Modelling the scaling properties of human mobility
Chaoming Song,Chaoming Song,Tal Koren,Tal Koren,Pu Wang,Pu Wang,Albert-László Barabási,Albert-László Barabási,Albert-László Barabási +8 more
TL;DR: Empirical data is used to show that the predictions of the CTRW models are in systematic conflict with the empirical results, and two principles that govern human trajectories are introduced, allowing for a statistically self-consistent microscopic model for individual human mobility.
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Abstract: Individual human trajectories are characterized by fat-tailed distributions of jump sizes and waiting times, suggesting the relevance of continuous-time random-walk (CTRW) models for human mobility. However, human traces are barely random. Given the importance of human mobility, from epidemic modelling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile-phone traces, to show that the predictions of the CTRW models are in systematic conflict with the empirical results. We introduce two principles that govern human trajectories, allowing us to build a statistically self-consistent microscopic model for individual human mobility. The model accounts for the empirically observed scaling laws, but also allows us to analytically predict most of the pertinent scaling exponents.
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An introduction to probability theory and its applications - 3/E. volume 3
William Feller
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Abstract: The classic text for understanding complex statistical probability An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivreLaplace theorem.
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The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
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Understanding individual human mobility patterns
Marta C. González,A R Cesar Hidalgo,A R Cesar Hidalgo,Albert-László Barabási,Albert-László Barabási,Albert-László Barabási +5 more
TL;DR: In this article, the authors study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period and find that the individual travel patterns collapse into a single spatial probability distribution, indicating that humans follow simple reproducible patterns.
Limits of Predictability in Human Mobility
Chaoming Song,Zehui Qu,Zehui Qu,Nicholas Blumm,Nicholas Blumm,Albert-László Barabási,Albert-László Barabási +6 more
TL;DR: Analysis of the trajectories of people carrying cell phones reveals that human mobility patterns are highly predictable, and a remarkable lack of variability in predictability is found, which is largely independent of the distance users cover on a regular basis.
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