Skip to content

jaxfne Suite No. 3: Scale-Dependent Low-Frequency Structure in Proxy Field Readouts

A compact tutorial demonstrating population scaling, spatiotemporal density preservation, and validation of 1/f^alpha absolute power-law structure in simulated field readouts.

Open in Colab

Learning Objectives

After completing this tutorial, you will understand:

  1. Noisy Asynchronous Spiking — how drive heterogeneity and randomized states establish stable asynchronous-irregular dynamics.
  2. Density Preservation — how to scale population size N while holding spatiotemporal density constant by expanding declared spatial extent.
  3. Absolute Power Spectrum — how to estimate whole-window absolute power spectral density from proxy readouts.
  4. Log-Log Power-Law Fit — how to fit 1/f^alpha slope exponents across population scales in the 1-80 Hz band.
  5. Scale Curves — how to validate slope exponents, low-frequency absolute power, and synchrony metrics across sizes.

Biological/Computational Question

Question: How does scaling the population size N while preserving constant spatiotemporal density alter the absolute power-law exponent in aggregate field readouts?

Context: In a noisy asynchronous-irregular regime, independent fluctuations average out under projection, leaving low-frequency modes to scale with population size. Ensuring constant density prevents confounding local packaging density with population scale.

Mathematical Glossary Flow

Here, we outline the foundational equations defining the readout projection:

1. Readout Projection Equation

  • Formal definition: $\(Y_c(t) = \sum_{n=1}^{N} W_{cn} S_n(t)\)$
  • Definition of terms:
  • \(Y_c(t)\): Simulated/proxy readout at channel/contact \(c\) and time \(t\).
  • \(W_{cn}\): Projection weight from source element \(n\) to channel/contact \(c\).
  • \(S_n(t)\): Native/proxy source feature from neuron/source element \(n\).
  • \(N\): Number of source elements, varied across scales.
  • \(c\): Readout channel/contact index.
  • Worded equation: The channel signal is the weighted sum of source activity across the modeled source population.
  • Implementation location: fields.py
  • Scope boundary: This is a proxy source-to-readout projection unless a run supplies physical geometry, calibrated source units, conductivity, boundary conditions, gauge handling, a physical field solver, and validation evidence.

2. Whole-Window Absolute Power Spectrum

  • Formal definition: $\(P(f) = \frac{|Y(f)|^2}{\text{normalization}}\)$
  • Worded description: Absolute power at frequency f is the squared magnitude of the windowed, detrended Fourier transform.

3. Log-Log Power-Law Fit

  • Formal definition: $\(\log_{10}(P(f)) = \beta_0 - \alpha \log_{10}(f)\)$
  • Worded description: The scaling exponent alpha is the negative slope of absolute power fit on log-log axes in the 1-80 Hz frequency band.

Canonical Import

Every notebook script and library call standardizes to the canonical import:

import jaxfne as jtfne

All public APIs are called through the unified jtfne namespace.

Simulation Workflow

The tutorial walks through the standard jaxfne workflow:

Configuration -> construct -> simulate -> whole-window absolute power -> log-log polyfit -> scale curves
  1. Configuration: Set up a scale-dependent configuration using jtfne.Configuration().
  2. Construction: Build the model with jtfne.construct(cfg).
  3. Simulation: Run the vectorized dynamics with jtfne.simulate(model, sim).
  4. Spectral Estimation: Compute whole-window absolute power spectrum P(f) on log-log axes.
  5. Scale Curves: Fit exponent alpha and plot slope, low-frequency absolute power, and synchrony versus scale.