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Standalone point:
- Builds on Script 1/2, but adds the first local state dynamic.
- A node does not respond automatically when a signal arrives.
- It responds only if its local live state has recovered from previous activation.
- Therefore repeated waves can pass, weaken, or fail.
Didactic status:
- Still not a CNNA Schur/DtN model.
- First transition from kinematic schedules to stateful response propagation.
"""
from __future__ import annotations
from dataclasses import dataclass
from typing import Literal, Tuple
import gradio as gr
import matplotlib.pyplot as plt
import numpy as np
try:
from modules.common import (
BASE,
activity_from_schedule,
count_visible_packets,
exact_regular_schedule,
launch_offsets,
make_heatmap,
make_snapshot_comparison,
make_timing_error_plot,
time_grid,
timing_error,
transport_diffusion_residuals,
response_profile,
)
except ModuleNotFoundError: # direct execution as python modules/script_XX.py
from common import (
BASE,
activity_from_schedule,
count_visible_packets,
exact_regular_schedule,
launch_offsets,
make_heatmap,
make_snapshot_comparison,
make_timing_error_plot,
time_grid,
timing_error,
transport_diffusion_residuals,
response_profile,
)
RefractoryMode = Literal["binary", "partial_recovery"]
FailurePolicy = Literal["block", "attenuate"]
# Script 3 intentionally uses a stress default so the new refractory gate is visible.
# The Script-1/2 baseline remains available by setting T_launch back to BASE.launch_interval.
SCRIPT3_DEMO_LAUNCH_INTERVAL = 2.00
SCRIPT3_DEMO_SNAPSHOT_TIME = 18.00
@dataclass(frozen=True)
class RefractoryParams:
n_people: int = BASE.n_people
tau_mean: float = BASE.tau
tau_jitter: float = 0.0
activation_time: float = BASE.activation_time
refractory_time: float = BASE.refractory_time
seat_spacing: float = BASE.seat_spacing
launch_count: int = BASE.launch_count
launch_interval: float = SCRIPT3_DEMO_LAUNCH_INTERVAL
damping_per_node: float = 0.0
dt: float = BASE.dt
t_max: float = BASE.t_max
snapshot_time: float = SCRIPT3_DEMO_SNAPSHOT_TIME
refractory_mode: RefractoryMode = "binary"
failure_policy: FailurePolicy = "block"
wrap_ring: bool = False
seed: int = 7
def edge_delay_schedule(params: RefractoryParams) -> Tuple[np.ndarray, np.ndarray]:
"""Return edge delays τ_i and raw jitter ξ_i.
Edge i is the delay from node i to node i+1 in the open-chain case.
For ring mode the last edge N-1 goes from node N-1 back to node 0.
Zero-jitter is constructed exactly as a constant array to avoid turning
binary floating point drift into a false model diagnostic.
"""
n = max(0, int(params.n_people))
edge_count = n if bool(params.wrap_ring) else max(n - 1, 0)
tau = float(params.tau_mean)
sigma = max(float(params.tau_jitter), 0.0)
if edge_count == 0:
return np.zeros(0, dtype=float), np.zeros(0, dtype=float)
if sigma == 0.0:
return np.full(edge_count, tau, dtype=float), np.zeros(edge_count, dtype=float)
rng = np.random.default_rng(int(params.seed))
raw_jitter = rng.normal(0.0, sigma, size=edge_count)
edge_delays = np.clip(tau + raw_jitter, 0.02, None)
return edge_delays, raw_jitter
def _recovery_factor(delta_since_last: float, params: RefractoryParams) -> float:
"""Local live-state gate for a new response attempt.
delta_since_last measures the time between the current arrival and the node's
previous activation. The node is still active for T_act, then refractory for
T_ref. In binary mode it accepts only after the full recovery gap. In partial
mode it recovers linearly after the active period.
"""
if not np.isfinite(delta_since_last):
return 1.0
t_act = max(float(params.activation_time), 0.0)
t_ref = max(float(params.refractory_time), 1e-12)
full_gap = t_act + t_ref
if str(params.refractory_mode) == "binary":
return 1.0 if delta_since_last >= full_gap else 0.0
# partial_recovery: active phase gives zero response; refractory phase recovers linearly.
return float(np.clip((delta_since_last - t_act) / t_ref, 0.0, 1.0))
def propagate_events(
params: RefractoryParams,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
"""Propagate launch signals through local refractory gates.
