28,306 research outputs found
Description of stochastic and chaotic series using visibility graphs
Nonlinear time series analysis is an active field of research that studies
the structure of complex signals in order to derive information of the process
that generated those series, for understanding, modeling and forecasting
purposes. In the last years, some methods mapping time series to network
representations have been proposed. The purpose is to investigate on the
properties of the series through graph theoretical tools recently developed in
the core of the celebrated complex network theory. Among some other methods,
the so-called visibility algorithm has received much attention, since it has
been shown that series correlations are captured by the algorithm and
translated in the associated graph, opening the possibility of building
fruitful connections between time series analysis, nonlinear dynamics, and
graph theory. Here we use the horizontal visibility algorithm to characterize
and distinguish between correlated stochastic, uncorrelated and chaotic
processes. We show that in every case the series maps into a graph with
exponential degree distribution P (k) ~ exp(-{\lambda}k), where the value of
{\lambda} characterizes the specific process. The frontier between chaotic and
correlated stochastic processes, {\lambda} = ln(3/2), can be calculated
exactly, and some other analytical developments confirm the results provided by
extensive numerical simulations and (short) experimental time series
A Random Matrix Approach to Dynamic Factors in macroeconomic data
We show how random matrix theory can be applied to develop new algorithms to
extract dynamic factors from macroeconomic time series. In particular, we
consider a limit where the number of random variables N and the number of
consecutive time measurements T are large but the ratio N / T is fixed. In this
regime the underlying random matrices are asymptotically equivalent to Free
Random Variables (FRV).Application of these methods for macroeconomic
indicators for Poland economy is also presented.Comment: arXiv admin note: text overlap with arXiv:physics/0512090 by other
author
On the Outage Probability of the Full-Duplex Interference-Limited Relay Channel
In this paper, we study the performance, in terms of the asymptotic error
probability, of a user which communicates with a destination with the aid of a
full-duplex in-band relay. We consider that the network is
interference-limited, and interfering users are distributed as a Poisson point
process. In this case, the asymptotic error probability is upper bounded by the
outage probability (OP). We investigate the outage behavior for well-known
cooperative schemes, namely, decode-and-forward (DF) and compress-and-forward
(CF) considering fading and path loss. For DF we determine the exact OP and
develop upper bounds which are tight in typical operating conditions. Also, we
find the correlation coefficient between source and relay signals which
minimizes the OP when the density of interferers is small. For CF, the
achievable rates are determined by the spatial correlation of the
interferences, and a straightforward analysis isn't possible. To handle this
issue, we show the rate with correlated noises is at most one bit worse than
with uncorrelated noises, and thus find an upper bound on the performance of
CF. These results are useful to evaluate the performance and to optimize
relaying schemes in the context of full-duplex wireless networks.Comment: 30 pages, 4 figures. Final version. To appear in IEEE JSAC Special
Issue on Full-duplex Wireless Communications and Networks, 201
A Random Matrix Approach to VARMA Processes
We apply random matrix theory to derive spectral density of large sample
covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2)
processes. In particular, we consider a limit where the number of random
variables N and the number of consecutive time measurements T are large but the
ratio N/T is fixed. In this regime the underlying random matrices are
asymptotically equivalent to Free Random Variables (FRV). We apply the FRV
calculus to calculate the eigenvalue density of the sample covariance for
several VARMA-type processes. We explicitly solve the VARMA(1,1) case and
demonstrate a perfect agreement between the analytical result and the spectra
obtained by Monte Carlo simulations. The proposed method is purely algebraic
and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic
Femtosecond Covariance Spectroscopy
The success of non-linear optics relies largely on pulse-to-pulse
consistency. In contrast, covariance based techniques used in photoionization
electron spectroscopy and mass spectrometry have shown that wealth of
information can be extracted from noise that is lost when averaging multiple
measurements. Here, we apply covariance based detection to nonlinear optical
spectroscopy, and show that noise in a femtosecond laser is not necessarily a
liability to be mitigated, but can act as a unique and powerful asset. As a
proof of principle we apply this approach to the process of stimulated Raman
scattering in alpha-quartz. Our results demonstrate how nonlinear processes in
the sample can encode correlations between the spectral components of
ultrashort pulses with uncorrelated stochastic fluctuations. This in turn
provides richer information compared to the standard non-linear optics
techniques that are based on averages over many repetitions with well-behaved
laser pulses. These proof-of-principle results suggest that covariance based
nonlinear spectroscopy will improve the applicability of fs non-linear
spectroscopy in wavelength ranges where stable, transform limited pulses are
not available such as, for example, x-ray free electron lasers which naturally
have spectrally noisy pulses ideally suited for this approach
- …