1,063 research outputs found
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 illustrate analytical results by
numerical simulation. Time pattern activity data from two other serial killers
further substantiate our analysis
Why does attention to web articles fall with time?
We analyze access statistics of a hundred and fifty blog entries and news
articles, for periods of up to three years. Access rate falls as an inverse
power of time passed since publication. The power law holds for periods of up
to thousand days. The exponents are different for different blogs and are
distributed between 0.6 and 3.2. We argue that the decay of attention to a web
article is caused by the link to it first dropping down the list of links on
the website's front page, and then disappearing from the front page and its
subsequent movement further into background. The other proposed explanations
that use a decaying with time novelty factor, or some intricate theory of human
dynamics cannot explain all of the experimental observations.Comment: To appear in JASIS
Stochastic modeling of Congress
We analyze the dynamics of growth of the number of congressmen supporting the
resolution HR1207 to audit the Federal Reserve. The plot of the total number of
co-sponsors as a function of time is of "Devil's staircase" type. The
distribution of the numbers of new co-sponsors joining during a particular day
(step height) follows a power law. The distribution of the length of intervals
between additions of new co-sponsors (step length) also follows a power law. We
use a modification of Bak-Tang-Wiesenfeld sandpile model to simulate the
dynamics of Congress and obtain a good agreement with the data
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