Returns
-------
event_times:
Shape (launch_count, N). Accepted activation time or NaN.
response_strength:
Shape (launch_count, N). Local response amplitude. 1 = full response,
0 = blocked or unreached.
status:
Shape (launch_count, N). 1 accepted, 0 blocked at this node, -1 unreached.
edge_delays:
Edge delay schedule.
raw_jitter:
Raw ξ values used to build edge_delays.
"""
n = max(0, int(params.n_people))
launches = launch_offsets(params.launch_count, params.launch_interval)
m_count = len(launches)
event_times = np.full((m_count, n), np.nan, dtype=float)
response_strength = np.zeros((m_count, n), dtype=float)
status = np.full((m_count, n), -1.0, dtype=float)
last_activation = np.full(n, -np.inf, dtype=float)
edge_delays, raw_jitter = edge_delay_schedule(params)
for m, launch_time in enumerate(launches):
arrival_time = float(launch_time)
node = 0
visited_edges = 0
max_edges = n if bool(params.wrap_ring) else max(n - 1, 0)
while 0 <= node < n:
delta = arrival_time - last_activation[node]
recovery = _recovery_factor(delta, params)
accepted = False
local_strength = 0.0
if str(params.failure_policy) == "block":
if recovery > 0.0:
accepted = True
local_strength = 1.0 if str(params.refractory_mode) == "binary" else recovery
else: # attenuate
accepted = True
local_strength = recovery
if not accepted or local_strength <= 0.0:
status[m, node] = 0.0
break
status[m, node] = 1.0
event_times[m, node] = arrival_time
response_strength[m, node] = local_strength
last_activation[node] = arrival_time
if not bool(params.wrap_ring):
if node >= n - 1:
break
edge_idx = node
arrival_time = arrival_time + float(edge_delays[edge_idx])
node = node + 1
else:
if visited_edges >= max_edges - 1:
break
edge_idx = node
arrival_time = arrival_time + float(edge_delays[edge_idx])
node = (node + 1) % n
visited_edges += 1
return event_times, response_strength, status, edge_delays, raw_jitter
def activity_from_events(
times: np.ndarray,
event_times: np.ndarray,
response_strength: np.ndarray,
activation_time: float,
damping_per_node: float,
) -> np.ndarray:
"""Build H[t, i] from accepted stateful events."""
if event_times.ndim != 2:
raise ValueError("event_times must have shape (launch_count, n_people)")
launch_count, n = event_times.shape
heights = np.zeros((len(times), n), dtype=float)
node_damping = np.exp(-max(float(damping_per_node), 0.0) * np.arange(n, dtype=float))
for m in range(launch_count):
for i in range(n):
t0 = event_times[m, i]
amp = float(response_strength[m, i]) * float(node_damping[i])
if not np.isfinite(t0) or amp <= 0.0:
continue
local = times - float(t0)
heights[:, i] = np.maximum(heights[:, i], amp * response_profile(local, activation_time))
return heights
def first_activation_times(event_times: np.ndarray) -> np.ndarray:
"""First accepted activation per node; NaN if no accepted event reached it."""
if event_times.size == 0:
return np.zeros(0, dtype=float)
with np.errstate(all="ignore"):
first = np.nanmin(event_times, axis=0)
first[~np.isfinite(first)] = np.nan
return first
def first_wave_reference_from_edges(n: int, edge_delays: np.ndarray, tau_mean: float) -> np.ndarray:
"""Reference schedule for the first launch using the same edge delays.
With zero jitter this is exactly i·τ. With jitter it matches Script 2's
cumulative edge-delay schedule, so refractory failures are not confused with
timing noise.
"""
if n <= 0:
return np.zeros(0, dtype=float)
if edge_delays.size == 0:
return np.zeros(n, dtype=float)
if np.all(edge_delays == float(tau_mean)):
return exact_regular_schedule(n, float(tau_mean))
out = np.zeros(n, dtype=float)
if n > 1:
out[1:] = np.cumsum(edge_delays[: n - 1])
return out
def make_response_deficit_plot(positions: np.ndarray, status: np.ndarray):
"""Plot missing accepted responses relative to the ideal Script-1 launch count.
