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

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

Higher order clustering coefficients in Barabasi-Albert networks

Higher order clustering coefficients $C(x)$ are introduced for random networks. The coefficients express probabilities that the shortest distance between any two nearest neighbours of a certain vertex $i$ equals $x$, when one neglects all paths crossing the node $i$. Using $C(x)$ 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 $m$. 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

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