100,498 research outputs found
Forecasting with time series imaging
Feature-based time series representations have attracted substantial
attention in a wide range of time series analysis methods. Recently, the use of
time series features for forecast model averaging has been an emerging research
focus in the forecasting community. Nonetheless, most of the existing
approaches depend on the manual choice of an appropriate set of features.
Exploiting machine learning methods to extract features from time series
automatically becomes crucial in state-of-the-art time series analysis. In this
paper, we introduce an automated approach to extract time series features based
on time series imaging. We first transform time series into recurrence plots,
from which local features can be extracted using computer vision algorithms.
The extracted features are used for forecast model averaging. Our experiments
show that forecasting based on automatically extracted features, with less
human intervention and a more comprehensive view of the raw time series data,
yields highly comparable performances with the best methods in the largest
forecasting competition dataset (M4) and outperforms the top methods in the
Tourism forecasting competition dataset
Two-dimensional Noncommutative atom Gas with Anandan interaction
Landau like quantization of the Anandan system in a special electromagnetic
field is studied. Unlike the cases of the AC system and the HMW system, the
torques of the system on the magnetic dipole and the electric dipole don't
vanish. By constructing Heisenberg algebra, the Landau analog levels and
eigenstates on commutative space, NC space and NC phase space are obtained
respectively. By using the coherent state method, some statistical properties
of such free atom gas are studied and the expressions of some thermodynamic
quantities related to revolution direction are obtained. Two particular cases
of temperature are discussed and the more simple expressions of the free energy
on the three spaces are obtained. We give the relation between the value of
and revolution direction clearly, and find Landau like levels of the
Anandan system are invariant and the levels between the AC system and the HMW
system are interchanged each other under Maxwell dual transformations on the
three spaces. The two sets of eigenstates labelled by can be related
by a supersymmetry transformation on commutative space, but the phenomenon
don't occur on NC situation. We emphasize that some results relevant to Anandan
interaction are suitable for the cases of AC interaction and HMW interaction
under special conditions.Comment: Latex, 10 page
Approximation properties of simple Lie groups made discrete
In this paper we consider the class of connected simple Lie groups equipped
with the discrete topology. We show that within this class of groups the
following approximation properties are equivalent: (1) the Haagerup property;
(2) weak amenability; (3) the weak Haagerup property. In order to obtain the
above result we prove that the discrete group GL(2,K) is weakly amenable with
constant 1 for any field K.Comment: 15 pages. Final version. To appear in J. Lie Theor
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