Script 1 assumes every launch reaches every node. Script 3 may block a launch
at a gate; downstream nodes are then not reached. This plot is therefore the
correct default-visible deviation for the refractory module. Pure timing error
of accepted events can remain zero while the response count already differs.
"""
fig, ax = plt.subplots(figsize=(10, 3.6))
if status.size == 0:
ax.set_title("Script 3: fehlende Responses gegen ideale Referenz — keine Daten")
return fig
accepted_counts = np.sum(status == 1.0, axis=0)
launch_count = status.shape[0]
deficit = launch_count - accepted_counts
blocked_counts = np.sum(status == 0.0, axis=0)
unreached_counts = np.sum(status == -1.0, axis=0)
ax.plot(positions, deficit, marker="o", linewidth=1.5, markersize=3, label="fehlende akzeptierte Responses")
ax.plot(positions, blocked_counts, linestyle="--", linewidth=1.2, label="direkt blockiert")
ax.plot(positions, unreached_counts, linestyle=":", linewidth=1.2, label="nicht erreicht")
ax.set_xlabel("Knoten / Sitzposition xᵢ")
ax.set_ylabel("Anzahl Launches")
ax.set_title("Script 3: Response-Defizit relativ zum idealen Script-1-Wellenzug")
ax.set_ylim(-0.05, max(1.0, float(launch_count)) + 0.2)
ax.grid(True, alpha=0.3)
ax.legend(loc="best")
fig.tight_layout()
return fig
def make_refractory_map(positions: np.ndarray, status: np.ndarray):
"""Plot launch × node acceptance map.
Values:
-1 = signal did not reach this node because an earlier gate stopped the wave.
0 = signal reached this node but was blocked by local refractory state.
1 = node accepted and responded.
"""
fig, ax = plt.subplots(figsize=(10, 3.8))
if status.size == 0:
ax.set_title("Refraktär-/Failure-Map: keine Daten")
return fig
extent = [positions[0], positions[-1], -0.5, status.shape[0] - 0.5]
im = ax.imshow(status, aspect="auto", origin="lower", extent=extent, vmin=-1.0, vmax=1.0)
cbar = fig.colorbar(im, ax=ax)
cbar.set_label("-1 nicht erreicht · 0 blockiert · 1 akzeptiert")
ax.set_xlabel("Knoten / Sitzposition xᵢ")
ax.set_ylabel("Startimpuls m")
ax.set_title("Script 3: Refraktär-/Failure-Map pro Launch und Knoten")
fig.tight_layout()
return fig
def simulate(
params: RefractoryParams,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]:
n = int(params.n_people)
times = time_grid(params.t_max, params.dt)
positions = params.seat_spacing * np.arange(n, dtype=float)
launches = launch_offsets(params.launch_count, params.launch_interval)
event_times, strengths, status, edge_delays, raw_jitter = propagate_events(params)
heights = activity_from_events(times, event_times, strengths, params.activation_time, params.damping_per_node)
reference_activation = exact_regular_schedule(n, params.tau_mean)
reference = activity_from_schedule(times, reference_activation, launches, params.activation_time)
return times, positions, launches, event_times, strengths, status, edge_delays, raw_jitter, heights, reference
def run_model(
n_people: int,
tau_mean: float,
tau_jitter: float,
activation_time: float,
refractory_time: float,
seat_spacing: float,
launch_count: int,
launch_interval: float,
damping_per_node: float,
refractory_mode: str,
failure_policy: str,
wrap_ring: bool,
dt: float,
t_max: float,
snapshot_time: float,
seed: int,
):
params = RefractoryParams(
n_people=int(n_people),
tau_mean=float(tau_mean),
tau_jitter=float(tau_jitter),
activation_time=float(activation_time),
refractory_time=float(refractory_time),
seat_spacing=float(seat_spacing),
launch_count=int(launch_count),
launch_interval=float(launch_interval),
damping_per_node=float(damping_per_node),
refractory_mode=str(refractory_mode), # type: ignore[arg-type]
failure_policy=str(failure_policy), # type: ignore[arg-type]
