24,238 research outputs found
Bayesian Nonparametric Inference of Switching Linear Dynamical Systems
Many complex dynamical phenomena can be effectively modeled by a system that
switches among a set of conditionally linear dynamical modes. We consider two
such models: the switching linear dynamical system (SLDS) and the switching
vector autoregressive (VAR) process. Our Bayesian nonparametric approach
utilizes a hierarchical Dirichlet process prior to learn an unknown number of
persistent, smooth dynamical modes. We additionally employ automatic relevance
determination to infer a sparse set of dynamic dependencies allowing us to
learn SLDS with varying state dimension or switching VAR processes with varying
autoregressive order. We develop a sampling algorithm that combines a truncated
approximation to the Dirichlet process with efficient joint sampling of the
mode and state sequences. The utility and flexibility of our model are
demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA
stock index, and a maneuvering target tracking application.Comment: 50 pages, 7 figure
L\'{e}vy flights in inhomogeneous environments
We study the long time asymptotics of probability density functions (pdfs) of
L\'{e}vy flights in different confining potentials. For that we use two models:
Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics.
It turns out that the semigroup modeling provides much stronger confining
properties than the standard Langevin one. Since contractive semigroups set a
link between L\'{e}vy flights and fractional (pseudo-differential) Hamiltonian
systems, we can use the latter to control the long - time asymptotics of the
pertinent pdfs. To do so, we need to impose suitable restrictions upon the
Hamiltonian and its potential. That provides verifiable criteria for an
invariant pdf to be actually an asymptotic pdf of the semigroup-driven
jump-type process. For computational and visualization purposes our
observations are exemplified for the Cauchy driver and its response to external
polynomial potentials (referring to L\'{e}vy oscillators), with respect to both
dynamical mechanisms.Comment: Major revisio
On Reduced Input-Output Dynamic Mode Decomposition
The identification of reduced-order models from high-dimensional data is a
challenging task, and even more so if the identified system should not only be
suitable for a certain data set, but generally approximate the input-output
behavior of the data source. In this work, we consider the input-output dynamic
mode decomposition method for system identification. We compare excitation
approaches for the data-driven identification process and describe an
optimization-based stabilization strategy for the identified systems
Deviations from Gaussianity in deterministic discrete time dynamical systems
In this paper we examine the deviations from Gaussianity for two types of random variable converging to a normal distribution, namely sums of random variables generated by a deterministic discrete time map and a linearly damped variable driven by a deterministic map. We demonstrate how Edgeworth expansions provide a universal description of the deviations from the limiting normal distribution. We derive explicit expressions for these asymptotic expansions and provide numerical evidence of their accuracy
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