Suite No. 2 Upgrade: Izhikevich to V1-V4 Spectrolaminar Proxy Readouts¶

Pipeline: Emitter -> Source -> Field -> Probe -> Objective -> Optimizer.

Learning objectives¶

Configure one reduced Izhikevich emitter through jaxfne.
Compare E/PV/SST/VIP reduced-emitter presets through package-level arrays.
Build net1, a 100-emitter uniformly sampled 3D column.
Generate raster, LFP-proxy, CSD-proxy, EEG-proxy, MEG-proxy, and EMM-proxy figures without tutorial-local plotting functions.
Configure a V1-V4 six-layer scaffold with feedforward and feedback metadata.
Tune solver-tuned noise amplitude toward a firing-rate target with the Suite No. 2 AGSDR-Adam utility.

Question¶

How far can a compact jaxfne grammar carry the workflow from one reduced emitter to a two-area laminar scaffold while preserving reusable source/field/probe readouts?

Mathematical glossary flow¶

Reduced Izhikevich emitter¶

Formal equation:

\[\frac{dv_i}{dt}=0.04v_i^2+5v_i+140-u_i+I_i(t), \qquad \frac{du_i}{dt}=a_i(b_i v_i-u_i)\]

Reset rule:

\[v_i\ge 30 \Rightarrow v_i\leftarrow c_i,\quad u_i\leftarrow u_i+d_i\]

Terms: \(v_i\) is the reduced voltage-proxy state, \(u_i\) is recovery, \(a,b,c,d\) set class-specific dynamics, and \(I_i(t)\) combines base drive, recurrent input, and stochastic drive.

Worded equation: voltage changes according to intrinsic recovery, a nonlinear voltage term, and input current; threshold events reset the emitter state.

Implementation: jaxfne.emitters.IzhikevichEmitter, jaxfne.emitters.simulate_eig_izhikevich, and Suite No. 2 config builders.

Source/readout projection¶

Formal equation:

\[Y_c(t)=\sum_n W_{cn}S_n(t)\]

Terms: \(S_n(t)\) is a source proxy from emitter \(n\), \(W_{cn}\) is a declared projection weight, and \(Y_c(t)\) is a channel/contact readout.

Worded equation: each readout channel is a weighted sum of source activity.

Implementation: jaxfne.fields.LinearReadout, jaxfne.fields.project_laminar_sources, and jaxfne.vis.* figure functions.

Package-level workflow¶

The notebook uses only package-level helpers:

import jaxfne as jtfne

cfg_net1 = jtfne.suite2_net1_config(seed=7, n=100, duration_ms=1000.0, dt_ms=0.1)
model_net1 = jtfne.construct(cfg_net1)
bundle_net1 = jtfne.suite2_run_bundle(model_net1, seed=7, duration_ms=1000.0, dt_ms=0.1)
fig_panel = jtfne.vis.spectrolaminar_suite(bundle_net1["signals"], max_freq_hz=80.0)

V1-V4 scaffold:

cfg_v1v4 = jtfne.suite2_v1_v4_config(seed=7, n_per_area=400, duration_ms=1000.0, dt_ms=0.1)
model_v1v4 = jtfne.construct(cfg_v1v4)

Figures¶

Core figures are generated by reusable visualization functions:

jtfne.vis.raster(..., sort_by="z")
jtfne.vis.lfp_traces(...)
jtfne.vis.csd_traces(...)
jtfne.vis.eeg(...)
jtfne.vis.meg(...)
jtfne.vis.emm(...)
jtfne.vis.spectrolaminar_suite(...)
jtfne.vis.circuit3d(...)

Configuration Reference¶

All Suite No. 2 workflows are specified through the chainable Configuration API. Every field listed here stores in cfg.metadata; none are physical statuss.

