5,958 research outputs found
Inter-vehicle gap statistics on signal-controlled crossroads
We investigate a microscopical structure in a chain of cars waiting at a red
signal on signal-controlled crossroads. Presented is an one-dimensional
space-continuous thermodynamical model leading to an excellent agreement with
the data measured.Moreover, we demonstrate that an inter-vehicle spacing
distribution disclosed in relevant traffic data agrees with the thermal-balance
distribution of particles in the thermodynamical traffic gas (discussed in [1])
with a high inverse temperature (corresponding to a strong traffic congestion).
Therefore, as we affirm, such a system of stationary cars can be understood as
a specific state of the traffic sample operating inside a congested traffic
stream.Comment: 6 pages, 4 figures, accepted for publication in J. Phys. A: Math.
Theo
Reversible Jump Metropolis Light Transport using Inverse Mappings
We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample
space and their interactions with multiple sampling techniques. We observe that
incorporating the sampling technique into the state of the Markov Chain, as
done in Multiplexed Metropolis Light Transport (MMLT), impedes the ability of
the chain to properly explore the path space, as transitions between sampling
techniques lead to disruptive alterations of path samples. To address this
issue, we reformulate Multiplexed MLT in the Reversible Jump MCMC framework
(RJMCMC) and introduce inverse sampling techniques that turn light paths into
the random numbers that would produce them. This allows us to formulate a novel
perturbation that can locally transition between sampling techniques without
changing the geometry of the path, and we derive the correct acceptance
probability using RJMCMC. We investigate how to generalize this concept to
non-invertible sampling techniques commonly found in practice, and introduce
probabilistic inverses that extend our perturbation to cover most sampling
methods found in light transport simulations. Our theory reconciles the
inverses with RJMCMC yielding an unbiased algorithm, which we call Reversible
Jump MLT (RJMLT). We verify the correctness of our implementation in canonical
and practical scenarios and demonstrate improved temporal coherence, decrease
in structured artifacts, and faster convergence on a wide variety of scenes
Locating and quantifying gas emission sources using remotely obtained concentration data
We describe a method for detecting, locating and quantifying sources of gas
emissions to the atmosphere using remotely obtained gas concentration data; the
method is applicable to gases of environmental concern. We demonstrate its
performance using methane data collected from aircraft. Atmospheric point
concentration measurements are modelled as the sum of a spatially and
temporally smooth atmospheric background concentration, augmented by
concentrations due to local sources. We model source emission rates with a
Gaussian mixture model and use a Markov random field to represent the
atmospheric background concentration component of the measurements. A Gaussian
plume atmospheric eddy dispersion model represents gas dispersion between
sources and measurement locations. Initial point estimates of background
concentrations and source emission rates are obtained using mixed L2-L1
optimisation over a discretised grid of potential source locations. Subsequent
reversible jump Markov chain Monte Carlo inference provides estimated values
and uncertainties for the number, emission rates and locations of sources
unconstrained by a grid. Source area, atmospheric background concentrations and
other model parameters are also estimated. We investigate the performance of
the approach first using a synthetic problem, then apply the method to real
data collected from an aircraft flying over: a 1600 km^2 area containing two
landfills, then a 225 km^2 area containing a gas flare stack
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