Cross-Correlation (xcorr) Visualizer

🚧 Work in progress 🚧
View how correlations between outputs of small networks vary as a function of circuit parameters

Try the demo here,

• the default network structure has A delivering input to B, and B delivering input to C (A->B->C)
  • the strength of these connections is set by the weight slider
  • these connections are delayed according to the delay slider
  • additive noise is injected at each noise, with it's magnitude set by the sliders for each row
• peaks in cross-correlation at negative time-lags can indicate a directional dependence from node i to node j ⚠️ (causality not guaranteed) ⚠️
  • how do parameters such as noise levels impact the clarity of these xcorr peaks?
  • look for peaks in xcorr for connections which aren't in the network
    • how could these be distinguished from "true" direct connections?
• click controls to see how to change settings
• consider hitting c after major parameter changes to refresh the cross-correlation,
  • otherwise the results will be a mix of the last N samples

Upcoming Features: 🔮

• Computing "coincidence index" as a measure of connectivity
  • need to verify normalization of cross-correlations
  • highlight significant connections
  • add axis labels for xcorr lags
• Edittable circuit structure ( see circuit-visualizer-p5https://github.com/awillats/circuit-visualizer-p5)
  • better visualization of current circuit structure
• [~] Dropdown menu for noise models
  • for now, cycle through with n
• Edittable buffer length for cross-correlation
• Exportable quantitative results
• include autoregressive dynamics
  • for now, Perlin noise setting reasonably approximates nodes with autoregression

Highly-relevant publications:

• How Connectivity, Background Activity, and Synaptic Properties Shape the Cross-Correlation between Spike Trains Srdjan Ostojic, Nicolas Brunel and Vincent Hakim (2009)
• Connectivity inference from neural recording data: Challenges, mathematical bases and research directions Ildefons Magrans de Abril, Junichiro Yoshimoto, Kenji Doya (2018)
• Evaluation of the Performance of Information Theory-Based Methods and Cross-Correlation to Estimate the Functional Connectivity in Cortical Networks Garofalo et al. (2009)

known minor bugs: 🐞

• occasional visual glitch with cross-correlations
  • might be related to switching between models/settings?
• Poisson noise model is additive, but doesn't respect non-negativity

Early observations: 🔍

• finer auto-correlations mean easier connectivity inference

• impact of variances on identifiability depends strongly on...

  • which connection is being examined
  • inputs and outputs to that connection
  • ( stay tuned for a more general hypothesis on relationship between ground truth structure, variance, and Signal-to-noise ratio for Identifiability )

• how you normalize matters more when signals are more different from each other

  • (i.e. normalizing in reciprocal circuits)
  • buffer lenghts longer than ~2k(5k) significantly slow-down script
    • likely computing xcorr not rendering it

• reciprocal circuits with STRONG-ish weights (0.6 < |w| < 1) ...>>

  • circuit was A<=>B->C
    • w = 0.9, 0.8, -0.7
    • |w| > 1 leads to instability
  • exhibit harmonics in xcorr
    • multiples of base syn. delay
  • also have xcorr mirrored at positive and negative lags
  • harmonics in autocorr bleed over, even into non-recurrent links!
  • longer delays make harmonics easier to separate
  • resonance may put higher demand on proper normalization
  • inhibitory weights are surprisingly similar to excitatory weights in this setting

• reciprocal circuits with WEAK weights (0.1 < |w| < .6) ...>>

  • confirmed for w = 0.2, 0.4
  • xcorr behaves much more simply, can be interpretted much like non-reciprocal case

Simple findings:

• delay has predictable signature on xcorr
  • (if autocorr is minimal, influence is delta function)

Repo organization: 🗂️

core files / UI:

• sketch.js the heart of the demo
• index.html just handles page structure and imports
• style.css sets color scheme and text size
• ui-node.js used for interactive parameter sliders, extends dragPoints from dynamics-visualizer-p5

notes:

• README.md landing page / intro
• TASKS.md semi-organized to-do list
• DEVNOTES.md unfiltered ramblings about what to do next

computational methods:

• signal-generation.js generates random signals
  • has Gaussian, Poisson, and Perlin noise models for now
• signal-analysis.js computes cross-correlations
• network-simulation.js
  • extends AdjMat from circuit-visualizer-p5

key libraries:

• p5js for graphics and interactivity
• numjs for some math
• markdown-it for rendering markdown

Related projects:

• 🕸️ circuit-visualizer-p5 code, demo
• 🌀 dynamics-visualizer-p5 code, demo