52,759 research outputs found
Spectral rate theory for projected two-state kinetics
Classical rate theories often fail in cases where the observable(s) or order
parameter(s) used are poor reaction coordinates or the observed signal is
deteriorated by noise, such that no clear separation between reactants and
products is possible. Here, we present a general spectral two-state rate theory
for ergodic dynamical systems in thermal equilibrium that explicitly takes into
account how the system is observed. The theory allows the systematic estimation
errors made by standard rate theories to be understood and quantified. We also
elucidate the connection of spectral rate theory with the popular Markov state
modeling (MSM) approach for molecular simulation studies. An optimal rate
estimator is formulated that gives robust and unbiased results even for poor
reaction coordinates and can be applied to both computer simulations and
single-molecule experiments. No definition of a dividing surface is required.
Another result of the theory is a model-free definition of the reaction
coordinate quality (RCQ). The RCQ can be bounded from below by the directly
computable observation quality (OQ), thus providing a measure allowing the RCQ
to be optimized by tuning the experimental setup. Additionally, the respective
partial probability distributions can be obtained for the reactant and product
states along the observed order parameter, even when these strongly overlap.
The effects of both filtering (averaging) and uncorrelated noise are also
examined. The approach is demonstrated on numerical examples and experimental
single-molecule force probe data of the p5ab RNA hairpin and the apo-myoglobin
protein at low pH, here focusing on the case of two-state kinetics
Maximizing information on the environment by dynamically controlled qubit probes
We explore the ability of a qubit probe to characterize unknown parameters of
its environment. By resorting to quantum estimation theory, we analytically
find the ultimate bound on the precision of estimating key parameters of a
broad class of ubiquitous environmental noises ("baths") which the qubit may
probe. These include the probe-bath coupling strength, the correlation time of
generic bath spectra, the power laws governing these spectra, as well as their
dephasing times T2. Our central result is that by optimizing the dynamical
control on the probe under realistic constraints one may attain the maximal
accuracy bound on the estimation of these parameters by the least number of
measurements possible. Applications of this protocol that combines dynamical
control and estimation theory tools to quantum sensing are illustrated for a
nitrogen-vacancy center in diamond used as a probe.Comment: 8 pages + 6 pages (appendix), 3 Figure
Comment of Global dynamics of biological systems
In a recent study, (Grigorov, 2006) analyzed temporal gene expression
profiles (Arbeitman et al., 2002) generated in a Drosophila experiment using
SSA in conjunction with Monte-Carlo SSA. The author (Grigorov, 2006) makes
three important claims in his article, namely:
Claim1: A new method based on the theory of nonlinear time series analysis is
used to capture the global dynamics of the fruit-fly cycle temporal gene
expression profiles.
Claim 2: Flattening of a significant part of the eigen-spectrum confirms the
hypothesis about an underly-ing high-dimensional chaotic generating process.
Claim 3: Monte-Carlo SSA can be used to establish whether a given time series
is distinguishable from any well-defined process including deterministic chaos.
In this report we present fundamental concerns with respect to the above
claims (Grigorov, 2006) in a systematic manner with simple examples. The
discussion provided especially discourages the choice of SSA for inferring
nonlinear dynamical structure form time series obtained in any biological
paradigm.Comment: 6 pages, 2 figure
Estimation of Power System Inertia Using Nonlinear Koopman Modes
We report a new approach to estimating power system inertia directly from
time-series data on power system dynamics. The approach is based on the
so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a
nonlinear generalization of linear modal decomposition through spectral
analysis of the Koopman operator for nonlinear dynamical systems. The KMD-based
approach is thus applicable to dynamic data that evolve in nonlinear regime of
power system characteristics. Its effectiveness is numerically evaluated with
transient stability simulations of the IEEE New England test system.Comment: 10 pages, 4 figures, conferenc
Noise-robust quantum sensing via optimal multi-probe spectroscopy
The dynamics of quantum systems are unavoidably influenced by their
environment and in turn observing a quantum system (probe) can allow one to
measure its environment: Measurements and controlled manipulation of the probe
such as dynamical decoupling sequences as an extension of the Ramsey
interference measurement allow to spectrally resolve a noise field coupled to
the probe. Here, we introduce fast and robust estimation strategies for the
characterization of the spectral properties of classical and quantum dephasing
environments. These strategies are based on filter function orthogonalization,
optimal control filters maximizing the relevant Fisher Information and
multi-qubit entanglement. We investigate and quantify the robustness of the
schemes under different types of noise such as finite-precision measurements,
dephasing of the probe, spectral leakage and slow temporal fluctuations of the
spectrum.Comment: 13 pages, 14 figure
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