wrap_ring=bool(wrap_ring),
dt=float(dt),
t_max=float(t_max),
snapshot_time=float(snapshot_time),
seed=int(seed),
)
(
times,
positions,
launches,
event_times,
strengths,
status,
edge_delays,
raw_jitter,
heights,
reference,
) = simulate(params)
first_actual = first_activation_times(event_times)
edge_reference = first_wave_reference_from_edges(params.n_people, edge_delays, params.tau_mean)
errors = timing_error(first_actual, edge_reference)
errors[~np.isfinite(first_actual)] = np.nan
tau_emp = float(np.mean(edge_delays)) if edge_delays.size else float(params.tau_mean)
sigma_emp = 0.0 if float(params.tau_jitter) == 0.0 else float(np.std(edge_delays))
c_emp = params.seat_spacing / max(tau_emp, 1e-12)
sigma2 = float(np.var(edge_delays)) if edge_delays.size else 0.0
d_eff = 0.0 if sigma2 <= 1e-30 else (params.seat_spacing**2 * sigma2) / (2.0 * max(tau_emp, 1e-12) ** 3)
r_transport, r_diffusion = transport_diffusion_residuals(times, positions, heights, c_emp, d_eff)
no_extra_irregularity = (float(params.tau_jitter) == 0.0) and (float(params.damping_per_node) == 0.0)
full_recovery_gap = max(float(params.activation_time), 0.0) + max(float(params.refractory_time), 0.0)
gate_should_matter = float(params.launch_interval) < full_recovery_gap
heat_title = (
"Script 3: Refraktär-Gate aktiv — Wellen können lokal scheitern"
if gate_should_matter
else "Script 3: Refraktär-Gate aktiv — Default lässt vollständige Erholung zu"
)
heatmap = make_heatmap(times, positions, heights, heat_title)
snapshot = make_snapshot_comparison(
times,
positions,
heights,
reference,
params.snapshot_time,
"Script 3 simuliert",
)
schedule = make_timing_error_plot(
positions,
errors,
"Script 3: erster akzeptierter Launch — Timing-Fehler relativ zur edge-basierten Referenz",
)
response_deficit = make_response_deficit_plot(positions, status)
refractory_map = make_refractory_map(positions, status)
snapshot_idx = int(np.argmin(np.abs(times - params.snapshot_time)))
visible_packets = count_visible_packets(heights[snapshot_idx, :])
active_nodes = int(np.sum(heights[snapshot_idx, :] > 0.05))
accepted = int(np.sum(status == 1.0))
blocked = int(np.sum(status == 0.0))
unreached = int(np.sum(status == -1.0))
total_attempt_slots = int(status.size)
pass_rate = accepted / max(total_attempt_slots, 1)
full_launches = int(np.sum(np.all(status == 1.0, axis=1))) if status.size else 0
failed_launches = int(params.launch_count) - full_launches
first_block_per_launch = []
for m in range(status.shape[0]):
blocked_nodes = np.where(status[m, :] == 0.0)[0]
first_block_per_launch.append(int(blocked_nodes[0]) if blocked_nodes.size else None)
first_blocks_text = ", ".join("–" if x is None else str(x) for x in first_block_per_launch)
max_abs_error = float(np.nanmax(np.abs(errors))) if np.any(np.isfinite(errors)) else float("nan")
max_abs_delta_snapshot = float(np.max(np.abs(heights[snapshot_idx, :] - reference[snapshot_idx, :]))) if heights.size else 0.0
launch_spacing_nodes = params.launch_interval / max(tau_emp, 1e-12)
refractory_warning = "Ja — spätere Launches können in noch nicht erholte Knoten laufen." if gate_should_matter else "Nein — Default-Abstand lässt volle Erholung zu."
zero_note = "Ja — bis auf das neue Refraktär-Gate." if no_extra_irregularity else "Nein — Timing-Streuung oder Dämpfung ist aktiv."
interpretation = f"""
## Script 3 — Interpretation
**Neue lokale Regel: Refraktär-Gate / endliche Responsefähigkeit**
Script 1 und 2 zeichnen Aktivierungen im Wesentlichen aus einem Schedule. Script 3 macht daraus
zum ersten Mal eine lokale Zustandsdynamik:
```text
ansprechbar → aktiv → refraktär → ansprechbar
Signal kommt bei Knoten i an.
