114,349 research outputs found
Solitons as a signature of the modulation instability in the discrete nonlinear Schrodinger equation
The effect of the modulation instability on the propagation of solitary waves
along one-dimensional discrete nonlinear Schr\"odinger equation with cubic
nonlinearity is revisited. A self-contained quasicontinuum approximation is
developed to derive closed-form expressions for small-amplitude solitary waves.
The notion that the existence of nonlinear solitary waves is a signature of the
modulation instability is used to analytically study instability effects on
solitons during propagation. In particular, we concern with instability effects
in the dark region, where other analytical methods as the standard modulation
analysis of planewaves do not provide any information on solitons. The region
of high-velocity solitons is studied anew showing that solitons are less prone
to intabilities in this region. An analytical upper boundary for the
self-defocusing instability is defined.Comment: 16 pages, An important comment on the staggering transformation is
now include
Size matters: some stylized facts of the stock market revisited
We reanalyze high resolution data from the New York Stock Exchange and find a
monotonic (but not power law) variation of the mean value per trade, the mean
number of trades per minute and the mean trading activity with company
capitalization. We show that the second moment of the traded value distribution
is finite. Consequently, the Hurst exponents for the corresponding time series
can be calculated. These are, however, non-universal: The persistence grows
with larger capitalization and this results in a logarithmically increasing
Hurst exponent. A similar trend is displayed by intertrade time intervals.
Finally, we demonstrate that the distribution of the intertrade times is better
described by a multiscaling ansatz than by simple gap scaling.Comment: 10 pages, 13 figures, 2 tables, accepted to Eur. Phys. J. B, updated
references, fixed some minor error
Bayesian kernel-based system identification with quantized output data
In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC)
methods to provide an estimate of the system. In particular, we show how to
design a Gibbs sampler which quickly converges to the target distribution.
Numerical simulations show a substantial improvement in the accuracy of the
estimates over state-of-the-art kernel-based methods when employed in
identification of systems with quantized data.Comment: Submitted to IFAC SysId 201
Learning the Structure for Structured Sparsity
Structured sparsity has recently emerged in statistics, machine learning and
signal processing as a promising paradigm for learning in high-dimensional
settings. All existing methods for learning under the assumption of structured
sparsity rely on prior knowledge on how to weight (or how to penalize)
individual subsets of variables during the subset selection process, which is
not available in general. Inferring group weights from data is a key open
research problem in structured sparsity.In this paper, we propose a Bayesian
approach to the problem of group weight learning. We model the group weights as
hyperparameters of heavy-tailed priors on groups of variables and derive an
approximate inference scheme to infer these hyperparameters. We empirically
show that we are able to recover the model hyperparameters when the data are
generated from the model, and we demonstrate the utility of learning weights in
synthetic and real denoising problems
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