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Stochastic modeling of a serial killer.

M V Simkin¹, V P Roychowdhury¹

¹Department of Electrical Engineering, University of California, Los Angeles, CA 90095-1594, United States.

Journal of Theoretical Biology

|April 12, 2014

Summary

This study reveals serial killer activity follows a power law, modeled by neuronal excitation triggering murders. This mathematical pattern, observed in one killer and two others, explains inter-murder intervals.

Keywords:

Branching process Neural networks Power laws

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Area of Science:

Criminology
Mathematical Psychology
Neuroscience

Background:

Serial killer activity exhibits complex temporal patterns.
Previous analyses have not fully explained the statistical distribution of inter-murder intervals.

Purpose of the Study:

To analyze the temporal activity patterns of a serial killer.
To propose and validate a mathematical model for inter-murder intervals.
To investigate the underlying neuro-mathematical mechanisms of serial killing.

Main Methods:

Analysis of cumulative murders over time, identifying a "Devil's staircase" pattern.
Statistical analysis of inter-murder intervals, revealing a power-law distribution (exponent 1.4).
Modeling neuronal excitation as a branching process approximated by a random walk.

Main Results:

The "Devil's staircase" pattern describes the cumulative murders.
Inter-murder intervals follow a power law (exponent 1.4), consistent with random walk return times (exponent 1.5).
Numerical simulations and data from two additional serial killers support the proposed model.

Conclusions:

The study provides a mathematical framework for understanding serial killer temporal activity.
Neuronal excitation exceeding a threshold, modeled as a random walk, explains inter-murder interval distributions.
The findings offer insights into the behavioral patterns of serial offenders.