Interspike Local Variation

Calculate Shinomoto local variation Lv = 3/(n−1) × sum(((ISI[i]−ISI[i+1])/(ISI[i]+ISI[i+1]))²) for positive consecutive intervals. This is the original Lv without a refractory-period correction.

Description

Local variation summarizes adjacent-interval irregularity using normalized differences.

Local variation summarizes adjacent-interval irregularity using normalized differences. It differs from variability measured across the whole interval distribution.^[1]

When to use Interspike Local Variation

Use this tool to calculate Shinomoto local variation Lv = 3/(n−1) × sum(((ISI[i]−ISI[i+1])/(ISI[i]+ISI[i+1]))²) for positive consecutive intervals. This is the original Lv without a refractory-period correction.

Prepare the task-specific rates, comparable response-time means, identified spike train, processed ERP or estimated spectra requested. Confirm units, preprocessing, sample pairing and caller-fitted model coefficients.

How to use Interspike Local Variation and understand its results

Prepare the task-specific rates, comparable response-time means, identified spike train, processed ERP or estimated spectra requested. Confirm units, preprocessing, sample pairing and caller-fitted model coefficients.
Enter intervalsMs using the field table and calculation rules, then run the tool.
Read localVariation. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
intervalsMs	Positive consecutive interspike intervals. (ms)	list of number; strictly above: 0; minimum entries: 2; maximum entries: 100000	Required

Enter two through 100,000 strictly positive consecutive intervals in milliseconds. Scale each neighboring pair by its larger value before computing the ratio to reduce numeric overflow, then return localVariation. Equal adjacent intervals contribute zero.

Lv=3/(n−1) Σ[((ISI_i−ISI_(i+1))/(ISI_i+ISI_(i+1)))²]

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
localVariation	Dimensionless local variation.	number; minimum: 0; maximum: 3

json

{
  "input": {
    "intervalsMs": [
      10,
      20,
      10
    ]
  },
  "output": {
    "localVariation": 0.3333333333333333
  }
}

Limitations and assumptions

This implements original Lv without a refractory correction. It does not estimate spike counts, firing rate or classify neuron type.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Spike Train Interspike Intervals: Calculate consecutive interspike intervals from strictly increasing timestamps for a single identified spike train. This does not assign spikes to neurons or perform spike sorting. For a complementary task, use Spike Count Fano Factor: Calculate the empirical Fano factor as population variance (divisor n) divided by mean spike count across equal-duration repeated trials. The caller supplies counts for one neuron; a zero mean is undefined.

References

Interspike Local Variation — tool.io

Similar or alternative tools

Spike Train Interspike Intervals
Calculate consecutive interspike intervals from strictly increasing timestamps for a single identified spike train. This does not assign spikes to neurons or perform spike sorting.
Spike Count Fano Factor
Calculate the empirical Fano factor as population variance (divisor n) divided by mean spike count across equal-duration repeated trials. The caller supplies counts for one neuron; a zero mean is undefined.