. Sikström, A. Smart (2007). Listen to the noise: noise is beneficial for cognitive performance in ADHD, J Child Psychol Psychiatry, 48(8), 840–847. doi:10.1111/j.1469-7610.2007.01749.x.
  • Additional SR background from Moss, Ward, Sannita (2004).

If you use this in a paper, please credit the above and link back to this repository.

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License

MIT License