1,509 research outputs found
Excitable human dynamics driven by extrinsic events in massive communities
Using empirical data from a social media site (Twitter) and on trading
volumes of financial securities, we analyze the correlated human activity in
massive social organizations. The activity, typically excited by real-world
events and measured by the occurrence rate of international brand names and
trading volumes, is characterized by intermittent fluctuations with bursts of
high activity separated by quiescent periods. These fluctuations are broadly
distributed with an inverse cubic tail and have long-range temporal
correlations with a power spectrum. We describe the activity by a
stochastic point process and derive the distribution of activity levels from
the corresponding stochastic differential equation. The distribution and the
corresponding power spectrum are fully consistent with the empirical
observations.Comment: 9 pages, 3 figure
Ecosystems with mutually exclusive interactions self-organize to a state of high diversity
Ecological systems comprise an astonishing diversity of species that
cooperate or compete with each other forming complex mutual dependencies. The
minimum requirements to maintain a large species diversity on long time scales
are in general unknown. Using lichen communities as an example, we propose a
model for the evolution of mutually excluding organisms that compete for space.
We suggest that chain-like or cyclic invasions involving three or more species
open for creation of spatially separated sub-populations that subsequently can
lead to increased diversity. In contrast to its non-spatial counterpart, our
model predicts robust co-existence of a large number of species, in accordance
with observations on lichen growth. It is demonstrated that large species
diversity can be obtained on evolutionary timescales, provided that
interactions between species have spatial constraints. In particular, a phase
transition to a sustainable state of high diversity is identified.Comment: 4 pages, 4 figure
Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes
We propose a dynamical scheme for the combined processes of fragmentation and
merging as a model system for cluster dynamics in nature and society displaying
scale invariant properties. The clusters merge and fragment with rates
proportional to their sizes, conserving the total mass. The total number of
clusters grows continuously but the full time-dependent distribution can be
rescaled over at least 15 decades onto a universal curve which we derive
analytically. This curve includes a scale free solution with a scaling exponent
of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure
Persistent punishment : users views of short prison sentences
Semi-structured interviews were conducted of 22 prisoners to gather information about the characteristic features of short prison sentences. Themes raised in comments included: the frequency and quality of sentences, addiction, family, and penal legitimacy. Most of the participants had extensive experience of prison, and the effects of this played out across sentences and years, accumulating and amplifying impacts. And, despite expressions of guilt and remorse, most participants saw their sentence as unjust, and mainly a reaction to offending history. We conclude by suggesting the need for research to shift focus from evaluating individual penal interventions towards more holistic and narrative accounts that cut across sentences
Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature
We investigate systems of nature where the common physical processes
diffusion and fragmentation compete. We derive a rate equation for the size
distribution of fragments. The equation leads to a third order differential
equation which we solve exactly in terms of Bessel functions. The stationary
state is a universal Bessel distribution described by one parameter, which fits
perfectly experimental data from two very different system of nature, namely,
the distribution of ice crystal sizes from the Greenland ice sheet and the
length distribution of alpha-helices in proteins.Comment: 4 pages, 3 figures, (minor changes
Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model
We show that the fractal growth described by the dielectric breakdown model
exhibits a phase transition in the multifractal spectrum of the growth measure.
The transition takes place because the tip-splitting of branches forms a fixed
angle. This angle is eta dependent but it can be rescaled onto an
``effectively'' universal angle of the DLA branching process. We derive an
analytic rescaling relation which is in agreement with numerical simulations.
The dimension of the clusters decreases linearly with the angle and the growth
becomes non-fractal at an angle close to 74 degrees (which corresponds to eta=
4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure
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