18,504 research outputs found
Restricting the nonlinearity parameter in soil greenhouse gas flux calculation for more reliable flux estimates
The static chamber approach is often used for greenhouse gas (GHG) flux measurements, whereby the flux is deduced from the increase of species concentration after closing the chamber. Since this increase changes diffusion gradients between chamber air and soil air, a nonlinear increase is expected. Lateral gas flow and leakages also contribute to non linearity.
Several models have been suggested to account for this non linearity, the most recent being the Hutchinson±Mosier regression model (HMR). However, the practical application of these models is challenging because the researcher needs to decide for each flux whether a nonlinear fit is appropriate or exaggerates flux estimates due to measurement artifacts. In the latter case, a flux estimate from the linear model is a more robust solution and introduces less arbitrary uncertainty to the data. We present the new, dynamic and reproducible flux calculation scheme, KAPPA.MAX, for an improved trade-off between bias and uncertainty (i.e. accuracy and precision). We develop a tool to simulate, visualise and optimise the flux calculation scheme for any specific static N2O chamber measurement system.
The decision procedure and visualisation tools are implemented in a package for the R software.
Finally, we demonstrate with this approach the performance of the applied flux calculation scheme for a measured flux dataset to estimate the actual bias and uncertainty. The KAPPA.MAX method effectively improved the decision between linear and nonlinear flux estimates reducing the bias at a minimal cost of uncertainty
Understanding the fine structure of electricity prices
This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a "jump-reversion" component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets
Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation
Many nonlinear partial differential equations (PDEs) display a coarsening
dynamics, i.e., an emerging pattern whose typical length scale increases
with time. The so-called coarsening exponent characterizes the time
dependence of the scale of the pattern, , and coarsening
dynamics can be described by a diffusion equation for the phase of the pattern.
By means of a multiscale analysis we are able to find the analytical expression
of such diffusion equations. Here, we propose a recipe to implement numerically
the determination of , the phase diffusion coefficient, as a
function of the wavelength of the base steady state .
carries all information about coarsening dynamics and, through the relation
, it allows us to determine the coarsening exponent. The
main conceptual message is that the coarsening exponent is determined without
solving a time-dependent equation, but only by inspecting the periodic
steady-state solutions. This provides a much faster strategy than a forward
time-dependent calculation. We discuss our method for several different PDEs,
both conserved and not conserved
Phenotypic evolution studied by layered stochastic differential equations
Time series of cell size evolution in unicellular marine algae (division
Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a
system of linear stochastic differential equations of hierarchical structure.
The data consists of size measurements of fossilized calcite platelets
(coccoliths) that cover the living cell, found in deep-sea sediment cores from
six sites in the world oceans and dated to irregular points in time. To
accommodate biological theory of populations tracking their fitness optima, and
to allow potentially interpretable correlations in time and space, the model
framework allows for an upper layer of partially observed site-specific
population means, a layer of site-specific theoretical fitness optima and a
bottom layer representing environmental and ecological processes. While the
modeled process has many components, it is Gaussian and analytically tractable.
A total of 710 model specifications within this framework are compared and
inference is drawn with respect to model structure, evolutionary speed and the
effect of global temperature.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS559 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Search via Quantum Walk
We propose a new method for designing quantum search algorithms for finding a
"marked" element in the state space of a classical Markov chain. The algorithm
is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of
the Markov chain. The main new idea is to apply quantum phase estimation to the
quantum walk in order to implement an approximate reflection operator. This
operator is then used in an amplitude amplification scheme. As a result we
considerably expand the scope of the previous approaches of Ambainis (2004) and
Szegedy (2004). Our algorithm combines the benefits of these approaches in
terms of being able to find marked elements, incurring the smaller cost of the
two, and being applicable to a larger class of Markov chains. In addition, it
is conceptually simple and avoids some technical difficulties in the previous
analyses of several algorithms based on quantum walk.Comment: 21 pages. Various modifications and improvements, especially in
Section
Extended Kramers-Moyal analysis applied to optical trapping
The Kramers-Moyal analysis is a well established approach to analyze
stochastic time series from complex systems. If the sampling interval of a
measured time series is too low, systematic errors occur in the analysis
results. These errors are labeled as finite time effects in the literature. In
the present article, we present some new insights about these effects and
discuss the limitations of a previously published method to estimate
Kramers-Moyal coefficients at the presence of finite time effects. To increase
the reliability of this method and to avoid misinterpretations, we extend it by
the computation of error estimates for estimated parameters using a Monte Carlo
error propagation technique. Finally, the extended method is applied to a data
set of an optical trapping experiment yielding estimations of the forces acting
on a Brownian particle trapped by optical tweezers. We find an increased
Markov-Einstein time scale of the order of the relaxation time of the process
which can be traced back to memory effects caused by the interaction of the
particle and the fluid. Above the Markov-Einstein time scale, the process can
be very well described by the classical overdamped Markov model for Brownian
motion.Comment: 14 pages, 18 figure
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