50,372 research outputs found
Estimating time delays between irregularly sampled time series
The time delay estimation between time series is a real-world problem in gravitational lensing, an area of astrophysics. Lensing is the most direct method of measuring the distribution of matter, which is often dark, and the accurate measurement of time delays set the scale to measure distances over cosmological scales. For our purposes, this means that we have to estimate a time delay between two or more noisy and irregularly sampled time series. Estimations have been made using statistical methods in the astrophysics literature, such as interpolation, dispersion analysis, discrete correlation function, Gaussian processes and Bayesian method, among others. Instead, this thesis proposes a kernel-based approach to estimating the time delay, which is inspired by kernel methods in the context of statistical and machine learning. Moreover, our methodology is evolved to perform model selection, regularisation and time delay estimation globally and simultaneously. Experimental results show that this approach is one of the most accurate methods for gaps (missing data) and distinct noise levels. Results on artificial and real data are shown
Evolino for recurrent support vector machines
Traditional Support Vector Machines (SVMs) need pre-wired finite time windows
to predict and classify time series. They do not have an internal state
necessary to deal with sequences involving arbitrary long-term dependencies.
Here we introduce a new class of recurrent, truly sequential SVM-like devices
with internal adaptive states, trained by a novel method called EVOlution of
systems with KErnel-based outputs (Evoke), an instance of the recent Evolino
class of methods. Evoke evolves recurrent neural networks to detect and
represent temporal dependencies while using quadratic programming/support
vector regression to produce precise outputs. Evoke is the first SVM-based
mechanism learning to classify a context-sensitive language. It also
outperforms recent state-of-the-art gradient-based recurrent neural networks
(RNNs) on various time series prediction tasks.Comment: 10 pages, 2 figure
Evaluating local correlation tracking using CO5BOLD simulations of solar granulation
Flows on the solar surface are linked to solar activity, and LCT is one of
the standard techniques for capturing the dynamics of these processes by
cross-correlating solar images. However, the link between contrast variations
in successive images to the underlying plasma motions has to be quantitatively
confirmed. Radiation hydrodynamics simulations of solar granulation
(e.g.,CO5BOLD) provide access to both the wavelength-integrated, emergent
continuum intensity and the 3D velocity field at various heights in the solar
atmosphere. Thus, applying LCT to continuum images yields horizontal proper
motions, which are then compared to the velocity field of the simulated
(non-magnetic) granulation. In this study, we evaluate the performance of an
LCT algorithm previously developed for bulk-processing Hinode G-band images,
establish it as a quantitative tool for measuring horizontal proper motions,
and clearly work out the limitations of LCT or similar techniques designed to
track optical flows. Horizontal flow maps and frequency distributions of the
flow speed were computed for a variety of LCT input parameters including the
spatial resolution, the width of the sampling window, the time cadence of
successive images, and the averaging time used to determine persistent flow
properties. Smoothed velocity fields from the hydrodynamics simulation at three
atmospheric layers (log tau=-1,0,and +1) served as a point of reference for the
LCT results. LCT recovers many of the granulation properties, e.g.,the shape of
the flow speed distributions, the relationship between mean flow speed and
averaging time, and also--with significant smoothing of the simulated velocity
field--morphological features of the flow and divergence maps. However, the
horizontal proper motions are grossly underestimated by as much as a factor of
three. The LCT flows match best the flows deeper in the atmosphere at log
tau=+1.Comment: 11 pages, 16 figures, accepted for publication in Astronomy and
Astrophysic
Exact equations for smoothed Wigner transforms and homogenization of wave propagation
The Wigner Transform (WT) has been extensively used in the formulation of
phase-space models for a variety of wave propagation problems including
high-frequency limits, nonlinear and random waves. It is well known that the WT
features counterintuitive 'interference terms', which often make computation
impractical. In this connection, we propose the use of the smoothed Wigner
Transform (SWT), and derive new, exact equations for it, covering a broad class
of wave propagation problems. Equations for spectrograms are included as a
special case. The 'taming' of the interference terms by the SWT is illustrated,
and an asymptotic model for the Schroedinger equation is constructed and
numerically verified.Comment: 16 pages, 8 figure
Temporal Feature Selection with Symbolic Regression
Building and discovering useful features when constructing machine learning models is the central task for the machine learning practitioner. Good features are useful not only in increasing the predictive power of a model but also in illuminating the underlying drivers of a target variable. In this research we propose a novel feature learning technique in which Symbolic regression is endowed with a ``Range Terminal\u27\u27 that allows it to explore functions of the aggregate of variables over time. We test the Range Terminal on a synthetic data set and a real world data in which we predict seasonal greenness using satellite derived temperature and snow data over a portion of the Arctic. On the synthetic data set we find Symbolic regression with the Range Terminal outperforms standard Symbolic regression and Lasso regression. On the Arctic data set we find it outperforms standard Symbolic regression, fails to beat the Lasso regression, but finds useful features describing the interaction between Land Surface Temperature, Snow, and seasonal vegetative growth in the Arctic
Tomographically reconstructed master equations for any open quantum dynamics
Memory effects in open quantum dynamics are often incorporated in the
equation of motion through a superoperator known as the memory kernel, which
encodes how past states affect future dynamics. However, the usual prescription
for determining the memory kernel requires information about the underlying
system-environment dynamics. Here, by deriving the transfer tensor method from
first principles, we show how a memory kernel master equation, for any quantum
process, can be entirely expressed in terms of a family of completely positive
dynamical maps. These can be reconstructed through quantum process tomography
on the system alone, either experimentally or numerically, and the resulting
equation of motion is equivalent to a generalised Nakajima-Zwanzig equation.
For experimental settings, we give a full prescription for the reconstruction
procedure, rendering the memory kernel operational. When simulation of an open
system is the goal, we show how our procedure yields a considerable advantage
for numerically calculating dynamics, even when the system is arbitrarily
periodically (or transiently) driven or initially correlated with its
environment. Namely, we show that the long time dynamics can be efficiently
obtained from a set of reconstructed maps over a much shorter time.Comment: 10+4 pages, 5 figure
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