Smoke config vs full config¶

import jaxfne as jtfne

# ── Smoke config (fast, 10 neurons, 100 ms) ─────────────────────────────────
cfg_smoke = jtfne.suite2_net1_config(seed=7, n=10, duration_ms=100.0, dt_ms=0.1)

# ── Full config (100 neurons, 1000 ms) ───────────────────────────────────────
cfg_full = jtfne.suite2_net1_config(seed=7, n=100, duration_ms=1000.0, dt_ms=0.1)

# ── V1-V4 multi-area scaffold ────────────────────────────────────────────────
cfg_v1v4 = jtfne.suite2_v1_v4_config(seed=7, n_per_area=400, duration_ms=1000.0, dt_ms=0.1)

The same 10-domain grammar applies to both:

cfg = (
    jtfne.Configuration()
    .runtime(seed=7, duration_ms=1000.0, dt_ms=0.1, dtype="float32")
    .column("V1", layers=["L1", "L2/3", "L4", "L5", "L6"], n=100)
    .cell_types({"E": 0.75, "PV": 0.10, "SST": 0.08, "VIP": 0.07})
    .connectivity(within_area="all_to_all_uniform_random", within_gain=0.45)
    .set_emitter("izhikevich", "cortical_eig")
    .probes(["spikes", "V_m", "source", "LFP", "CSD"], n_contacts=16)
    .field(domain="laminar_column", conductivity="proxy", boundary="mean_zero_neumann")
)

Runtime domain (`cfg.runtime`)¶

Parameter	Default	Unit / status	Description
`seed`	`42`	integer	PRNG seed for all random operations
`duration_ms`	`1000.0`	ms	Total simulation duration
`dt_ms`	`0.1`	ms	Fixed timestep (forward Euler)
`dtype`	`"float32"`	string	JAX array dtype (`"float32"` or `"float64"`)
`backend`	`"cpu"`	string	JAX backend (`"cpu"`, `"gpu"`)
`jit`	`True`	bool	Enable `jax.jit` compilation for main kernels
`vmap`	`True`	bool	Enable `jax.vmap` over trial batches
`n_trials`	`1`	integer	Number of stochastic trials

Column domain (`cfg.column`)¶

Parameter	Default	Unit / status	Description
`column_name`	`"single_column"`	string	Column/area identifier
`layers`	`["L1","L2/3","L4","L5","L6"]`	list	Layer labels (declarative)
`n`	`100`	integer	Total neuron count per column
`x_size_mm`	`0.5`	mm	Lateral x extent (proxy geometry)
`y_size_mm`	`0.5`	mm	Lateral y extent (proxy geometry)
`z_size_mm`	`1.6`	mm	Laminar depth extent (proxy geometry)
`geometry_status`	`"declared_metadata"`	string	Always `declared_metadata`; no 3D PDE grid

Cell-type domain (`cfg.cell_types`)¶

Cell type	Global fraction	Sign	Izhikevich preset	Drive default (a.u.)
`E` (excitatory)	`0.75`	`+1`	`cortical_eig`	`5.0`
`PV` (fast-spiking)	`0.10`	`−1`	`cortical_eig`	`3.0`
`SST` (Martinotti)	`0.08`	`−1`	`cortical_eig`	`3.5`
`VIP` (disinhibitory)	`0.07`	`−1`	`cortical_eig`	`3.0`

Izhikevich parameters by cell type (`cortical_eig` preset)¶

Parameter	E	PV	SST	VIP	Unit
a	0.02	0.10	0.02	0.02	1/ms
b	0.20	0.20	0.25	−0.10	dimensionless
c	−65.0	−65.0	−65.0	−55.0	mV
d	8.0	2.0	2.0	6.0	mV/ms
Spike threshold	30	30	30	30	mV
Reset V	−65	−65	−65	−55	mV

PV has high a (fast recovery) and low d (weak AHP) → fast-spiking. VIP has negative b (bistable subthreshold) and higher reset c → irregular firing.

