2,090 research outputs found
Dwell time symmetry in random walks and molecular motors
The statistics of steps and dwell times in reversible molecular motors differ
from those of cycle completion in enzyme kinetics. The reason is that a step is
only one of several transitions in the mechanochemical cycle. As a result,
theoretical results for cycle completion in enzyme kinetics do not apply to
stepping data. To allow correct parameter estimation, and to guide data
analysis and experiment design, a theoretical treatment is needed that takes
this observation into account. In this paper, we model the distribution of
dwell times and number of forward and backward steps using first passage
processes, based on the assumption that forward and backward steps correspond
to different directions of the same transition. We extend recent results for
systems with a single cycle and consider the full dwell time distributions as
well as models with multiple pathways, detectable substeps, and detachments.
Our main results are a symmetry relation for the dwell time distributions in
reversible motors, and a relation between certain relative step frequencies and
the free energy per cycle. We demonstrate our results by analyzing recent
stepping data for a bacterial flagellar motor, and discuss the implications for
the efficiency and reversibility of the force-generating subunits. Key words:
motor proteins; single molecule kinetics; enzyme kinetics; flagellar motor;
Markov process; non-equilibrium fluctuations.Comment: revtex, 15 pages, 8 figures, 2 tables. v2: Minor revision, corrected
typos, added references, and moved mathematical parts to new appendice
On particle filters applied to electricity load forecasting
We are interested in the online prediction of the electricity load, within
the Bayesian framework of dynamic models. We offer a review of sequential Monte
Carlo methods, and provide the calculations needed for the derivation of
so-called particles filters. We also discuss the practical issues arising from
their use, and some of the variants proposed in the literature to deal with
them, giving detailed algorithms whenever possible for an easy implementation.
We propose an additional step to help make basic particle filters more robust
with regard to outlying observations. Finally we use such a particle filter to
estimate a state-space model that includes exogenous variables in order to
forecast the electricity load for the customers of the French electricity
company \'Electricit\'e de France and discuss the various results obtained
Efficient Cosmological Parameter Estimation from Microwave Background Anisotropies
We revisit the issue of cosmological parameter estimation in light of current
and upcoming high-precision measurements of the cosmic microwave background
power spectrum. Physical quantities which determine the power spectrum are
reviewed, and their connection to familiar cosmological parameters is
explicated. We present a set of physical parameters, analytic functions of the
usual cosmological parameters, upon which the microwave background power
spectrum depends linearly (or with some other simple dependence) over a wide
range of parameter values. With such a set of parameters, microwave background
power spectra can be estimated with high accuracy and negligible computational
effort, vastly increasing the efficiency of cosmological parameter error
determination. The techniques presented here allow calculation of microwave
background power spectra times faster than comparably accurate direct
codes (after precomputing a handful of power spectra). We discuss various
issues of parameter estimation, including parameter degeneracies, numerical
precision, mapping between physical and cosmological parameters, and systematic
errors, and illustrate these considerations with an idealized model of the MAP
experiment.Comment: 22 pages, 12 figure
Hidden Markov Model with Binned Duration and Its Application
Hidden Markov models (HMM) have been widely used in various applications such as speech processing and bioinformatics. However, the standard hidden Markov model requires state occupancy durations to be geometrically distributed, which can be inappropriate in some real-world applications where the distributions on state intervals deviate signi cantly from the geometric distribution, such as multi-modal distributions and heavy-tailed distributions. The hidden Markov model with duration (HMMD) avoids this limitation by explicitly incor- porating the appropriate state duration distribution, at the price of signi cant computational expense. As a result, the applications of HMMD are still quited limited. In this work, we present a new algorithm - Hidden Markov Model with Binned Duration (HMMBD), whose result shows no loss of accuracy compared to the HMMD decoding performance and a com- putational expense that only diers from the much simpler and faster HMM decoding by a constant factor. More precisely, we further improve the computational complexity of HMMD from (TNN +TND) to (TNN +TND ), where TNN stands for the computational com- plexity of the HMM, D is the max duration value allowed and can be very large and D generally could be a small constant value
Uncertainty quantification in ocean state estimation
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2013Quantifying uncertainty and error bounds is a key outstanding challenge in ocean state
estimation and climate research. It is particularly difficult due to the large dimensionality
of this nonlinear estimation problem and the number of uncertain variables involved. The
âEstimating the Circulation and Climate of the Oceansâ (ECCO) consortium has
developed a scalable system for dynamically consistent estimation of global time-evolving
ocean state by optimal combination of ocean general circulation model (GCM)
with diverse ocean observations. The estimation system is based on the "adjoint method"
solution of an unconstrained least-squares optimization problem formulated with the
method of Lagrange multipliers for fitting the dynamical ocean model to observations.
