Understanding the impact of network structure on air travel pattern at different scales.

This study examines the global air travel demand pattern using complex network analysis. Using the data for the top 50 airports based on passenger volume rankings, we investigate the relationship between network measures of nodes (airports) in the global flight network and their passenger volume. The analysis explores the network measures at various spatial scales, from individual airports to metropolitan areas and countries. Different attributes, such as flight route length and the number of airlines, are considered in the analysis. Certain attributes are found to be more relevant than others, and specific network measure models are found to better capture the dynamics of global air travel demand than others. Among the models, PageRank is found to be the most correlated with total passenger volume. Moreover, distance-based measures perform worse than the ones emphasising the number of airlines, particularly those counting the number of airlines operating a route, including codeshare. Using the PageRank score weighted by the number of airlines, we find that airports in Asian cities tend to have more traffic than expected, while European and North American airports have the potential to attract more passenger volume given their connectivity pattern. Additionally, we combine the network measures with socio-economic variables such as population and GDP to show that the network measures could greatly augment the traditional approaches to modelling and predicting air travel demand. We'll also briefly discuss the implications of the findings in this study for airport planning and airline industry strategy.

Spatial point pattern and urban morphology: Perspectives from entropy, complexity, and networks.

Spatial organization of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects of the system. In this work, a framework to characterize the spatial pattern of urban locations based on the idea of entropy maximization is proposed. Three spatial length scales in the system with discerning interpretations in terms of the spatial arrangement of the locations are calculated. Using these length scales, two quantities are introduced to quantify the system's spatial pattern, namely, mass decoherence and space decoherence, whose combination enables the comparison of different cities in the world. The comparison reveals different types of urban morphology that could be attributed to the cities' geographical background and development status.

The complexity of sequences generated by the arc-fractal system.

We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs.

Abelian Manna model in three dimensions and below.

The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration, and area distribution of the model are obtained by using a high-accuracy moment analysis. Together with earlier results on lower-dimensional lattices, the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the coefficients of an ε expansion. By rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension, a remarkable relation is observed, satisfied by both regular and fractal lattices.

Abelian Manna model on two fractal lattices.

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension d(g)=ln 3/ln 2, with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2-τ)=d(w) generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where d(w)=2. Furthermore, we observe that the lattice dimension d(g), the fractal dimension of the random walk on the lattice d(w), and the critical exponent D form a plane in three-dimensional parameter space, i.e., they obey the linear relationship D=0.632(3)d(g)+0.98(1)d(w)-0.49(3).