1,412 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
Algorithmic Cooling of Spins: A Practicable Method for Increasing Polarization
An efficient technique to generate ensembles of spins that are highly
polarized by external magnetic fields is the Holy Grail in Nuclear Magnetic
Resonance (NMR) spectroscopy. Since spin-half nuclei have steady-state
polarization biases that increase inversely with temperature, spins exhibiting
high polarization biases are considered cool, even when their environment is
warm. Existing spin-cooling techniques are highly limited in their efficiency
and usefulness. Algorithmic cooling is a promising new spin-cooling approach
that employs data compression methods in open systems. It reduces the entropy
of spins on long molecules to a point far beyond Shannon's bound on reversible
entropy manipulations (an information-theoretic version of the 2nd Law of
Thermodynamics), thus increasing their polarization. Here we present an
efficient and experimentally feasible algorithmic cooling technique that cools
spins to very low temperatures even on short molecules. This practicable
algorithmic cooling could lead to breakthroughs in high-sensitivity NMR
spectroscopy in the near future, and to the development of scalable NMR quantum
computers in the far future. Moreover, while the cooling algorithm itself is
classical, it uses quantum gates in its implementation, thus representing the
first short-term application of quantum computing devices.Comment: 24 pages (with annexes), 3 figures (PS). This version contains no
major content changes: fixed bibliography & figures, modified
acknowledgement
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