1,941 research outputs found
Fisher information matrix for single molecules with stochastic trajectories
Tracking of objects in cellular environments has become a vital tool in
molecular cell biology. A particularly important example is single molecule
tracking which enables the study of the motion of a molecule in cellular
environments and provides quantitative information on the behavior of
individual molecules in cellular environments, which were not available before
through bulk studies. Here, we consider a dynamical system where the motion of
an object is modeled by stochastic differential equations (SDEs), and
measurements are the detected photons emitted by the moving fluorescently
labeled object, which occur at discrete time points, corresponding to the
arrival times of a Poisson process, in contrast to uniform time points which
have been commonly used in similar dynamical systems. The measurements are
distributed according to optical diffraction theory, and therefore, they would
be modeled by different distributions, e.g., a Born and Wolf profile for an
out-of-focus molecule. For some special circumstances, Gaussian image models
have been proposed. In this paper, we introduce a stochastic framework in which
we calculate the maximum likelihood estimates of the biophysical parameters of
the molecular interactions, e.g., diffusion and drift coefficients. More
importantly, we develop a general framework to calculate the Cram\'er-Rao lower
bound (CRLB), given by the inverse of the Fisher information matrix, for the
estimation of unknown parameters and use it as a benchmark in the evaluation of
the standard deviation of the estimates. There exists no established method,
even for Gaussian measurements, to systematically calculate the CRLB for the
general motion model that we consider in this paper. We apply the developed
methodology to simulated data of a molecule with linear trajectories and show
that the standard deviation of the estimates matches well with the square root
of the CRLB
Magnetic fields in molecular clouds: Limitations of the analysis of Zeeman observations
Context. Observations of Zeeman split spectral lines represent an important
approach to derive the structure and strength of magnetic fields in molecular
clouds. In contrast to the uncertainty of the spectral line observation itself,
the uncertainty of the analysis method to derive the magnetic field strength
from these observations is not been well characterized so far.
Aims. We investigate the impact of several physical quantities on the
uncertainty of the analysis method, which is used to derive the line-of-sight
(LOS) magnetic field strength from Zeeman split spectral lines.
Methods. We simulate the Zeeman splitting of the 1665 MHz OH line with the 3D
radiative transfer (RT) extension ZRAD. This extension is based on the line RT
code Mol3D (Ober et al. 2015) and has been developed for the POLArized
RadIation Simulator POLARIS (Reissl et al. 2016).
Results. Observations of the OH Zeeman effect in typical molecular clouds are
not significantly affected by the uncertainty of the analysis method. We
derived an approximation to quantify the range of parameters in which the
analysis method works sufficiently accurate and provide factors to convert our
results to other spectral lines and species as well. We applied these
conversion factors to CN and found that observations of the CN Zeeman effect in
typical molecular clouds are neither significantly affected by the uncertainty
of the analysis method. In addition, we found that the density has almost no
impact on the uncertainty of the analysis method, unless it reaches values
higher than those typically found in molecular clouds. Furthermore, the
uncertainty of the analysis method increases, if both the gas velocity and the
magnetic field show significant variations along the line-of-sight. However,
this increase should be small in Zeeman observations of most molecular clouds
considering typical velocities of ~1 km/s.Comment: 9 pages, 6 figure
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
Pennsylvania\u27s Family Responsibility Statute-Corruption of Blood and Denial of Equal Protection
Differences in High-School Student Learning by Instruction Type and MBTI Personality Type
Differentiated instruction is a part of the education process today, and it is a time-consuming process used to attempt to reach more students and increase their learning and education. There is currently little empirical research dedicated to measuring the academic effects of differentiated instruction in the classroom. This research examined differentiated instruction in the form of learning styles (audio and visual) combined with personality types in an attempt to determine if there is a measurable significant effect on the academic achievement of students based on their own personality types and different applied learning styles in the classroom. No statistically significant differences were found between different personality types and instruction types
The effect of a nucleating agent on lamellar growth in melt-crystallizing polyethylene oxide
The effects of a (non co-crystallizing) nucleating agent on secondary
nucleation rate and final lamellar thickness in isothermally melt-crystallizing
polyethylene oxide are considered. SAXS reveals that lamellae formed in
nucleated samples are thinner than in the pure samples crystallized at the same
undercoolings. These results are in quantitative agreement with growth rate
data obtained by calorimetry, and are interpreted as the effect of a local
decrease of the basal surface tension, determined mainly by the nucleant
molecules diffused out of the regions being about to crystallize. Quantitative
agreement with a simple lattice model allows for some interpretation of the
mechanism.Comment: submitted to Journal of Applied Physics (first version on 22 Apr
2002
State Space Formulas for Coprime Factorization
In this paper we will give a uniform approach to the derivation of state space formulas of coprime factorizations, of different types, for rational matrix functions
Higher Order Variational Integrators: a polynomial approach
We reconsider the variational derivation of symplectic partitioned
Runge-Kutta schemes. Such type of variational integrators are of great
importance since they integrate mechanical systems with high order accuracy
while preserving the structural properties of these systems, like the
symplectic form, the evolution of the momentum maps or the energy behaviour.
Also they are easily applicable to optimal control problems based on mechanical
systems as proposed in Ober-Bl\"obaum et al. [2011].
Following the same approach, we develop a family of variational integrators
to which we refer as symplectic Galerkin schemes in contrast to symplectic
partitioned Runge-Kutta. These two families of integrators are, in principle
and by construction, different one from the other. Furthermore, the symplectic
Galerkin family can as easily be applied in optimal control problems, for which
Campos et al. [2012b] is a particular case.Comment: 12 pages, 1 table, 23rd Congress on Differential Equations and
Applications, CEDYA 201
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