62,581 research outputs found
Implications of Z-normalization in the matrix profile
Companies are increasingly measuring their products and services, resulting in a rising amount of available time series data, making techniques to extract usable information needed. One state-of-the-art technique for time series is the Matrix Profile, which has been used for various applications including motif/discord discovery, visualizations and semantic segmentation. Internally, the Matrix Profile utilizes the z-normalized Euclidean distance to compare the shape of subsequences between two series. However, when comparing subsequences that are relatively flat and contain noise, the resulting distance is high despite the visual similarity of these subsequences. This property violates some of the assumptions made by Matrix Profile based techniques, resulting in worse performance when series contain flat and noisy subsequences. By studying the properties of the z-normalized Euclidean distance, we derived a method to eliminate this effect requiring only an estimate of the standard deviation of the noise. In this paper we describe various practical properties of the z-normalized Euclidean distance and show how these can be used to correct the performance of Matrix Profile related techniques. We demonstrate our techniques using anomaly detection using a Yahoo! Webscope anomaly dataset, semantic segmentation on the PAMAP2 activity dataset and for data visualization on a UCI activity dataset, all containing real-world data, and obtain overall better results after applying our technique. Our technique is a straightforward extension of the distance calculation in the Matrix Profile and will benefit any derived technique dealing with time series containing flat and noisy subsequences
Nonequilibrium dynamics of a stochastic model of anomalous heat transport
We study the dynamics of covariances in a chain of harmonic oscillators with
conservative noise in contact with two stochastic Langevin heat baths. The
noise amounts to random collisions between nearest-neighbour oscillators that
exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math.
Theor. 42 (2009) 025001], we have studied the stationary state of this system
with fixed boundary conditions, finding analytical exact expressions for the
temperature profile and the heat current in the thermodynamic (continuum)
limit. In this paper we extend the analysis to the evolution of the covariance
matrix and to generic boundary conditions. Our main purpose is to construct a
hydrodynamic description of the relaxation to the stationary state, starting
from the exact equations governing the evolution of the correlation matrix. We
identify and adiabatically eliminate the fast variables, arriving at a
continuity equation for the temperature profile T(y,t), complemented by an
ordinary equation that accounts for the evolution in the bulk. Altogether, we
find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica
Real-time turbulence profiling with a pair of laser guide star Shack–Hartmann wavefront sensors for wide-field adaptive optics systems on large to extremely large telescopes
Real-time turbulence profiling is necessary to tune tomographic wavefront reconstruction algorithms for wide-field adaptive optics (AO) systems on large to extremely large telescopes, and to perform a variety of image post-processing tasks involving point-spread function reconstruction. This paper describes a computationally efficient and accurate numerical technique inspired by the slope detection and ranging (SLODAR) method to perform this task in real time from properly selected Shack–Hartmann wavefront sensor measurements accumulated over a few hundred frames from a pair of laser guide stars, thus eliminating the need for an additional instrument. The algorithm is introduced, followed by a theoretical influence function analysis illustrating its impulse response to high-resolution turbulence profiles. Finally, its performance is assessed in the context of the Thirty Meter Telescope multi-conjugate adaptive optics system via end-to-end wave optics Monte Carlo simulations
Galaxy Modeling with Compound Elliptical Shapelets
Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have
become important tools in galaxy modeling, particularly for the purpose of
extracting ellipticity and morphological information from astronomical data.
However, the standard shapelet basis functions cannot compactly represent
galaxies with high ellipticity or large Sersic index, and the resulting
underfitting bias has been shown to present a serious challenge for
weak-lensing methods based on shapelets. We present here a new convolution
relation and a compound "multi-scale" shapelet basis to address these problems,
and provide a proof-of-concept demonstration using a small sample of nearby
galaxies.Comment: 14 pages, 7 figure
Photon-number distributions of twin beams generated in spontaneous parametric down-conversion and measured by an intensified CCD camera
The measurement of photon-number statistics of fields composed of photon
pairs, generated in spontaneous parametric down-conversion and detected by an
intensified CCD camera is described. Final quantum detection efficiencies,
electronic noises, finite numbers of detector pixels, transverse intensity
spatial profiles of the detected beams as well as losses of single photons from
a pair are taken into account in a developed general theory of photon-number
detection. The measured data provided by an iCCD camera with single-photon
detection sensitivity are analyzed along the developed theory. Joint
signal-idler photon-number distributions are recovered using the reconstruction
method based on the principle of maximum likelihood. The range of applicability
of the method is discussed. The reconstructed joint signal-idler photon-number
distribution is compared with that obtained by a method that uses superposition
of signal and noise and minimizes photoelectron entropy. Statistics of the
reconstructed fields are identified to be multi-mode Gaussian. Elements of the
measured as well as the reconstructed joint signal-idler photon-number
distributions violate classical inequalities. Sub-shot-noise correlations in
the difference of the signal and idler photon numbers as well as partial
suppression of odd elements in the distribution of the sum of signal and idler
photon numbers are observed.Comment: 14 pages, 14 figure
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