39,901 research outputs found
Efficient state-space inference of periodic latent force models
Latent force models (LFM) are principled approaches to incorporating solutions to differen-tial equations within non-parametric inference methods. Unfortunately, the developmentand application of LFMs can be inhibited by their computational cost, especially whenclosed-form solutions for the LFM are unavailable, as is the case in many real world prob-lems where these latent forces exhibit periodic behaviour. Given this, we develop a newsparse representation of LFMs which considerably improves their computational efficiency,as well as broadening their applicability, in a principled way, to domains with periodic ornear periodic latent forces. Our approach uses a linear basis model to approximate onegenerative model for each periodic force. We assume that the latent forces are generatedfrom Gaussian process priors and develop a linear basis model which fully expresses thesepriors. We apply our approach to model the thermal dynamics of domestic buildings andshow that it is effective at predicting day-ahead temperatures within the homes. We alsoapply our approach within queueing theory in which quasi-periodic arrival rates are mod-elled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs.Further, we show that state estimates obtained using periodic latent force models can re-duce the root mean squared error to 17% of that from non-periodic models and 27% of thenearest rival approach which is the resonator model (S ̈arkk ̈a et al., 2012; Hartikainen et al.,2012.
On the Existence and Uniqueness of Global Solutions for the KdV Equation with Quasi-Periodic Initial Data
We consider the KdV equation with quasi-periodic initial data whose Fourier coefficients decay
exponentially and prove existence and uniqueness, in the class of functions
which have an expansion with exponentially decaying Fourier coefficients, of a
solution on a small interval of time, the length of which depends on the given
data and the frequency vector involved. For a Diophantine frequency vector and
for small quasi-periodic data (i.e., when the Fourier coefficients obey with sufficiently small,
depending on and the frequency vector), we prove global
existence and uniqueness of the solution. The latter result relies on our
recent work \cite{DG} on the inverse spectral problem for the quasi-periodic
Schr\"{o}dinger equation.Comment: 26 pages, to appear in J. Amer. Math. So
Improving Power Spectral Estimation using Multitapering: Precise asteroseismic modeling of stars, exoplanets, and beyond
Asteroseismic time-series data have imprints of stellar oscillation modes,
whose detection and characterization through time-series analysis allows us to
probe stellar interiors physics. Such analyses usually occur in the Fourier
domain by computing the Lomb-Scargle (LS) periodogram, an estimator of the
\textit{power spectrum} underlying unevenly-sampled time-series data. However,
the LS periodogram suffers from the statistical problems of (1) inconsistency
(or noise) and (2) bias due to high spectral leakage. In addition, it is
designed to detect strictly periodic signals but is unsuitable for
non-sinusoidal periodic or quasi-periodic signals. Here, we develop a
multitaper spectral estimation method that tackles the inconsistency and bias
problems of the LS periodogram. We combine this multitaper method with the
Non-Uniform Fast Fourier Transform (\texttt{mtNUFFT}) to more precisely
estimate the frequencies of asteroseismic signals that are non-sinusoidal
periodic (e.g., exoplanet transits) or quasi-periodic (e.g., pressure modes).
We illustrate this using a simulated and the Kepler-91 red giant light curve.
Particularly, we detect the Kepler-91b exoplanet and precisely estimate its
period, days, in the frequency domain using the multitaper
F-test alone. We also integrate \texttt{mtNUFFT} into the \texttt{PBjam}
package to obtain a Kepler-91 age estimate of Gyr. This \%
improvement in age precision relative to the Gyr APOKASC-2
(uncorrected) estimate illustrates that \texttt{mtNUFFT} has promising
implications for Galactic archaeology, in addition to stellar interiors and
exoplanet studies. Our frequency analysis method generally applies to
time-domain astronomy and is implemented in the public Python package
\texttt{tapify}, available at \url{https://github.com/aaryapatil/tapify}.Comment: 32 pages (3 pages in the Appendix), 14 figures, 2 tables, Submitted
to A
Efficient State-Space Inference of Periodic Latent Force Models
Latent force models (LFM) are principled approaches to incorporating
solutions to differential equations within non-parametric inference methods.
Unfortunately, the development and application of LFMs can be inhibited by
their computational cost, especially when closed-form solutions for the LFM are
unavailable, as is the case in many real world problems where these latent
forces exhibit periodic behaviour. Given this, we develop a new sparse
representation of LFMs which considerably improves their computational
efficiency, as well as broadening their applicability, in a principled way, to
domains with periodic or near periodic latent forces. Our approach uses a
linear basis model to approximate one generative model for each periodic force.
We assume that the latent forces are generated from Gaussian process priors and
develop a linear basis model which fully expresses these priors. We apply our
approach to model the thermal dynamics of domestic buildings and show that it
is effective at predicting day-ahead temperatures within the homes. We also
apply our approach within queueing theory in which quasi-periodic arrival rates
are modelled as latent forces. In both cases, we demonstrate that our approach
can be implemented efficiently using state-space methods which encode the
linear dynamic systems via LFMs. Further, we show that state estimates obtained
using periodic latent force models can reduce the root mean squared error to
17% of that from non-periodic models and 27% of the nearest rival approach
which is the resonator model.Comment: 61 pages, 13 figures, accepted for publication in JMLR. Updates from
earlier version occur throughout article in response to JMLR review
Quasi-periodic acceleration of electrons in the flare on 2012 July 19
Quasi-periodic pulsations (QPPs) of nonthermal emission in an M7.7 class flare on 2012 July 19 are investigated
with spatially resolved observations at microwave and HXR bands and with spectral observations at decimetric,
metric waves. Microwave emission at 17 GHz of two footpoints, HXR emission at 20–50 keV of the north
footpoint and loop top, and type III bursts at 0.7–3 GHz show prominent in-phase oscillations at 270 s. The
microwave emission of the loop leg has less pulsation but stronger emission. Through the estimation of plasma
density around the loop top from EUV observations, we find that the local plasma frequency would be 1.5 GHz or
even higher. Thus, type III bursts at 700 MHz originate above the loop top. Quasi-periodic acceleration or injection
of energetic electrons is proposed to dominate these in-phase QPPs of nonthermal emission from footpoints, loop
top, and above. In the overlying region, drifting pulsations (DPS) at 200–600 MHz oscillate at a distinct period
(200 s). Its global structure drifts toward lower frequency, which is closely related to upward plasmoids observed
simultaneously from EUV emission. Hence, nonthermal emission from overlying plasmoids and underlying flaring
loops show different oscillating periods. Two individual systems of quasi-periodic acceleration of electrons are
proposed to coincide in the bi-direction outflows from the reconnection region
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