Connectivity domain (`cfg.connectivity`)¶

Parameter	Default	Unit / status	Description
`within_area`	`"all_to_all_uniform_random"`	string	Recurrent topology mode
`within_gain`	`0.45`	dimensionless	Global weight scale (net1); `0.35` for V1-V4
`E_weight_range`	`(0.5, 2.0)`	a.u.	Excitatory weight range
`I_weight_range`	`(-1.5, -0.5)`	a.u.	Inhibitory weight range
`synaptic_tau_ms`	`5.0`	ms	Exponential synapse decay constant
`sign_policy`	`"intrinsic"`	string	Sign from emitter type, not overridden
`seed`	`None`	integer	Edge-weight PRNG seed

Drive domain (`cfg.drive`)¶

Parameter	Default	Unit / status	Description
`baseline_drive_by_cell_type`	`{"E": 5.0, "PV": 3.0, "SST": 3.5, "VIP": 3.0}`	a.u.	Constant external drive per cell type
`noise_policy`	`"additive_poisson"`	string	Stochastic drive mode
`noise_amplitude`	`0.5`	a.u.	Noise scale (tuned by `suite2_tune_noise_agsdr_adam`)
`time_schedule`	`"constant"`	string	Drive profile (`"constant"`, `"pulse"`, `"ramp"`)
`trial_variability`	`False`	bool	Vary seed across trials

Inter-column connectivity domain (`cfg.inter_column_connectivity`)¶

For V1-V4 only. Declarative metadata; connectivity is stored as parameter dicts, resolved into sparse matrices only at simulate() time.

Parameter	Default	Unit / status	Description
`source_area`	`"V1"`	string	Feedforward origin
`target_area`	`"V4"`	string	Feedforward target
`mode`	`"sparse"`	string	Topology (`"sparse"`, `"all_to_all"`)
`p_feedforward`	`0.3`	probability	V1→V4 connection probability
`p_feedback`	`0.2`	probability	V4→V1 connection probability
`feedforward_weight_range`	`(0.5, 2.0)`	a.u.	V1→V4 weight range
`feedback_weight_range`	`(0.3, 1.5)`	a.u.	V4→V1 weight range
`layer_to_layer_map`	`{"L2/3": "L4", "L5": "L1"}`	dict	Declared source→target layer routing

Field domain (`cfg.field`)¶

Parameter	Value	Status
`domain`	`"laminar_column"`	Proxy geometry
`conductivity`	`"proxy"`	Not calibrated
`boundary`	`"mean_zero_neumann"`	Boundary convention
`field_solver_status`	`"linear_solver"`	Immutable
`amplitude_status`	`False`	Immutable
`source_projection_mode`	`"proxy_no_field_solve"`	Proxy only

Probe domain (`cfg.probes`)¶

Probe mode	Default contacts	Returns	Scope
`"spikes"`	N neurons	`bool [N, T]`	Spike indicator
`"V_m"`	N neurons	`float32 [N, T]`	Voltage-proxy
`"source"`	N neurons	`float32 [N, T]`	Source current proxy
`"LFP"`	16	`float32 [Z, T]`	LFP-proxy
`"CSD"`	16	`float32 [Z, T]`	CSD-proxy (2nd spatial derivative)
`"EEG"`	4	`float32 [4, T]`	EEG proxy (declared leadfield)
`"MEG"`	4	`float32 [4, T]`	MEG proxy (declared leadfield)
`"EMM"`	1	`float32 [1, T]`	Signaling-energy proxy

All probes carry units_or_status: "proxy_relative_units" and amplitude_status: false.

Objective domain (`cfg.objective`)¶

Parameter	Default	Description
`firing_rate_target`	`{"E": 8.0, "PV": 15.0, "SST": 4.0, "VIP": 2.0}`	Target Hz per cell type
`band_definitions`	`{"alpha_beta": (8.0, 25.0), "gamma": (40.0, 150.0)}`	Hz ranges
`rejection_gates`	`{"max_firing_rate": (0.0, 200.0)}`	Hard acceptance bounds

Optimizer domain (`cfg.optimizer`)¶

Parameter	Default	Description
`optimizer_family`	`"AGSDR"`	Optimizer type (`"AGSDR"`, `"random_search"`)
`surrogate_status`	`"soft_rate_surrogate"`	Inner-loop approximation; not for statements
`budget`	`50`	Optimization iterations
`hard_gates`	`{"model_status": "computational_scaffold"}`	Cannot be overridden