The dynamical consistency requirement of ocean state estimation necessitates this
approach over sequential data assimilation and reanalysis smoothing techniques. In
addition, it is computationally advantageous because calculation and storage of large
covariance matrices is not required. However, this is also a drawback of the adjoint
method, which lacks a native formalism for error propagation and quantification of
assimilated uncertainty. The objective of this dissertation is to resolve that limitation by
developing a feasible computational methodology for uncertainty analysis in dynamically
consistent state estimation, applicable to the large dimensionality of global ocean models.
Hessian (second derivative-based) methodology is developed for Uncertainty
Quantification (UQ) in large-scale ocean state estimation, extending the gradient-based
adjoint method to employ the second order geometry information of the model-data
misfit function in a high-dimensional control space. Large error covariance matrices are
evaluated by inverting the Hessian matrix with the developed scalable matrix-free
numerical linear algebra algorithms. Hessian-vector product and Jacobian derivative
codes of the MIT general circulation model (MITgcm) are generated by means of
algorithmic differentiation (AD). Computational complexity of the Hessian code is
reduced by tangent linear differentiation of the adjoint code, which preserves the speedup
of adjoint checkpointing schemes in the second derivative calculation. A Lanczos
algorithm is applied for extracting the leading rank eigenvectors and eigenvalues of the
Hessian matrix. The eigenvectors represent the constrained uncertainty patterns. The
inverse eigenvalues are the corresponding uncertainties. The dimensionality of UQ
calculations is reduced by eliminating the uncertainty null-space unconstrained by the
supplied observations. Inverse and forward uncertainty propagation schemes are designed
for assimilating observation and control variable uncertainties, and for projecting these
uncertainties onto oceanographic target quantities. Two versions of these schemes are
developed: one evaluates reduction of prior uncertainties, while another does not require
prior assumptions. The analysis of uncertainty propagation in the ocean model is time-resolving.
It captures the dynamics of uncertainty evolution and reveals transient and
stationary uncertainty regimes.
The system is applied to quantifying uncertainties of Antarctic Circumpolar Current
(ACC) transport in a global barotropic configuration of the MITgcm. The model is
constrained by synthetic observations of sea surface height and velocities. The control
space consists of two-dimensional maps of initial and boundary conditions and model
parameters. The size of the Hessian matrix is O(1010) elements, which would require
O(60GB) of uncompressed storage. It is demonstrated how the choice of observations
and their geographic coverage determines the reduction in uncertainties of the estimated
transport. The system also yields information on how well the control fields are
constrained by the observations. The effects of controls uncertainty reduction due to
decrease of diagonal covariance terms are compared to dynamical coupling of controls
through off-diagonal covariance terms. The correlations of controls introduced by
observation uncertainty assimilation are found to dominate the reduction of uncertainty of
transport. An idealized analytical model of ACC guides a detailed time-resolving
understanding of uncertainty dynamics.This thesis was supported in part by the National Science Foundation (NSF)
Collaboration in Mathematical Geosciences (CMG) grant ARC-0934404, and the
Department of Energy (DOE) ISICLES initiative under LANL sub-contract 139843-1.
Partial funding was provided by the department of Mechanical Engineering at MIT and
by the Academic Programs Office at WHOI. My participation in the IMA "Large-scale
Inverse Problems and Quantification of Uncertainty" workshop was partially funded by
IMA NSF grants
A Probabilistic Model of Local Sequence Alignment That Simplifies Statistical Significance Estimation
Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (λ) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (âForwardâ scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (âViterbiâ scores) are Gumbel-distributed with constant λâ=âlog 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments
- âŠ