405,718 research outputs found
Stochastic dynamics and the predictability of big hits in online videos
The competition for the attention of users is a central element of the
Internet. Crucial issues are the origin and predictability of big hits, the few
items that capture a big portion of the total attention. We address these
issues analyzing 10 million time series of videos' views from YouTube. We find
that the average gain of views is linearly proportional to the number of views
a video already has, in agreement with usual rich-get-richer mechanisms and
Gibrat's law, but this fails to explain the prevalence of big hits. The reason
is that the fluctuations around the average views are themselves heavy tailed.
Based on these empirical observations, we propose a stochastic differential
equation with L\'evy noise as a model of the dynamics of videos. We show how
this model is substantially better in estimating the probability of an ordinary
item becoming a big hit, which is considerably underestimated in the
traditional proportional-growth models.Comment: Manuscript (8 pages and 5 figures
Relations between a typical scale and averages in the breaking of fractal distribution
We study distributions which have both fractal and non-fractal scale regions
by introducing a typical scale into a scale invariant system. As one of models
in which distributions follow power law in the large scale region and deviate
further from the power law in the smaller scale region, we employ 2-dim quantum
gravity modified by the term. As examples of distributions in the real
world which have similar property to this model, we consider those of personal
income in Japan over latest twenty fiscal years. We find relations between the
typical scale and several kinds of averages in this model, and observe that
these relations are also valid in recent personal income distributions in Japan
with sufficient accuracy. We show the existence of the fiscal years so called
bubble term in which the gap has arisen in power law, by observing that the
data are away from one of these relations. We confirm, therefore, that the
distribution of this model has close similarity to those of personal income. In
addition, we can estimate the value of Pareto index and whether a big gap
exists in power law by using only these relations. As a result, we point out
that the typical scale is an useful concept different from average value and
that the distribution function derived in this model is an effective tool to
investigate these kinds of distributions.Comment: 17 pages, latex, 13 eps figure
A Taste of Cosmology
This is the summary of two lectures that aim to give an overview of
cosmology. I will not try to be too rigorous in derivations, nor to give a full
historical overview. The idea is to provide a "taste" of cosmology and some of
the interesting topics it covers. The standard cosmological model is presented
and I highlight the successes of cosmology over the past decade or so. Keys to
the development of the standard cosmological model are observations of the
cosmic microwave background and of large-scale structure, which are introduced.
Inflation and dark energy and the outlook for the future are also discussed.
Slides from the lectures are available from the school website:
physicschool.web.cern.ch/PhysicSchool/CLASHEP/CLASHEP2011/.Comment: 16 pages, contribution to the 2011 CERN-Latin-American School of
High-Energy Physics, Natal, Brazil, 23 March-5 April 2011, edited by C.
Grojean, M. Mulders and M. Spiropul
Big data analyses reveal patterns and drivers of the movements of southern elephant seals
The growing number of large databases of animal tracking provides an
opportunity for analyses of movement patterns at the scales of populations and
even species. We used analytical approaches, developed to cope with big data,
that require no a priori assumptions about the behaviour of the target agents,
to analyse a pooled tracking dataset of 272 elephant seals (Mirounga leonina)
in the Southern Ocean, that was comprised of >500,000 location estimates
collected over more than a decade. Our analyses showed that the displacements
of these seals were described by a truncated power law distribution across
several spatial and temporal scales, with a clear signature of directed
movement. This pattern was evident when analysing the aggregated tracks despite
a wide diversity of individual trajectories. We also identified marine
provinces that described the migratory and foraging habitats of these seals.
Our analysis provides evidence for the presence of intrinsic drivers of
movement, such as memory, that cannot be detected using common models of
movement behaviour. These results highlight the potential for big data
techniques to provide new insights into movement behaviour when applied to
large datasets of animal tracking.Comment: 18 pages, 5 figures, 6 supplementary figure
Data Modeling with Large Random Matrices in a Cognitive Radio Network Testbed: Initial Experimental Demonstrations with 70 Nodes
This short paper reports some initial experimental demonstrations of the
theoretical framework: the massive amount of data in the large-scale cognitive
radio network can be naturally modeled as (large) random matrices. In
particular, using experimental data we will demonstrate that the empirical
spectral distribution of the large sample covariance matrix---a Hermitian
random matrix---agree with its theoretical distribution (Marchenko-Pastur law).
On the other hand, the eigenvalues of the large data matrix ---a non-Hermitian
random matrix---are experimentally found to follow the single ring law, a
theoretical result that has been discovered relatively recently. To our best
knowledge, our paper is the first such attempt, in the context of large-scale
wireless network, to compare theoretical predictions with experimental
findings.Comment: 4 pages, 11 figure
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