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Congestion and Carbon Emissions
Published in Donald L. Fisher, William J. Horrey, John D. Lee, Michael A. Regan, Handbook of Human Factors for Automated, Connected, and Intelligent Vehicles, 2020
Konstantinos V. Katsikopoulos, Ana Paula Bortoleto
Mainstream transportation theory employs game theory in order to describe and prescribe the behavioral aspects of traffic management systems, including parking management systems. Nevertheless, as noted above, it might be that parking behavior is better described by simple rules of thumb (Hester et al., 2002). More surprisingly, it might also be that such simple parking behavior in fact leads to better system performance than the purported “optimal” parking behavior suggested by game theory, as the following study found.
Modelling acute myeloid leukaemia in a continuum of differentiation states
Published in Letters in Biomathematics, 2018
H. Cho, K. Ayers, L. de Pills, Y.-H. Kuo, J. Park, A. Radunskaya, R. C. Rockne
Schiebinger et al. (2017) have proposed a model and algorithm for constructing a directed graph oriented in pseudotime given temporal data. The OT algorithm itself is a classical problem studied in the mathematical area of Transportation Theory, which aims to optimally transport and allocate resources given certain cost functions. Schiebinger et al. (2017) apply this theory to a time series of reduced dimension single-cell gene expression profiles. The time series is made up of a sequence of samples , at different times for . Suppose that each sample consists of points in . A distribution is defined by each sample . For each set : where represents a Delta Distribution centred at x: Together, as a sequence, these inferred distributions form what is known as an ‘empirical developmental process’. The goal is then to determine, as closely as possible, what the true underlying Markov developmental process is by examining what are known as transport maps between pairs and . A transport map for a pair is a distribution π defined on such that and are the two marginal distributions of π. Thus, given a function that represents the cost to transport some unit mass from x to y, the goal is to minimize subject to Schienbinger et al. further refine this algorithm by including a growth term in their transport plan to allow for cellular proliferation between time points. This differs from the classical OT algorithm in that the classical OT algorithm is formulated with conservation of mass in mind. OT can thus be used to estimate the ancestors and descendants of a set of cells. Cells are clustered using the Louvain-Jaccard community detection algorithm on the reduced dimension gene expression data in 20-dimensional space. Schienbinger et al. thus identified 33 cell nodes, which were then used as starting populations from which developmental trajectories could be analysed. These can be thought of as nodes on a graph visualized with force-directed layout embedding, and edges represent the motion in pseudotime.