3,199 research outputs found
Human Dynamics: The Correspondence Patterns of Darwin and Einstein
While living in different historical era, Charles Darwin (1809-1882) and
Albert Einstein (1879-1955) were both prolific correspondents: Darwin sent
(received) at least 7,591 (6,530) letters during his lifetime while Einstein
sent (received) over 14,500 (16,200). Before email scientists were part of an
extensive university of letters, the main venue for exchanging new ideas and
results. But were the communication patterns of the pre-email times any
different from the current era of instant access? Here we show that while the
means have changed, the communication dynamics has not: Darwin's and Einstein's
pattern of correspondence and today's electronic exchanges follow the same
scaling laws. Their communication belongs, however, to a different universality
class from email communication, providing evidence for a new class of phenomena
capturing human dynamics.Comment: Supplementary Information available at http://www.nd.edu/~network
Higher order clustering coefficients in Barabasi-Albert networks
Higher order clustering coefficients are introduced for random
networks. The coefficients express probabilities that the shortest distance
between any two nearest neighbours of a certain vertex equals , when one
neglects all paths crossing the node . Using we found that in the
Barab\'{a}si-Albert (BA) model the average shortest path length in a node's
neighbourhood is smaller than the equivalent quantity of the whole network and
the remainder depends only on the network parameter . Our results show that
small values of the standard clustering coefficient in large BA networks are
due to random character of the nearest neighbourhood of vertices in such
networks.Comment: 10 pages, 4 figure
Citation Statistics from 110 Years of Physical Review
Publicly available data reveal long-term systematic features about citation
statistics and how papers are referenced. The data also tell fascinating
citation histories of individual articles.Comment: This is esssentially identical to the article that appeared in the
June 2005 issue of Physics Toda
Corrugated waveguide under scaling investigation
Some scaling properties for classical light ray dynamics inside a
periodically corrugated waveguide are studied by use of a simplified
two-dimensional nonlinear area-preserving map. It is shown that the phase space
is mixed. The chaotic sea is characterized using scaling arguments revealing
critical exponents connected by an analytic relationship. The formalism is
widely applicable to systems with mixed phase space, and especially in studies
of the transition from integrability to non-integrability, including that in
classical billiard problems.Comment: A complete list of my papers can be found in:
http://www.rc.unesp.br/igce/demac/denis
Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings
By using a semi-analytical dynamical mean-field approximation previously
proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we
have studied the synchronization of stochastic, small-world (SW) networks of
FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity
between results for {\it diffusive} and {\it sigmoid} couplings have been
discussed. It has been shown that with introducing the weak heterogeneity to
regular networks, the synchronization may be slightly increased for diffusive
couplings, while it is decreased for sigmoid couplings. This increase in the
synchronization for diffusive couplings is shown to be due to their local,
negative feedback contributions, but not due to the shorten average distance in
SW networks. Synchronization of SW networks depends not only on their structure
but also on the type of couplings.Comment: 17 pages, 8 figures, accepted in Phys. Rev. E with some change
On the Geometric Principles of Surface Growth
We introduce a new equation describing epitaxial growth processes. This
equation is derived from a simple variational geometric principle and it has a
straightforward interpretation in terms of continuum and microscopic physics.
It is also able to reproduce the critical behavior already observed, mound
formation and mass conservation, but however does not fit a divergence form as
the most commonly spread models of conserved surface growth. This formulation
allows us to connect the results of the dynamic renormalization group analysis
with intuitive geometric principles, whose generic character may well allow
them to describe surface growth and other phenomena in different areas of
physics
The Sznajd Consensus Model with Continuous Opinions
In the consensus model of Sznajd, opinions are integers and a randomly chosen
pair of neighbouring agents with the same opinion forces all their neighbours
to share that opinion. We propose a simple extension of the model to continuous
opinions, based on the criterion of bounded confidence which is at the basis of
other popular consensus models. Here the opinion s is a real number between 0
and 1, and a parameter \epsilon is introduced such that two agents are
compatible if their opinions differ from each other by less than \epsilon. If
two neighbouring agents are compatible, they take the mean s_m of their
opinions and try to impose this value to their neighbours. We find that if all
neighbours take the average opinion s_m the system reaches complete consensus
for any value of the confidence bound \epsilon. We propose as well a weaker
prescription for the dynamics and discuss the corresponding results.Comment: 11 pages, 4 figures. To appear in International Journal of Modern
Physics
Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface
We investigate the statistics of Iso-height lines of (2+1)-dimensional
Kardar-Parisi-Zhang model at different level sets around the mean height in the
saturation regime. We find that the exponent describing the distribution of the
height-cluster size behaves differently for level cuts above and below the mean
height, while the fractal dimensions of the height-clusters and their
perimeters remain unchanged. The winding angle statistics also confirms again
the conformal invariance of these contour lines in the same universality class
of self-avoiding random walks (SAWs).Comment: 5 pages, 5 figure
On the Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann
In the consensus model of Krause-Hegselmann, opinions are real numbers
between 0 and 1 and two agents are compatible if the difference of their
opinions is smaller than the confidence bound parameter \epsilon. A randomly
chosen agent takes the average of the opinions of all neighbouring agents which
are compatible with it. We propose a conjecture, based on numerical evidence,
on the value of the consensus threshold \epsilon_c of this model. We claim that
\epsilon_c can take only two possible values, depending on the behaviour of the
average degree d of the graph representing the social relationships, when the
population N goes to infinity: if d diverges when N goes to infinity,
\epsilon_c equals the consensus threshold \epsilon_i ~ 0.2 on the complete
graph; if instead d stays finite when N goes to infinity, \epsilon_c=1/2 as for
the model of Deffuant et al.Comment: 15 pages, 7 figures, to appear in International Journal of Modern
Physics C 16, issue 2 (2005
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