Tuesday, January 17, 2012

Mathematicians Reveal Serial Killer's Pattern of Murder: A Simple Mathematical Model of the Brain Explains the Pattern of Murders by a Serial Killer Say Researchers

Stochastic modeling of a serial killer
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.
Subjects: Physics and Society (physics.soc-ph); Neurons and Cognition (q-bio.NC)
Cite as: arXiv:1201.2458v1 [physics.soc-ph]

""On 20 November 1990, Andrei Chikatilo was arrested in Rostov, a Russian state bordering the Ukraine. After nine days in custody, Chikatilo confessed to the murder of 36 girls, boys and women over a 12 year period. He later confessed to a further 20 murders, making him one of the most prolific serial killers in modern history.

Today, 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.

Simkin and Roychowdhury used their model to simulate the pattern of firing in a brain to see how often it surpasses a given threshold long enough for a murder to take place.""

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