5,825 research outputs found
Stochastic Desertification
The process of desertification is usually modeled as a first order
transition, where a change of an external parameter (e.g. precipitation) leads
to a catastrophic bifurcation followed by an ecological regime shift. However,
vegetation elements like shrubs and trees undergo a stochastic birth-death
process with an absorbing state; such a process supports a second order
continuous transition with no hysteresis. We present a numerical study of a
minimal model that supports bistability and catastrophic shift on spatial
domain with demographic noise and an absorbing state. When the external
parameter varies adiabatically the transition is continuous and the front
velocity renormalizes to zero at the extinction transition. Below the
transition one may identify three modes of desertification: accumulation of
local catastrophes, desert invasion and global collapse. A catastrophic regime
shift occurs as a dynamical hysteresis, when the pace of environmental
variations is too fast. We present some empirical evidence, suggesting that the
mid-holocene desertification of the Sahara was, indeed, continuous
A simple interpretation of quantum mirages
In an interesting new experiment the electronic structure of a magnetic atom
adsorbed on the surface of Cu(111), observed by STM, was projected into a
remote location on the same surface. The purpose of the present paper is to
interpret this experiment with a model Hamiltonian, using ellipses of the size
of the experimental ones, containing about 2300 atoms. The charge distribution
for the different wavefunctions is analyzed, in particular, for those with
energy close to the Fermi energy of copper Ef. Some of them show two symmetric
maxima located on the principal axis of the ellipse but not necessarily at the
foci. If a Co atom is adsorbed at the site where the wavefunction with energy
has a maximum and the interaction is small, the main effect of the
adsorbed atom will be to split this particular wavefunction in two. The total
charge density will remain the same but the local density of states will
present a dip at Ef at any site where the charge density is large enough. We
relate the presence of this dip to the observation of quantum mirages. Our
interpretation suggests that other sites, apart from the foci of the ellipses,
can be used for projecting atomic images and also indicates the conditions for
other non magnetic adsorbates to produce mirages.Comment: 3 pages, 3 Fig
Carcass and meat quality of different pig genotypes in an organic extensive outdoor fatting system
Carcass, meat, and fat quality were evaluated of 37 castrates of 4 different genotypes [Pi*Du*GLR (10), Pi*AS (7), Du (10), Du*GLR (10)] kept on grass clover and fed with coarse meal made up of farm grown cereal and grain legumes without optimising the amount of amino acids and their relation to the energy content. Due to the energy surplus in the diet and in relation to the diminishing muscularity of the genotypes (corresponding to the above-mentioned sequence) lean meat contents were on a low level whereas intramuscular fat contents increased distinctly. Sensory meat quality was only at a medium level and did not differ noticeably between the genotypes. It is concluded that adipose carcasses associated with increased intramuscular fat contents do not lead automatically to higher sensory meat qualities. Therefore the system boundaries of organic pig fattening cannot be used without further efforts supplying market niches for pork of high eating quality
Ensemble Kalman filter for neural network based one-shot inversion
We study the use of novel techniques arising in machine learning for inverse
problems. Our approach replaces the complex forward model by a neural network,
which is trained simultaneously in a one-shot sense when estimating the unknown
parameters from data, i.e. the neural network is trained only for the unknown
parameter. By establishing a link to the Bayesian approach to inverse problems,
an algorithmic framework is developed which ensures the feasibility of the
parameter estimate w.r. to the forward model. We propose an efficient,
derivative-free optimization method based on variants of the ensemble Kalman
inversion. Numerical experiments show that the ensemble Kalman filter for
neural network based one-shot inversion is a promising direction combining
optimization and machine learning techniques for inverse problems
The end of the road
After some 60 years in research, a few months before my final retirement (there were a few temporary ones), the time has come to reminisce
Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition
The process of desertification in the semi-arid climatic zone is considered
by many as a catastrophic regime shift, since the positive feedback of
vegetation density on growth rates yields a system that admits alternative
steady states. Some support to this idea comes from the analysis of static
patterns, where peaks of the vegetation density histogram were associated with
these alternative states. Here we present a large-scale empirical study of
vegetation dynamics, aimed at identifying and quantifying directly the effects
of positive feedback. To do that, we have analyzed vegetation density across
of the African Sahel region, with spatial
resolution of meters, using three consecutive snapshots. The
results are mixed. The local vegetation density (measured at a single pixel)
moves towards the average of the corresponding rainfall line, indicating a
purely negative feedback. On the other hand, the chance of spatial clusters (of
many "green" pixels) to expand in the next census is growing with their size,
suggesting some positive feedback. We show that these apparently contradicting
results emerge naturally in a model with positive feedback and strong
demographic stochasticity, a model that allows for a catastrophic shift only in
a certain range of parameters. Static patterns, like the double peak in the
histogram of vegetation density, are shown to vary between censuses, with no
apparent correlation with the actual dynamical features
Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
The ensemble Kalman inversion is widely used in practice to estimate unknown
parameters from noisy measurement data. Its low computational costs,
straightforward implementation, and non-intrusive nature makes the method
appealing in various areas of application. We present a complete analysis of
the ensemble Kalman inversion with perturbed observations for a fixed ensemble
size when applied to linear inverse problems. The well-posedness and
convergence results are based on the continuous time scaling limits of the
method. The resulting coupled system of stochastic differential equations
allows to derive estimates on the long-time behaviour and provides insights
into the convergence properties of the ensemble Kalman inversion. We view the
method as a derivative free optimization method for the least-squares misfit
functional, which opens up the perspective to use the method in various areas
of applications such as imaging, groundwater flow problems, biological problems
as well as in the context of the training of neural networks
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