Simulation Execution¶

Core pipeline¶

import jaxfne as jtfne

cfg = jtfne.suite2_net1_config(seed=7, n=100, duration_ms=1000.0, dt_ms=0.1)
model = jtfne.construct(cfg)

# Run bundle: returns signals, report, and config
bundle = jtfne.suite2_run_bundle(model, seed=7, duration_ms=1000.0, dt_ms=0.1)

signals = bundle["signals"]   # Signals namedtuple
report  = bundle["report"]    # JSON-safe metadata dict

Solver semantics (per timestep)¶

The integration uses forward Euler with fixed dt_ms:

Evaluate recurrent input: I_rec = W @ S_prev (dense or sparse edge-list)
Evaluate external drive: I_ext = baseline_drive + I_noise(noise_amplitude, key)
Update v and u via Izhikevich equations
Detect threshold: if v >= 30, record spike, reset v = c, u = u + d
Update synaptic traces: exponential decay tau = synaptic_tau_ms
Record all probe outputs for this timestep

Numerical bounds¶

Quantity	Clamp / reset	Value
Membrane potential `v`	Hard clip	`[-100, +50]` mV
Spike threshold	Hard	30 mV
Reset value	Cell-type specific	`c` parameter
Synaptic trace	Decay only	Never negative

Output structure¶

suite2_run_bundle() returns:

{
    "signals": Signals(
        spikes   = jnp.array([N_neurons, N_steps]),   # bool
        V_m      = jnp.array([N_neurons, N_steps]),   # float32
        source   = jnp.array([N_neurons, N_steps]),   # float32
        LFP      = jnp.array([N_contacts, N_steps]),  # float32 proxy
        CSD      = jnp.array([N_contacts, N_steps]),  # float32 proxy
        # ...EEG, MEG, EMM if requested
    ),
    "report": {
        "seed": 7,
        "duration_ms": 1000.0,
        "dt_ms": 0.1,
        "n_steps": 10000,
        "firing_rate_per_cell_type": {"E": ..., "PV": ..., "SST": ..., "VIP": ...},
        "status_fields": {
            "run_status": "tutorial_scaffold",
            "model_status": "computational_scaffold",
            "field_solver_status": "linear_solver",
            "amplitude_status": False,
        },
    },
}

Noise tuning¶

Use suite2_tune_noise_agsdr_adam to tune noise_amplitude toward the firing-rate target:

tuned_model, tune_report = jtfne.suite2_tune_noise_agsdr_adam(
    model,
    seed=7,
    duration_ms=500.0,   # shorter for tuning runs
    dt_ms=0.1,
    n_steps=30,
)
# Re-run with tuned model:
bundle_tuned = jtfne.suite2_run_bundle(tuned_model, seed=7, duration_ms=1000.0, dt_ms=0.1)

The surrogate optimizer minimizes the squared deviation from the firing-rate target. The surrogate path is for inner-loop optimization only; it does not produce physical amplitude statuss.

Manifest & Reproducibility¶

Every simulation run should be accompanied by a manifest capturing all inputs and outputs for auditability.

Manifest structure¶

import jaxfne as jtfne

manifest = jtfne.manifest(
    config=cfg,
    signals=bundle["signals"],
    report=bundle["report"],
    seed=7,
)
# Validate manifest is JSON-safe (no NaN/Inf)
import json
json.dumps(manifest, allow_nan=False)  # must not raise

The manifest includes:

{
  "version":      "0.3.14",
  "seed":         7,
  "duration_ms":  1000.0,
  "dt_ms":        0.1,
  "n_steps":      10000,
  "configuration": { "...": "..." },
  "outputs": {
    "spikes":   {"shape": [100, 10000], "dtype": "bool"},
    "V_m":      {"shape": [100, 10000], "dtype": "float32"},
    "LFP":      {"shape": [16,  10000], "dtype": "float32"}
  },
  "statistics": {
    "firing_rate_mean_per_cell_type": {"E": 8.3, "PV": 14.7, "SST": 3.8, "VIP": 1.9}
  },
  "status_fields": {
    "run_status": "tutorial_scaffold",
    "model_status": "computational_scaffold",
    "field_solver_status": "linear_solver",
    "amplitude_status": false
  }
}

