11,168 research outputs found
A century of enzyme kinetics. Should we believe in the Km and vmax estimates?
The application of the quasi-steady-state approximation (QSSA) in biochemical kinetics allows the reduction of a complex biochemical system with an initial fast transient into a simpler system. The simplified system yields insights into the behavior of the biochemical reaction, and analytical approximations can be obtained to determine its kinetic parameters. However, this process can lead to inaccuracies due to the inappropriate application of the QSSA. Here we present a number of approximate solutions and determine in which regions of the initial enzyme and substrate concentration parameter space they are valid. In particular, this illustrates that experimentalists must be careful to use the correct approximation appropriate to the initial conditions within the parameter space
Analog, hybrid, and digital simulation
Analog, hybrid, and digital computerized simulation technique
Reliability in Constrained Gauss-Markov Models: An Analytical and Differential Approach with Applications in Photogrammetry
This report was prepared by Jackson Cothren, a graduate research associate in the Department of Civil and Environmental Engineering and Geodetic Science at the Ohio State University, under the supervision of Professor Burkhard Schaffrin.This report was also submitted to the Graduate School of the Ohio State University as a dissertation in partial fulfillment of the requirements for the Ph.D. degree.Reliability analysis explains the contribution of each observation in an estimation model
to the overall redundancy of the model, taking into account the geometry of the network
as well as the precision of the observations themselves. It is principally used to design
networks resistant to outliers in the observations by making the outliers more detectible
using standard statistical tests.It has been studied extensively, and principally, in Gauss-
Markov models. We show how the same analysis may be extended to various
constrained Gauss-Markov models and present preliminary work for its use in
unconstrained Gauss-Helmert models. In particular, we analyze the prominent reliability
matrix of the constrained model to separate the contribution of the constraints to the
redundancy of the observations from the observations themselves. In addition, we make
extensive use of matrix differential calculus to find the Jacobian of the reliability matrix
with respect to the parameters that define the network through both the original design
and constraint matrices. The resulting Jacobian matrix reveals the sensitivity of
reliability matrix elements highlighting weak areas in the network where changes in
observations may result in unreliable observations. We apply the analytical framework to
photogrammetric networks in which exterior orientation parameters are directly observed
by GPS/INS systems. Tie-point observations provide some redundancy and even a few
collinear tie-point and tie-point distance constraints improve the reliability of these
direct observations by as much as 33%. Using the same theory we compare networks in
which tie-points are observed on multiple images (n-fold points) and tie-points are
observed in photo pairs only (two-fold points). Apparently, the use of two-fold tiepoints
does not significantly degrade the reliability of the direct exterior observation
observations. Coplanarity constraints added to the common two-fold points do not add
significantly to the reliability of the direct exterior orientation observations. The
differential calculus results may also be used to provide a new measure of redundancy
number stability in networks. We show that a typical photogrammetric network with n-fold
tie-points was less stable with respect to at least some tie-point movement than an
equivalent network with n-fold tie-points decomposed into many two-fold tie-points
Algorithms and Data Structures for Multi-Adaptive Time-Stepping
Multi-adaptive Galerkin methods are extensions of the standard continuous and
discontinuous Galerkin methods for the numerical solution of initial value
problems for ordinary or partial differential equations. In particular, the
multi-adaptive methods allow individual and adaptive time steps to be used for
different components or in different regions of space. We present algorithms
for efficient multi-adaptive time-stepping, including the recursive
construction of time slabs and adaptive time step selection. We also present
data structures for efficient storage and interpolation of the multi-adaptive
solution. The efficiency of the proposed algorithms and data structures is
demonstrated for a series of benchmark problems.Comment: ACM Transactions on Mathematical Software 35(3), 24 pages (2008
Discrete spherical means of directional derivatives and Veronese maps
We describe and study geometric properties of discrete circular and spherical
means of directional derivatives of functions, as well as discrete
approximations of higher order differential operators. For an arbitrary
dimension we present a general construction for obtaining discrete spherical
means of directional derivatives. The construction is based on using the
Minkowski's existence theorem and Veronese maps. Approximating the directional
derivatives by appropriate finite differences allows one to obtain finite
difference operators with good rotation invariance properties. In particular,
we use discrete circular and spherical means to derive discrete approximations
of various linear and nonlinear first- and second-order differential operators,
including discrete Laplacians. A practical potential of our approach is
demonstrated by considering applications to nonlinear filtering of digital
images and surface curvature estimation
On the Szeg\"o-Asymptotics for Doubly-Dispersive Gaussian Channels
We consider the time-continuous doubly-dispersive channel with additive
Gaussian noise and establish a capacity formula for the case where the channel
correlation operator is represented by a symbol which is periodic in time and
fulfills some further integrability and smoothness conditions. The key to this
result is a new Szeg\"o formula for certain pseudo-differential operators. The
formula justifies the water-filling principle along time and frequency in terms
of the time--continuous time-varying transfer function (the symbol).Comment: 5 pages, to be presented at ISIT 2011, minor typos corrected,
references update
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