5,841 research outputs found
Fast recursive filters for simulating nonlinear dynamic systems
A fast and accurate computational scheme for simulating nonlinear dynamic
systems is presented. The scheme assumes that the system can be represented by
a combination of components of only two different types: first-order low-pass
filters and static nonlinearities. The parameters of these filters and
nonlinearities may depend on system variables, and the topology of the system
may be complex, including feedback. Several examples taken from neuroscience
are given: phototransduction, photopigment bleaching, and spike generation
according to the Hodgkin-Huxley equations. The scheme uses two slightly
different forms of autoregressive filters, with an implicit delay of zero for
feedforward control and an implicit delay of half a sample distance for
feedback control. On a fairly complex model of the macaque retinal horizontal
cell it computes, for a given level of accuracy, 1-2 orders of magnitude faster
than 4th-order Runge-Kutta. The computational scheme has minimal memory
requirements, and is also suited for computation on a stream processor, such as
a GPU (Graphical Processing Unit).Comment: 20 pages, 8 figures, 1 table. A comparison with 4th-order Runge-Kutta
integration shows that the new algorithm is 1-2 orders of magnitude faster.
The paper is in press now at Neural Computatio
ВІДНОВЛЕННЯ ДИНАМІЧНИХ СПОТВОРЕНЬ ВИХІДНОГО КАНАЛУ, ПЕРЕДАЧЕЮ БЕЗПЕРЕРВНИХ СИГНАЛІВ
Signal restoring algorithms, subjected to essential dynamic distortions in channels transmitting continuous signals in conditions of noise availability are considered in this paper. It is shown, that the application of developed algorithms digital filtration made possible to avoid unstable operation of operator inversion of the channel. For maintenance stability of the delivered problem solution with the purpose of maximum use additional a priory information on required signal and noise regularization methods of ill posed problems are used. Some results of computer experiments are shown.Signal restoring algorithms, subjected to essential dynamic distortions in channels transmitting continuous signals in conditions of noise availability are considered in this paper. It is shown, that the application of developed algorithms digital filtration made possible to avoid unstable operation of operator inversion of the channel. For maintenance stability of the delivered problem solution with the purpose of maximum use additional a priory information on required signal and noise regularization methods of ill posed problems are used. Some results of computer experiments are shown
Recursive Monte Carlo filters: Algorithms and theoretical analysis
Recursive Monte Carlo filters, also called particle filters, are a powerful
tool to perform computations in general state space models. We discuss and
compare the accept--reject version with the more common sampling importance
resampling version of the algorithm. In particular, we show how auxiliary
variable methods and stratification can be used in the accept--reject version,
and we compare different resampling techniques. In a second part, we show laws
of large numbers and a central limit theorem for these Monte Carlo filters by
simple induction arguments that need only weak conditions. We also show that,
under stronger conditions, the required sample size is independent of the
length of the observed series.Comment: Published at http://dx.doi.org/10.1214/009053605000000426 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fusing Loop and GPS Probe Measurements to Estimate Freeway Density
In an age of ever-increasing penetration of GPS-enabled mobile devices, the
potential of real-time "probe" location information for estimating the state of
transportation networks is receiving increasing attention. Much work has been
done on using probe data to estimate the current speed of vehicle traffic (or
equivalently, trip travel time). While travel times are useful to individual
drivers, the state variable for a large class of traffic models and control
algorithms is vehicle density. Our goal is to use probe data to supplement
traditional, fixed-location loop detector data for density estimation. To this
end, we derive a method based on Rao-Blackwellized particle filters, a
sequential Monte Carlo scheme. We present a simulation where we obtain a 30\%
reduction in density mean absolute percentage error from fusing loop and probe
data, vs. using loop data alone. We also present results using real data from a
19-mile freeway section in Los Angeles, California, where we obtain a 31\%
reduction. In addition, our method's estimate when using only the real-world
probe data, and no loop data, outperformed the estimate produced when only loop
data were used (an 18\% reduction). These results demonstrate that probe data
can be used for traffic density estimation
Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation
Parameter inference is a fundamental problem in data-driven modeling. Given
observed data that is believed to be a realization of some parameterized model,
the aim is to find parameter values that are able to explain the observed data.
In many situations, the dominant sources of uncertainty must be included into
the model, for making reliable predictions. This naturally leads to stochastic
models. Stochastic models render parameter inference much harder, as the aim
then is to find a distribution of likely parameter values. In Bayesian
statistics, which is a consistent framework for data-driven learning, this
so-called posterior distribution can be used to make probabilistic predictions.
We propose a novel, exact and very efficient approach for generating posterior
parameter distributions, for stochastic differential equation models calibrated
to measured time-series. The algorithm is inspired by re-interpreting the
posterior distribution as a statistical mechanics partition function of an
object akin to a polymer, where the measurements are mapped on heavier beads
compared to those of the simulated data. To arrive at distribution samples, we
employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale
integration. A separation of time scales naturally arises if either the number
of measurement points or the number of simulation points becomes large.
Furthermore, at least for 1D problems, we can decouple the harmonic modes
between measurement points and solve the fastest part of their dynamics
analytically. Our approach is applicable to a wide range of inference problems
and is highly parallelizable.Comment: 15 pages, 8 figure
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