Reproducibility¶

To reproduce a run exactly:

cfg2 = jtfne.suite2_net1_config(seed=7, n=100, duration_ms=1000.0, dt_ms=0.1)
model2 = jtfne.construct(cfg2)
bundle2 = jtfne.suite2_run_bundle(model2, seed=7, duration_ms=1000.0, dt_ms=0.1)

# Outputs are bit-identical to bundle["signals"] within float32 rounding
import jax.numpy as jnp
assert jnp.allclose(bundle["signals"].V_m, bundle2["signals"].V_m)

Validation gates¶

Before accepting any output:

Gate	Check	Remediation
Finiteness	`jnp.all(jnp.isfinite(signals.V_m))`	Reduce drive or dt_ms
Firing rate	Per-cell-type rate in `[0.1, 150]` Hz	Adjust within_gain or drive
Spectral positivity	All band powers ≥ 0	Check CSD/LFP output
JSON-safety	`json.dumps(manifest, allow_nan=False)`	Never export NaN/Inf
Status fields	`amplitude_status == False`	Never override

Simulation-only outputs: The manifest records configuration and output statistics. PDE residuals, convergence diagnostics, and calibration certificates are outside scope — the proxy field operator requires none.

Interpretation of Results¶

Expected firing rates¶

Cell type	Expected range	Target (tuned)
E (pyramidal)	5–15 Hz	8 Hz
PV (fast-spiking)	10–30 Hz	15 Hz
SST (Martinotti)	2–10 Hz	4 Hz
VIP (disinhibitory)	1–5 Hz	2 Hz

If observed rates are >2× outside these ranges, the network is unstable or frozen.

Expected spectrolaminar proxy power¶

LFP power is in proxy relative units (not µV²):

Alpha/beta (8–25 Hz): Typically highest in layers 4 and 5/6. Range [0.1, 1.0] proxy units.
Gamma (40–150 Hz): Often highest in superficial layers (L2/3, L4). Range [0.02, 0.3] proxy units.

Cell-type roles¶

Cell type	Role	Ablation effect
E	Primary driver; recurrent excitation	Network goes silent (too little) or unstable (too much)
PV	Fast feedback inhibition	Loss causes runaway firing and loss of gamma
SST	Dendritic inhibition	Loss reduces layer-specific selectivity
VIP	Disinhibition of E via PV suppression	Loss reduces gain modulation

Null comparison¶

To confirm spectrolaminar features are not artifactual: 1. Shuffle spike times within each trial (preserves firing rate) 2. Recompute LFP/CSD proxy from shuffled spikes 3. Real band power should exceed shuffled by >2× for meaningful signal

When to discard a run¶

Discard if any of the following: - Any signal contains NaN or Inf - Any cell-type firing rate is outside [0.1, 150] Hz - amplitude_status was overridden (not possible via public API) - Manifest JSON serialization fails

Failure Modes¶

Symptom	Likely cause	Remediation
All neurons silent (rate ≈ 0 Hz)	Drive too low or inhibition too strong	Increase `baseline_drive_by_cell_type["E"]`; decrease `within_gain`
Runaway firing (>100 Hz sustained)	Drive too high or E dominance	Decrease drive; increase PV/SST drive
NaN or Inf in output	Numerical overflow; `dt_ms` too large	Reduce `dt_ms` to 0.05; reduce drive amplitude
Flat LFP (no oscillations)	Insufficient recurrent feedback	Increase `within_gain`; check synaptic tau
VIP neurons always silent	VIP drive below threshold	Increase `baseline_drive_by_cell_type["VIP"]`
CSD all zeros	Source projection degenerate	Check `n_contacts >= 3`; verify column height > 0
Slow JIT compile (>60 s)	Shape instability / recompilation loop	Fix `n`, `n_steps`, `n_contacts` before first run
Suite runs differ across machines	x64 not enabled consistently	Call `jtfne.enable_x64()` before array construction

