Spike Train
stochastic-process · 37 views
stochastic-processpoint-process
What It Is
Integrate-and-fire neuron model --- quiescent charging with sudden discharge spikes
Interpretation
Standard analysis sees: anti-persistent; low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); stationary. The atlas additionally detects Time Reversibility:ordinal_reversal_distance. It sits beside Henon Map in the atlas (standard-bank rank 68) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.62
asymmetry0.69
occupancy0.62
short-range corr0.54
long-range memory0.12
spectral colour0.59
periodicity0.42
complexity0.08
time-irreversibility0.01
volatility clustering0.62
multifractality0.31
dimensionality0.26
nonstationarity0.12
What the atlas adds
Time Reversibility:ordinal_reversal_distance+2.9z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
WaveformAsymmetry:waveform_asymmetry | +3.0z | bank-miss 2.1σ |
H² × ℝ (Thurston):depth_height_corr | -2.6z | bank-miss 1.1σ |
Multi-Scale Wasserstein:w_fine | +2.3z | bank-miss 1.3σ |
Composition
dtypefloat64
range[0.01544, 1.362]
unique values16054 / 16384
mean ± std0.579 ± 0.275
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Spike_Train.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Spike_Train.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Spike_Train.png)
Inflation (Substitution) > barcode
/d_curve/Spike_Train.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Spike_Train.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Spike_Train.png)
Ulam Spiral (Sacks) > default
/default/Spike_Train.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Mackey-Glass | 5.02 | cross-origin |
| Sprott-B | 5.03 | cross-origin |
| Henon Map | 5.12 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:CO_trev_1_num | rank 302/306 | -2.7877 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 2/306 | 1.0699 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_fine | rank 4/306 | 0.2138 |
WaveformAsymmetry › WaveformAsymmetry:waveform_asymmetry | rank 4/306 | 0.9413 |
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