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