Dense recurrent matrix on small CPUs¶

For n > 500, the dense W @ S matrix multiply becomes expensive on CPU. Use the recurrent_backend="edge_list" option in RuntimeConfig to switch to a sparse edge-list kernel:

from jaxfne.core import RuntimeConfig
rt = RuntimeConfig(recurrent_backend="edge_list")
sim = jtfne.simulation(duration_ms=1000.0, dt_ms=0.1, seed=7, runtime=rt)

Exercises¶

Smoke first: Run suite2_net1_config(n=10, duration_ms=100.0) before attempting n=100 to confirm the full pipeline executes.
PV ablation: Set baseline_drive_by_cell_type["PV"] = 0.0 and rerun. Observe how gamma-band power changes when fast inhibition is removed.
SST ablation: Repeat with SST = 0.0. Compare to PV ablation — SST loss tends to broaden layer selectivity rather than collapse gamma.
Noise tuning convergence: Run suite2_tune_noise_agsdr_adam for 10, 20, and 50 steps. Plot the objective value versus iteration count.
V1-V4 feedforward dominance: In suite2_v1_v4_config, set p_feedback = 0.0 (feedforward only). Does V4 gamma power decrease?
Contact density sweep: Vary n_contacts from 4 to 32 and plot the spatial resolution of the CSD-proxy profile.
Null check: Shuffle spike times in bundle["signals"].spikes and recompute LFP/CSD. Confirm real band power > 2× shuffled power.

Coverage boundary¶

This tutorial covers reduced emitters, declared source projection, relative proxy readouts, and package-level figure generation. Solver-tuned amplitudes, subject-specific head geometry, and empirical parameter fitting belong to later workflows.

Extended Mathematical Glossary¶

Source tensor construction¶

Formal equation:

\[S[t, n] = \begin{cases} R[t] & \text{(spike proxy mode)} \\ I_{\text{decomposed}}[t, n] + I_{\text{synap}}[t, n] & \text{(decomposed mode)} \\ I_{\text{total}}[t, n] & \text{(total current mode)} \end{cases}\]

Terms: - \(S[t, n]\): source proxy from emitter \(n\) at timestep \(t\) - \(R[t]\): population spike rate (relative units) - \(I_{\text{decomposed}}\): capacitive + ionic current - \(I_{\text{synap}}\): synaptic input current - \(I_{\text{total}}\): membrane current (total of all sources)

Worded equation: source proxy is selected from available current decompositions or spike rate, validated for finite values and single-source consistency.

Implementation location: jaxfne.fields.construct_source_tensor

Scope boundary: Proxy relative units. Physical amplitude calibration is outside scope.

Geometric projection tensor (laminar approximation)¶

Formal equation:

\[\mathbf{M}_{cn} = \frac{e^{-\frac{1}{2} \left( \frac{z_c - z_n}{\sigma} \right)^2}}{\sum_{m=1}^{N} e^{-\frac{1}{2} \left( \frac{z_c - z_m}{\sigma} \right)^2}}\]

Terms: - \(\mathbf{M}_{cn}\): entry of the row-normalized geometric projection tensor (mapping contact \(c\) to emitter \(n\)) - \(z_c\): relative laminar depth coordinate of contact \(c\) - \(z_n\): relative laminar depth coordinate of emitter \(n\) - \(\sigma\): declared standard deviation (width parameter) of the Gaussian profile

Worded equation: the geometric projection operator is a row-normalized Gaussian weight matrix representing a homogeneous, isotropic infinite-medium proxy operator design note, not current calibrated field-solver evidence.

Implementation location: jaxfne.fields._row_normalize and jaxfne.fields.project_laminar_sources

Scope boundary: Homogeneous isotropic infinite-medium proxy operator. Calibrated field-solver evidence is outside scope; this is a proxy operator design only.