Knoten i antwortet nur, wenn seit seiner letzten Aktivierung mindestens
T_act + T_ref vergangen ist.
```
Minimal-binär:
```text
response_i = 1, falls Δt_i ≥ T_act + T_ref
response_i = 0, sonst
```
Bei `partial_recovery` wird die Erholung linear angenähert:
```text
response_i = clamp((Δt_i - T_act) / T_ref, 0, 1)
```
| Größe | Wert |
|---|---:|
| Knotenanzahl N | {params.n_people} |
| Startimpulse launch_count | {params.launch_count} |
| Startabstand T_launch | {params.launch_interval:.3f} s |
| Erholungsschwelle T_act + T_ref | {full_recovery_gap:.3f} s |
| Startabstand in Knoten T_launch/mean(τ_i) | {launch_spacing_nodes:.2f} Knoten |
| Refraktärwarnung T_launch < T_act+T_ref | {refractory_warning} |
| Refraktärmodus | {params.refractory_mode} |
| Failure-Policy | {params.failure_policy} |
| Ringmodus | {params.wrap_ring} |
| sichtbare Pakete im Snapshot | {visible_packets} |
| aktive Knoten im Snapshot | {active_nodes} |
| akzeptierte Knoten-Launch-Ereignisse | {accepted} |
| blockierte Ereignisse | {blocked} |
| nicht erreichte Ereignisse | {unreached} |
| Pass-Rate akzeptiert / Slots | {pass_rate:.3f} |
| vollständig durchgelaufene Launches | {full_launches} |
| gescheiterte Launches | {failed_launches} |
| erster Block pro Launch | {first_blocks_text} |
| mean(τ_i) | {tau_emp:.4f} s |
| std(τ_i) | {sigma_emp:.4e} s |
| Dämpfung pro Knoten α | {params.damping_per_node:.5f} |
| max. Timing-Fehler des ersten akzeptierten Launchs | {max_abs_error:.4e} s |
| max. Snapshot-Abweichung gegen Script 1 | {max_abs_delta_snapshot:.4e} |
| heuristisches D_eff aus Timing-Streuung | {d_eff:.6e} |
| normierter Transport-Residualindikator | {r_transport:.4f} |
| normierter Transport-Diffusions-Residualindikator | {r_diffusion:.4f} |
| keine Script-2-Irregularität aktiv? | {zero_note} |
**Lesart:** Eine Welle ist jetzt nicht mehr garantiert. Die Propagation hängt vom lokalen
Live-Zustand ab. Damit wird aus einem vorgegebenen Wellenzug eine Response-Kette mit Gedächtnis.
Das ist der erste relevante Schritt in Richtung CNNA-Sprache: lokale Antwortfähigkeit, Relaxation,
Record/live-Unterscheidung und Scheitern einer Response-Propagation.
**Wichtiger Default-Hinweis:** Script 3 verwendet jetzt als Demonstrations-Default `T_launch = 2.0 s`.
Da `T_act + T_ref = 3.2 s`, laufen einige spätere Launches in noch nicht erholte Knoten.
Die gemeinsame Script-1/2-Baseline erhältst du durch `T_launch = 4.0 s`; dann bleibt das Gate korrekt,
aber im Plot weitgehend unsichtbar.
**Warum der Timing-Plot trotzdem null sein kann:** Bei `std(ξ)=0` verschiebt das Refraktär-Gate akzeptierte
Ereignisse nicht zeitlich; es akzeptiert oder blockiert sie. Die relevante Abweichung ist daher nicht
Timing-Drift, sondern Response-Defizit und Failure-Map.
**Unsicherheit / Modellgrenze:** Das ist noch kein Schur-/DtN-Netzwerk. Die Refraktärregel ist eine
kontrollierte lokale Automat-Regel. Im späteren CNNA-Modul müsste die Antwortfähigkeit aus der
live-Randantwort beziehungsweise einer lokalen Schur-/DtN-Response abgeleitet werden.
