130 research outputs found
Quantum system characterization with limited resources
The construction and operation of large scale quantum information devices
presents a grand challenge. A major issue is the effective control of coherent
evolution, which requires accurate knowledge of the system dynamics that may
vary from device to device. We review strategies for obtaining such knowledge
from minimal initial resources and in an efficient manner, and apply these to
the problem of characterization of a qubit embedded into a larger state
manifold, made tractable by exploiting prior structural knowledge. We also
investigate adaptive sampling for estimation of multiple parameters
Alfven wave scattering and the secondary to primary ratio
The cosmic ray abundances have traditionally been used to determine the elemental and isotopic nature of galactic ray sources and average measures of propagation conditions. Detailed studies of the physics of propagation are usually paired with relatively straightforward estimates of the secondary-to-primary (S/P) ratios. In the work reported here, calculations of elemental abundances are paired with a more careful treatment of the propagation process. It is shown that the physics of propagation does indeed leave specific traces of Galactic structure in cosmic ray abundances
Rapid quantitative pharmacodynamic imaging with Bayesian estimation
We recently described rapid quantitative pharmacodynamic imaging, a novel method for estimating sensitivity of a biological system to a drug. We tested its accuracy in simulated biological signals with varying receptor sensitivity and varying levels of random noise, and presented initial proof-of-concept data from functional MRI (fMRI) studies in primate brain. However, the initial simulation testing used a simple iterative approach to estimate pharmacokinetic-pharmacodynamic (PKPD) parameters, an approach that was computationally efficient but returned parameters only from a small, discrete set of values chosen a priori. Here we revisit the simulation testing using a Bayesian method to estimate the PKPD parameters. This improved accuracy compared to our previous method, and noise without intentional signal was never interpreted as signal. We also reanalyze the fMRI proof-of-concept data. The success with the simulated data, and with the limited fMRI data, is a necessary first step toward further testing of rapid quantitative pharmacodynamic imaging
Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography
We consider how to characterize the dynamics of a quantum system from a
restricted set of initial states and measurements using Bayesian analysis.
Previous work has shown that Hamiltonian systems can be well estimated from
analysis of noisy data. Here we show how to generalize this approach to systems
with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the
process for a range of three-level quantum systems. The results suggest that
the Bayesian estimation of the frequencies and dephasing rates is generally
highly accurate and the main source of errors are errors in the reconstructed
Hamiltonian basis.Comment: 6 pages, 3 figure
Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
The Fisher-matrix formalism is used routinely in the literature on
gravitational-wave detection to characterize the parameter-estimation
performance of gravitational-wave measurements, given parametrized models of
the waveforms, and assuming detector noise of known colored Gaussian
distribution. Unfortunately, the Fisher matrix can be a poor predictor of the
amount of information obtained from typical observations, especially for
waveforms with several parameters and relatively low expected signal-to-noise
ratios (SNR), or for waveforms depending weakly on one or more parameters, when
their priors are not taken into proper consideration. In this paper I discuss
these pitfalls; show how they occur, even for relatively strong signals, with a
commonly used template family for binary-inspiral waveforms; and describe
practical recipes to recognize them and cope with them.
Specifically, I answer the following questions: (i) What is the significance
of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When
is it necessary to take into account prior probability distributions for the
source parameters? (iii) When is the signal-to-noise ratio high enough to
believe the Fisher-matrix result? In addition, I provide general expressions
for the higher-order, beyond--Fisher-matrix terms in the 1/SNR expansions for
the expected parameter accuracies.Comment: 24 pages, 3 figures, previously known as "A User Manual for the
Fisher Information Matrix"; final, corrected PRD versio
MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity
The principle of maximum entropy is applied to the spectral analysis of a
data signal with general variance matrix and containing gaps in the record. The
role of the entropic regularizer is to prevent one from overestimating
structure in the spectrum when faced with imperfect data. Several arguments are
presented suggesting that the arbitrary prefactor should not be introduced to
the entropy term. The introduction of that factor is not required when a
continuous Poisson distribution is used for the amplitude coefficients. We
compare the formalism for when the variance of the data is known explicitly to
that for when the variance is known only to lie in some finite range. The
result of including the entropic measure factor is to suggest a spectrum
consistent with the variance of the data which has less structure than that
given by the forward transform. An application of the methodology to example
data is demonstrated.Comment: 15 pages, 13 figures, 1 table, major revision, final version,
Accepted for publication in Astrophysics & Space Scienc
Modeling the R2* relaxivity of blood at 1.5 Tesla
BOLD (Blood Oxygenation Level Dependent) imaging is used in fMRI to show differences in activation of the brain based on the relative changes of the T2* (= 1/R2*) signal of the blood. However, quantification of blood oxygenation level based on the T2* signal has been hindered by the lack of a predictive model which accurately correlates the T2* signal to the oxygenation level of blood. The T2* signal decay in BOLD imaging is generated due to blood containing paramagnetic deoxyhemoglobin (in comparison to diamagnetic oxyhemoglobin). This generates local field inhomogeneities, which cause protons to experience different phase shifts, leading to dephasing and the MR signal decay. The blood T2* signal has been shown to decay with a complex behavior1, termed Non-Lorenztian, and thus is not adequately described by the traditional model of simplemono-exponential decay. Theoretical calculations show that diffusion narrowing substantially affects signal loss in our data. Over the past decade, several theoretical models have been proposed to describe this Non-Lorenztian behavior in the blood T2* signal in BOLD fMRI imaging. The goal of this project was to investigate different models which have been proposed over the years and determine a semi-phenomenological model for the T2* behaviorusing actual MR blood data
Fitting a sum of exponentials to lattice correlation functions using a non-uniform prior
Excited states are extracted from lattice correlation functions using a
non-uniform prior on the model parameters. Models for both a single exponential
and a sum of exponentials are considered, as well as an alternate model for the
orthogonalization of the correlation functions. Results from an analysis of
torelon and glueball operators indicate the Bayesian methodology compares well
with the usual interpretation of effective mass tables produced by a
variational procedure. Applications of the methodology are discussed.Comment: 12 pages, 8 figures, 8 tables, major revision, final versio
Consistent Application of Maximum Entropy to Quantum-Monte-Carlo Data
Bayesian statistics in the frame of the maximum entropy concept has widely
been used for inferential problems, particularly, to infer dynamic properties
of strongly correlated fermion systems from Quantum-Monte-Carlo (QMC) imaginary
time data. In current applications, however, a consistent treatment of the
error-covariance of the QMC data is missing. Here we present a closed Bayesian
approach to account consistently for the QMC-data.Comment: 13 pages, RevTeX, 2 uuencoded PostScript figure
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