A Dynamical Model of Twitter Activity Profiles

The advent of the era of Big Data has allowed many researchers to dig into various socio-technical systems, including social media platforms. In particular, these systems have provided them with certain verifiable means to look into certain aspects of human behavior. In this work, we are specifically interested in the behavior of individuals on social media platforms---how they handle the information they get, and how they share it. We look into Twitter to understand the dynamics behind the users' posting activities---tweets and retweets---zooming in on topics that peaked in popularity. Three mechanisms are considered: endogenous stimuli, exogenous stimuli, and a mechanism that dictates the decay of interest of the population in a topic. We propose a model involving two parameters $\eta^\star$ and $\lambda$ describing the tweeting behaviour of users, which allow us to reconstruct the findings of Lehmann et al. (2012) on the temporal profiles of popular Twitter hashtags. With this model, we are able to accurately reproduce the temporal profile of user engagements on Twitter. Furthermore, we introduce an alternative in classifying the collective activities on the socio-technical system based on the model.Comment: 10 pages, 5 figure

Simulating Congestion Dynamics of Train Rapid Transit using Smart Card Data

Investigating congestion in train rapid transit systems (RTS) in today's urban cities is a challenge compounded by limited data availability and difficulties in model validation. Here, we integrate information from travel smart card data, a mathematical model of route choice, and a full-scale agent-based model of the Singapore RTS to provide a more comprehensive understanding of the congestion dynamics than can be obtained through analytical modelling alone. Our model is empirically validated, and allows for close inspection of the dynamics including station crowdedness, average travel duration, and frequency of missed trains---all highly pertinent factors in service quality. Using current data, the crowdedness in all 121 stations appears to be distributed log-normally. In our preliminary scenarios, we investigate the effect of population growth on service quality. We find that the current population (2 million) lies below a critical point; and increasing it beyond a factor of $\sim10\%$ leads to an exponential deterioration in service quality. We also predict that incentivizing commuters to avoid the most congested hours can bring modest improvements to the service quality provided the population remains under the critical point. Finally, our model can be used to generate simulated data for analytical modelling when such data are not empirically available, as is often the case.Comment: 10 pages, 5 figures, submitted to International Conference on Computational Science 201

Allelomimesis as universal clustering mechanism for complex adaptive systems

Animal and human clusters are complex adaptive systems and many are organized in cluster sizes $s$ that obey the frequency-distribution $D(s)\propto s^{-\tau}$. Exponent $\tau$ describes the relative abundance of the cluster sizes in a given system. Data analyses have revealed that real-world clusters exhibit a broad spectrum of $\tau$-values, $0.7\textrm{(tuna fish schools)}\leq\tau\leq 2.95\textrm{(galaxies)}$. We show that allelomimesis is a fundamental mechanism for adaptation that accurately explains why a broad spectrum of $\tau$-values is observed in animate, human and inanimate cluster systems. Previous mathematical models could not account for the phenomenon. They are hampered by details and apply only to specific systems such as cities, business firms or gene family sizes. Allelomimesis is the tendency of an individual to imitate the actions of its neighbors and two cluster systems yield different $\tau$ values if their component agents display different allelomimetic tendencies. We demonstrate that allelomimetic adaptation are of three general types: blind copying, information-use copying, and non-copying. Allelomimetic adaptation also points to the existence of a stable cluster size consisting of three interacting individuals.Comment: 8 pages, 5 figures, 2 table