The ability to foresee the next moves of a user is crucial to ubiquitous computing. Disregarding major differences in individuals' routines, recent ground-breaking analysis on mobile phone data suggests high predictability in mobility. By nature, however, mobile phone data offer very low spatial and temporal resolutions. It remains largely unknown how the predictability changes with respect to different spatial/temporal scales. Using high-resolution GPS data, this paper investigates the scaling effects on predictability. Given specified spatial-temporal scales, recorded trajectories are encoded into long strings of distinct locations, and several information-theoretic measures of predictability are derived. Somewhat surprisingly, high predictability is still present at very high spatial/temporal resolutions. Moreover, the predictability is independent of the overall mobility area covered. This suggests highly regular mobility behaviors. Moreover, by varying the scales over a wide range, an invariance is observed which suggests that certain trade-offs between the predicting accuracy and spatial-temporal resolution are unavoidable. As many applications in ubiquitous computing concern mobility, these findings should have direct implications.

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Biased random walk has been studied extensively over the past decade especially in the transport and communication networks communities. The mean first passage time (MFPT) of a biased random walk is an important performance indicator in those domains. While the fundamental matrix approach gives precise solution to MFPT, the computation is expensive and the solution lacks interpretability. Other approaches based on the Mean Field Theory relate MFPT to the node degree alone. However, nodes with the same degree may have very different local weight distribution, which may result in vastly different MFPT. We derive an approximate bound to the MFPT of biased random walk with short relaxation time on complex network where the biases are controlled by arbitrarily assigned node weights. We show that the MFPT of a node in this general case is closely related to not only its node degree, but also its local weight distribution. The MFPTs obtained from computer simulations also agree with the new theoretical analysis. Our result enables fast estimation of MFPT, which is useful especially to differentiate between nodes that have very different local node weight distribution even though they share the same node degrees.

Previous studies suggest that human mobility is highly regular in two respects. Firstly, individual's travels are governed by occasional exploration of new locations and preferential return to most frequently visited locations. Secondly, human mobility sequences exhibit high predictability. The existing model [1] is able to mimic exploration and preferential return, and fit actual mobility data. However, the high predictability issue is not addressed in this model. In this paper, we derive an upper bound of the predictability manifested by this model. Motivated by the incorrigible gap between the bound and the empirical results shown in [2], we further propose a new Markovian model by modifying the rule of preferential return to be conditional on the individuals' current location. We show both theoretically and empirically that the new Markovian model presents high predictability while preserving the desirable scaling properties of the original model in [1], making it the most complete model to date in capturing the essence of human mobility.

Identifying nodes that play important roles in network dynamics in large scale complex networks is crucial for both characterizing the network and resource management. Under the viral marketing setting, Diffusion Centrality (DC) estimates the influential power of an individual. For the transport and physics communities, a node is considered important in Markov centrality (MC) if it can be quickly reached from the other nodes. Because these networks could contain millions of nodes, any ranking algorithm must have low time requirements to be practically useful. In this paper, we show that both metrics are strongly correlated, and we present a new method to enable fast estimation of the two metrics for large scale networks. The new approach is further validated empirically by using both real and synthetic networks. Our results refined the intuition that the influential power of an individual is largely governed by the local topology, rather than the mere number of contacts (node degree) alone. This allows us to better characterize the properties of the nodes that affect the outcome of the two centrality metrics.