LFP-proxy linear projection¶

Formal equation:

\[\text{LFP}[t, c] = \sum_{n=1}^{N} K_{cn} \cdot S[t, n]\]

Terms: - \(\text{LFP}[t, c]\): LFP-proxy at contact \(c\) - \(K_{cn}\): row-normalized Gaussian kernel (contact \(c\) to emitter \(n\)) - \(S[t, n]\): source proxy from emitter \(n\)

Worded equation: LFP-proxy is a weighted sum of source-proxy traces, with weights from a row-stochastic contact kernel.

Implementation location: jaxfne.fields.project_laminar_sources

Scope boundary: Laminar proxy only. PDE solution and physical calibration are outside scope.

CSD-proxy (second spatial derivative)¶

Formal equation:

\[\text{CSD}[t, c] = -\frac{\partial^2 \Phi_e}{\partial z_c^2}\]

Terms: - \(\text{CSD}[t, c]\): current-source-density proxy at contact \(c\) - \(\Phi_e\): extracellular potential-proxy (LFP-proxy) - \(z_c\): laminar depth coordinate

Worded equation: CSD-proxy is the negative second spatial derivative of the potential-proxy along the contact axis, computed via finite differences.

Implementation location: jaxfne.fields.project_laminar_sources, lines ~130–133

Scope boundary: Proxy approximation only. Resistive-field PDE computation is outside scope.

EEG/MEG linear proxy readout¶

Formal equation:

\[Y_{\text{EEG/MEG}}[t, c] = \sum_{n=1}^{N} L_c[n] \cdot S[t, n]\]

Terms: - \(Y_{\text{EEG/MEG}}\): EEG or MEG proxy trace - \(L_c\): declared EEG/MEG leadfield for channel \(c\) (toy deterministic basis) - \(S[t, n]\): source proxy

Worded equation: EEG and MEG proxies are linear projections of source activity through declared (not empirically measured) leadfields.

Implementation location: jaxfne.fields.eeg_proxy_transform, jaxfne.fields.meg_proxy_transform, jaxfne.vis.eeg, jaxfne.vis.meg

Scope boundary: Declared geometry only. Relative proxy units; head geometry and real sensor placement are outside scope.

EMM-proxy (signaling-energy summary)¶

Formal equation:

\[E_{\text{proxy}}[t] = \lambda_1 R[t] + \lambda_2 \|S[t]\|_1 + \lambda_3 \|\Phi_e[t]\|_2^2\]

Terms: - \(E_{\text{proxy}}\): relative signaling-energy proxy (normalized) - \(R[t]\): spike rate proxy - \(S[t]\): source-proxy vector - \(\Phi_e[t]\): potential-proxy vector - \(\lambda_1, \lambda_2, \lambda_3\): weighting factors

Worded equation: EMM-proxy is a normalized weighted combination of spike rate, source L1-norm, and field L2-norm.

Implementation location: jaxfne.fields.emm_proxy_transform, jaxfne.vis.emm

Scope boundary: Relative proxy units only. Biophysical metabolism is outside scope.

Spectrolaminar band power summary¶

Formal equation:

\[P_{\text{band}}[c] = \frac{1}{|B|} \int_{f \in B} \text{PSD}[f, c] \, df\]

where \(B \in \{\text{alpha/beta} = [8, 25]\text{ Hz}, \text{gamma} = [40, 150]\text{ Hz}\}\)

Terms: - \(P_{\text{band}}[c]\): mean power in frequency band for contact \(c\) - \(\text{PSD}[f, c]\): power spectral density (Welch estimate) - \(B\): frequency band (alpha/beta or gamma)

Worded equation: Spectrolaminar profile is the mean PSD in each named frequency band, computed per contact.

Implementation location: jaxfne.fields.spectrolaminar_bandpower

Scope boundary: Relative power, proxy signal. Amplitude calibration is outside scope.

