Phase transitions in Paradigm models

In this letter we propose two general models for paradigm shift, deterministic propagation model (DM) and stochastic propagation model (SM). By defining the order parameter $m$ based on the diversity of ideas, $\Delta$, we study when and how the transition occurs as a cost $C$ in DM or an innovation probability $\alpha$ in SM increases. In addition, we also investigate how the propagation processes affect on the transition nature. From the analytical calculations and numerical simulations $m$ is shown to satisfy the scaling relation $m=1-f(C/N)$ for DM with the number of agents $N$. In contrast, $m$ in SM scales as $m=1-f(\alpha^a N)$.Comment: 5 pages, 3 figure

Quantifying discrepancies in opinion spectra from online and offline networks

Online social media such as Twitter are widely used for mining public opinions and sentiments on various issues and topics. The sheer volume of the data generated and the eager adoption by the online-savvy public are helping to raise the profile of online media as a convenient source of news and public opinions on social and political issues as well. Due to the uncontrollable biases in the population who heavily use the media, however, it is often difficult to measure how accurately the online sphere reflects the offline world at large, undermining the usefulness of online media. One way of identifying and overcoming the online-offline discrepancies is to apply a common analytical and modeling framework to comparable data sets from online and offline sources and cross-analyzing the patterns found therein. In this paper we study the political spectra constructed from Twitter and from legislators' voting records as an example to demonstrate the potential limits of online media as the source for accurate public opinion mining.Comment: 10 pages, 4 figure

Diffusive Capture Process on Complex Networks

We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the life time $of a lamb scales as \sim N$ and the survival probability $S(N\to \infty,t)$ becomes finite on scale-free networks with degree exponent $\gamma>3$. However, $S(N,t)$ for $\gamma<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree$k$,$n(k)$, decreases as$n(k)\sim k^{-\sigma}$. When$\gamma<3$,$n(k)$still increases anomalously for$k\approx k_{max}$. We analytically show that$n(k)$satisfies the relation$n(k)\sim k^2P(k)$and the total number of capture events$N_{tot}$is proportional to$, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $.Comment: 9 pages, 6 figure

Diffusive capture processes for information search

We show how effectively the diffusive capture processes (DCP) on complex networks can be applied to information search in the networks. Numerical simulations show that our method generates only 2% of traffic compared with the most popular flooding-based query-packet-forwarding (FB) algorithm. We find that the average searching time, , of the our model is more scalable than another well known $n$-random walker model and comparable to the FB algorithm both on real Gnutella network and scale-free networks with $\gamma =2.4$. We also discuss the possible relationship between and $$, the second moment of the degree distribution of the networks