11,295 research outputs found
Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data
Accurately modeling traffic speeds is a fundamental part of efficient
intelligent transportation systems. Nowadays, with the widespread deployment of
GPS-enabled devices, it has become possible to crowdsource the collection of
speed information to road users (e.g. through mobile applications or dedicated
in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced
speed data also brings very important challenges, such as the highly variable
measurement noise in the data due to a variety of driving behaviors and sample
sizes. When not properly accounted for, this noise can severely compromise any
application that relies on accurate traffic data. In this article, we propose
the use of heteroscedastic Gaussian processes (HGP) to model the time-varying
uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a
HGP conditioned on sample size and traffic regime (SRC-HGP), which makes use of
sample size information (probe vehicles per minute) as well as previous
observed speeds, in order to more accurately model the uncertainty in observed
speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we
empirically show that the proposed heteroscedastic models produce significantly
better predictive distributions when compared to current state-of-the-art
methods for both speed imputation and short-term forecasting tasks.Comment: 22 pages, Transportation Research Part C: Emerging Technologies
(Elsevier
Increasing powers in a degenerate parabolic logistic equation
The purpose of this paper is to study the asymptotic behavior of the positive
solutions of the problem as ,
where is a bounded domain and is a nonnegative function. We
deduce that the limiting configuration solves a parabolic obstacle problem, and
afterwards we fully describe its long time behavior.Comment: 15 page
Explosive synchronization enhanced by time-delayed coupling
We study the emergence of synchronization in scale-free networks by
considering the Kuramoto model of coupled phase oscillators. The natural
frequencies of oscillators are assumed to be correlated with their degrees and
a time delay is included in the system. This assumption allows enhancing the
explosive transition to reach the synchronous state. We provide an analytical
treatment developed in a star graph which reproduces results obtained in
scale-free networks. Our findings have important implications in understanding
the synchronization of complex networks, since the time delay is present in
most systems due to the finite speed of the signal transmission over a
distance.Comment: 5 pages, 7 figure
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