V1/V4 feedforward-feedback routing metadata¶

Formal equation:

\[W_{\text{ff/fb}}[i, j] = \begin{cases} > 0 & \text{if } \text{source} = V1, \text{target} = V4 \quad \text{(feedforward)} \\ > 0 & \text{if } \text{source} = V4, \text{target} = V1 \quad \text{(feedback)} \\ 0 & \text{otherwise} \end{cases}\]

Terms: - \(W_{\text{ff/fb}}\): connectivity matrix mask (declarative) - source/target: area (V1 or V4) and layer assignment

Worded equation: V1-to-V4 feedforward and V4-to-V1 feedback connectivity are declared as separate sparse weight matrices.

Implementation location: jaxfne.core.suite2_v1_v4_config, connectiv ity metadata section

Scope boundary: Declared metadata only. Fitted weights and anatomical validation are outside scope.

Figure Placeholders¶

The following figures are referenced in the notebook but not yet committed as PNG files. They will be generated by running the notebook:

Figure placeholder: spectrolaminar_suite_panel — Six-panel figure (raster, LFP-proxy, CSD-proxy, PSD, EEG-proxy, EMM-proxy). Generated by jtfne.vis.spectrolaminar_suite(). Available until generated by tutorials/jaxfne_suite_no_2_spectrolaminar_motif.ipynb.
Figure placeholder: circuit3d_layout_scatter — 3D scatter plot of V1-V4 emitter positions. Generated by jtfne.vis.circuit3d(). Available until generated by tutorials/jaxfne_suite_no_2_spectrolaminar_motif.ipynb.

These placeholders mark where final PNG or PDF figures should be placed once the notebook is executed and validated.

Suite No. 2 Upgrade: Izhikevich to V1-V4 Spectrolaminar Proxy Readouts¶

Learning objectives¶

Question¶

Mathematical glossary flow¶

Reduced Izhikevich emitter¶

Source/readout projection¶

Package-level workflow¶

Figures¶

Configuration Reference¶

Smoke config vs full config¶

Runtime domain (cfg.runtime)¶

Column domain (cfg.column)¶

Cell-type domain (cfg.cell_types)¶

Izhikevich parameters by cell type (cortical_eig preset)¶

Connectivity domain (cfg.connectivity)¶

Drive domain (cfg.drive)¶

Inter-column connectivity domain (cfg.inter_column_connectivity)¶

Field domain (cfg.field)¶

Probe domain (cfg.probes)¶

Objective domain (cfg.objective)¶

Optimizer domain (cfg.optimizer)¶

Simulation Execution¶

Core pipeline¶

Solver semantics (per timestep)¶

Numerical bounds¶

Output structure¶

Noise tuning¶

Manifest & Reproducibility¶

Manifest structure¶

Reproducibility¶

Validation gates¶

Interpretation of Results¶

Expected firing rates¶

Expected spectrolaminar proxy power¶

Cell-type roles¶

Null comparison¶

When to discard a run¶

Failure Modes¶

Dense recurrent matrix on small CPUs¶

Exercises¶

Coverage boundary¶

Extended Mathematical Glossary¶

Source tensor construction¶

Geometric projection tensor (laminar approximation)¶

LFP-proxy linear projection¶

CSD-proxy (second spatial derivative)¶

EEG/MEG linear proxy readout¶

EMM-proxy (signaling-energy summary)¶

Spectrolaminar band power summary¶

V1/V4 feedforward-feedback routing metadata¶

Figure Placeholders¶

Runtime domain (`cfg.runtime`)¶

Column domain (`cfg.column`)¶

Cell-type domain (`cfg.cell_types`)¶

Izhikevich parameters by cell type (`cortical_eig` preset)¶

Connectivity domain (`cfg.connectivity`)¶

Drive domain (`cfg.drive`)¶

Inter-column connectivity domain (`cfg.inter_column_connectivity`)¶

Field domain (`cfg.field`)¶

Probe domain (`cfg.probes`)¶

Objective domain (`cfg.objective`)¶

Optimizer domain (`cfg.optimizer`)¶