Mathematical Serial Killers

Serial Killer Chart via ArXiv

Serial Killer Chart via ArXiv

Amazing new study shows that there may be a valid mathematical model for the cyclic serial killer. I’ll leave analysis of the neuroscience and brain chemistry to those better qualified than I, however it seems to me that this just reinforces the typical view of such killers. Don’t we all think that the need grows in them until they have to kill again? I really thought at least the world of fiction had gotten that point across, whether it is scientifically true or not.

Mikhail Simkin and Vwani Roychowdhury at the University of California, Los Angeles, release a mathematical analysis of Chikatilo’s pattern of behaviour. They say the behaviour is well characterised by a power law and that this is exactly what would be expected if Chikatilo’s behaviour is caused by a certain pattern of neuronal firing in the brain.

Their thinking is based on the fundamental behaviour of neurons. When a neuron fires, it cannot fire again until it has recharged, a time known as the refractory period.

Each neuron is connected to thousands of others. Some of these will also be ready to fire and so can be triggered by the first neuron. These in turn will be connected to more neurons and so on. So it’s easy to see how a chain reaction of firings can sweep through the brain if conditions are ripe.

But this by itself cannot explain a serial killer’s behaviour. “We cannot expect that the killer commits murder right at the moment when neural excitation reaches a certain threshold. He needs time to plan and prepare his crime,” say Simkin and Roychowdhury.

Instead, they suggest that a serial killer only commits murder after the threshold has been exceeded for a certain period of time.

They also assume that the murder has a sedative effect on the killer, causing the neuronal activity to drop below the threshold.

The ArXiv blog post above does a great job of summarizing the work, the Forbes and Slashdot summaries were also excellent but I do like to follow the trail of links back to the source, even if it is the open blog but paywalled research paper site ArXiv. What am I complaining about, half the time I can’t understand the summary of the paper I can’t get to to read. From the ArXiv summary:

We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of “Devil’s staircase” type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We confirm analytical results by numerical simulation.

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