52,557 research outputs found
Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem
We present a new approach to solve the exponential retrieval problem. We
derive a stable technique, based on the singular value decomposition (SVD) of
lag-covariance and crosscovariance matrices consisting of covariance
coefficients computed for index translated copies of an initial time series.
For these matrices a generalized eigenvalue problem is solved. The initial
signal is mapped into the basis of the generalized eigenvectors and phase
portraits are consequently analyzed. Pattern recognition techniques could be
applied to distinguish phase portraits related to the exponentials and noise.
Each frequency is evaluated by unwrapping phases of the corresponding portrait,
detecting potential wrapping events and estimation of the phase slope.
Efficiency of the proposed and existing methods is compared on the set of
examples, including the white Gaussian and auto-regressive model noise
Detecting broken PT-symmetry
A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system 'respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which qualitatively locate the zeros of real polynomials in the complex plane. The interest and value of the present approach lies in the fact that it avoids diagonalization of the Hamiltonian at hand
On the use of stabilising transformations for detecting unstable periodic orbits in the Kuramoto-Sivashinsky equation
In this paper we develop further a method for detecting unstable periodic
orbits (UPOs) by stabilising transformations, where the strategy is to
transform the system of interest in such a way that the orbits become stable.
The main difficulty of using this method is that the number of transformations,
which were used in the past, becomes overwhelming as we move to higher
dimensions (Davidchack and Lai 1999; Schmelcher et al. 1997, 1998). We have
recently proposed a set of stabilising transformations which is constructed
from a small set of already found UPOs (Crofts and Davidchack 2006). The main
benefit of using the proposed set is that its cardinality depends on the
dimension of the unstable manifold at the UPO rather than the dimension of the
system. In a typical situation the dimension of the unstable manifold is much
smaller than the dimension of the system so the number of transformations is
much smaller. Here we extend this approach to high-dimensional systems of ODEs
and apply it to the model example of a chaotic spatially extended system -- the
Kuramoto-Sivashinsky equation. A comparison is made between the performance of
this new method against the competing methods of Newton-Armijo (NA) and
Levernberg-Marquardt (LM). In the latter case, we take advantage of the fact
that the LM algorithm is able to solve under-determined systems of equations,
thus eliminating the need for any additional constraints
An efficient CDMA decoder for correlated information sources
We consider the detection of correlated information sources in the ubiquitous
Code-Division Multiple-Access (CDMA) scheme. We propose a message-passing based
scheme for detecting correlated sources directly, with no need for source
coding. The detection is done simultaneously over a block of transmitted binary
symbols (word). Simulation results are provided demonstrating a substantial
improvement in bit-error-rate in comparison with the unmodified detector and
the alternative of source compression. The robustness of the error-performance
improvement is shown under practical model settings, including wrong estimation
of the generating Markov transition matrix and finite-length spreading codes.Comment: 11 page
- …