218,171 research outputs found
Cointegration in Frequency Domain
Existence of a cointegration relationship between two time series in the time domain imposes restrictions on the series zero-frequency behaviour in terms of their squared coherence, phase, and gain, in the frequency domain. I derive these restrictions by studying cross-spectral properties of a cointegrated bivariate system. Specifically, I demonstrate that if two difference stationary series, X(t) and Y(t), are cointegrated with a cointegrating vector [1 b] and thus share a common stochastic trend, then at the zero frequency, the squared coherence of (1 - L) X(t) and (1 - L) Y(t) will equal one, their phase will equal zero, and their gain will equal |b|.Common Stochastic Trend, Cointegration, Integration, Frequency Domain Anlysis, Cross-Spectrum, Zero-Frequency, Coherence, Squared Coherence, Phase, Gain, Cross-Spectral Properties, Bivariate Cointegrated System, Long Run Comovement
Uncovering interactions in the frequency domain
Oscillatory activity plays a critical role in regulating biological processes at levels ranging from subcellular, cellular, and
network to the whole organism, and often involves a large number of interacting elements. We shed light on this issue by
introducing a novel approach called partial Granger causality to reliably reveal interaction patterns in multivariate data with
exogenous inputs and latent variables in the frequency domain. The method is extensively tested with toy models, and
successfully applied to experimental datasets, including (1) gene microarray data of HeLa cell cycle; (2) in vivo multielectrode
array (MEA) local field potentials (LFPs) recorded from the inferotemporal cortex of a sheep; and (3) in vivo LFPs
recorded from distributed sites in the right hemisphere of a macaque monkey
Recommended from our members
Frequency-Domain Streak Camera And Tomography For Ultrafast Imaging Of Evolving And Channeled Plasma Accelerator Structures
We demonstrate a prototype Frequency Domain Streak Camera (FDSC) that can capture the picosecond time evolution of the plasma accelerator structure in a single shot. In our prototype Frequency-Domain Streak Camera, a probe pulse propagates obliquely to a sub-picosecond pump pulse that creates an evolving nonlinear index >bubble> in fused silica glass, supplementing a conventional Frequency Domain Holographic (FDH) probe-reference pair that co-propagates with the >bubble>. Frequency Domain Tomography (FDT) generalizes Frequency-Domain Streak Camera by probing the >bubble> from multiple angles and reconstructing its morphology and evolution using algorithms similar to those used in medical CAT scans. Multiplexing methods (Temporal Multiplexing and Angular Multiplexing) improve data storage and processing capability, demonstrating a compact Frequency Domain Tomography system with a single spectrometer.Physic
Time- and frequency-domain polariton interference
We present experimental observations of interference between an atomic spin
coherence and an optical field in a {\Lambda}-type gradient echo memory. The
interference is mediated by a strong classical field that couples a weak probe
field to the atomic coherence through a resonant Raman transition. Interference
can be observed between a prepared spin coherence and another propagating
optical field, or between multiple {\Lambda} transitions driving a single spin
coherence. In principle, the interference in each scheme can yield a near unity
visibility.Comment: 11 pages, 5 figure
Unraveling quantum dissipation in the frequency domain
We present a quantum Monte Carlo method for solving the evolution of an open
quantum system. In our approach, the density operator evolution is unraveled in
the frequency domain. Significant advantages of this approach arise when the
frequency of each dissipative event conveys information about the state of the
system.Comment: 4 pages, 4 Postscript figures, uses RevTe
Photoionization in the time and frequency domain
Ultrafast processes in matter, such as the electron emission following light
absorption, can now be studied using ultrashort light pulses of attosecond
duration (s) in the extreme ultraviolet spectral range. The lack of
spectral resolution due to the use of short light pulses may raise serious
issues in the interpretation of the experimental results and the comparison
with detailed theoretical calculations. Here, we determine photoionization time
delays in neon atoms over a 40 eV energy range with an interferometric
technique combining high temporal and spectral resolution. We spectrally
disentangle direct ionization from ionization with shake up, where a second
electron is left in an excited state, thus obtaining excellent agreement with
theoretical calculations and thereby solving a puzzle raised by seven-year-old
measurements. Our experimental approach does not have conceptual limits,
allowing us to foresee, with the help of upcoming laser technology, ultra-high
resolution time-frequency studies from the visible to the x-ray range.Comment: 5 pages, 4 figure
Frequency-domain waveform approximants capturing Doppler shifts
Gravitational wave astrophysics has only just begun, and as current detectors
are upgraded and new detectors are built, many new, albeit faint, features in
the signals will become accessible. One such feature is the presence of
time-dependent Doppler shifts, generated by the acceleration of the center of
mass of the gravitational-wave emitting system. We here develop a generic
method that takes a frequency-domain, gravitational-wave model devoid of
Doppler shifts and introduces modifications that incorporate them. Building
upon a perturbative expansion that assumes the Doppler-shift velocity is small
relative to the speed of light, the method consists of the inclusion of a
single term in the Fourier phase and two terms in the Fourier amplitude. We
validate the method through matches between waveforms with a Doppler shift in
the time domain and waveforms constructed with our method for two toy problems:
constant accelerations induced by a distant third body and Gaussian
accelerations that resemble a kick profile. We find mismatches below
for all of the astrophysically relevant cases considered, and
improve further at smaller velocities. The work presented here will allow for
the use of future detectors to extract new, faint features in the signal from
the noise.Comment: 11 pages, 5 figures, submitted to Phys. Rev.
- …