"""
return heatmap, snapshot, schedule, response_deficit, refractory_map, interpretation
def build_tab() -> None:
gr.Markdown(
r"""
## Script 3 — Refraktär-Gate: lokale Response kann scheitern
Dieses Modul baut auf Script 1/2 auf, fügt aber ein neues wesentliches Detail hinzu:
Ein Knoten reagiert nicht automatisch. Er reagiert nur, wenn seine lokale live-Response wieder frei ist.
Der Script-3-Default ist absichtlich ein Refraktär-Stresstest (`T_launch = 2.0 s`), damit das neue Gate sofort sichtbar wird.
Die gemeinsame Script-1/2-Baseline ist weiterhin verfügbar: `T_launch = 4.0 s` setzen.
"""
)
with gr.Row():
with gr.Column(scale=1):
n_people = gr.Slider(20, 240, value=BASE.n_people, step=1, label="N Menschen / Knoten")
tau_mean = gr.Slider(0.05, 0.80, value=BASE.tau, step=0.01, label="mittlere τ [s]")
tau_jitter = gr.Slider(0.00, 0.20, value=0.0, step=0.005, label="std(ξ) Timing-Streuung [s]")
activation_time = gr.Slider(0.20, 4.00, value=BASE.activation_time, step=0.05, label="T_act Aktivitätsdauer [s]")
refractory_time = gr.Slider(0.20, 8.00, value=BASE.refractory_time, step=0.05, label="T_ref Refraktärzeit [s]")
seat_spacing = gr.Slider(0.20, 3.00, value=BASE.seat_spacing, step=0.05, label="a Knotenabstand")
launch_count = gr.Slider(1, 12, value=BASE.launch_count, step=1, label="launch_count Startimpulse")
launch_interval = gr.Slider(0.50, 12.00, value=SCRIPT3_DEMO_LAUNCH_INTERVAL, step=0.10, label="T_launch Abstand der Startimpulse [s]")
damping_per_node = gr.Slider(0.00, 0.04, value=0.0, step=0.001, label="α Dämpfung pro Knoten")
refractory_mode = gr.Radio(
choices=["binary", "partial_recovery"],
value="binary",
label="Refraktärmodus",
)
failure_policy = gr.Radio(
choices=["block", "attenuate"],
value="block",
label="Failure-Policy",
)
wrap_ring = gr.Checkbox(value=False, label="Ringmodus statt offener Reihe")
dt = gr.Slider(0.01, 0.10, value=BASE.dt, step=0.01, label="dt Zeitauflösung [s]")
t_max = gr.Slider(4.00, 80.00, value=BASE.t_max, step=0.50, label="t_max [s]")
snapshot_time = gr.Slider(0.00, 80.00, value=SCRIPT3_DEMO_SNAPSHOT_TIME, step=0.10, label="Momentaufnahme t [s]")
seed = gr.Number(value=7, precision=0, label="Seed für reproduzierbare ξᵢ")
run = gr.Button("Simulation ausführen", variant="primary")
with gr.Column(scale=2):
heatmap = gr.Plot(label="Raum-Zeit-Aktivität")
snapshot = gr.Plot(label="Momentaufnahme gegen ideale Referenz")
schedule = gr.Plot(label="Timing-Fehler akzeptierter erster Durchlauf")
response_deficit = gr.Plot(label="Response-Defizit gegen ideale Referenz")
refractory_map = gr.Plot(label="Refraktär-/Failure-Map")
interpretation = gr.Markdown()
inputs = [
n_people,
tau_mean,
tau_jitter,
activation_time,
refractory_time,
seat_spacing,
launch_count,
launch_interval,
damping_per_node,
refractory_mode,
failure_policy,
wrap_ring,
dt,
t_max,
snapshot_time,
seed,
]
outputs = [heatmap, snapshot, schedule, response_deficit, refractory_map, interpretation]
run.click(run_model, inputs=inputs, outputs=outputs)
if __name__ == "__main__":
params = RefractoryParams()
t, x, launches, events, strengths, status, delays, jitter, h, ref = simulate(params)
print(
t.shape,
x.shape,
launches.shape,
events.shape,
strengths.shape,
status.shape,
delays.shape,
jitter.shape,
h.shape,
ref.shape,
)
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