73,000 research outputs found
Creature forcing and large continuum: The joy of halving
For let be the minimal number of
uniform -splitting trees needed to cover the uniform -splitting tree,
i.e., for every branch of the -tree, one of the -trees contains
. Let be the dual notion: For every branch , one of
the -trees guesses infinitely often. We show that it is consistent
that
for continuum many pairwise different cardinals and suitable
pairs . For the proof we introduce a new mixed-limit
creature forcing construction
Wide Angle Compton Scattering
We present the handbag contribution to Wide Angle Compton Scattering (WACS)
at moderately large momentum transfer obtained with a proton distribution
amplitude close to the asymptotic form. In comparison it is found to be
significantly larger than results from the hard scattering (pQCD) approach.Comment: 5 pages, 6 figures, to appear in proceedings of the "Second Workshop
on Physics with an Electron Polarized Light Ion Collider", MIT, Cambridge,
MA, Sept. 14-16, 200
Quantifying information transfer and mediation along causal pathways in complex systems
Measures of information transfer have become a popular approach to analyze
interactions in complex systems such as the Earth or the human brain from
measured time series. Recent work has focused on causal definitions of
information transfer excluding effects of common drivers and indirect
influences. While the former clearly constitutes a spurious causality, the aim
of the present article is to develop measures quantifying different notions of
the strength of information transfer along indirect causal paths, based on
first reconstructing the multivariate causal network (\emph{Tigramite}
approach). Another class of novel measures quantifies to what extent different
intermediate processes on causal paths contribute to an interaction mechanism
to determine pathways of causal information transfer. A rigorous mathematical
framework allows for a clear information-theoretic interpretation that can also
be related to the underlying dynamics as proven for certain classes of
processes. Generally, however, estimates of information transfer remain hard to
interpret for nonlinearly intertwined complex systems. But, if experiments or
mathematical models are not available, measuring pathways of information
transfer within the causal dependency structure allows at least for an
abstraction of the dynamics. The measures are illustrated on a climatological
example to disentangle pathways of atmospheric flow over Europe.Comment: 20 pages, 6 figure
Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information
Conditional independence testing is a fundamental problem underlying causal
discovery and a particularly challenging task in the presence of nonlinear and
high-dimensional dependencies. Here a fully non-parametric test for continuous
data based on conditional mutual information combined with a local permutation
scheme is presented. Through a nearest neighbor approach, the test efficiently
adapts also to non-smooth distributions due to strongly nonlinear dependencies.
Numerical experiments demonstrate that the test reliably simulates the null
distribution even for small sample sizes and with high-dimensional conditioning
sets. The test is better calibrated than kernel-based tests utilizing an
analytical approximation of the null distribution, especially for non-smooth
densities, and reaches the same or higher power levels. Combining the local
permutation scheme with the kernel tests leads to better calibration, but
suffers in power. For smaller sample sizes and lower dimensions, the test is
faster than random fourier feature-based kernel tests if the permutation scheme
is (embarrassingly) parallelized, but the runtime increases more sharply with
sample size and dimensionality. Thus, more theoretical research to analytically
approximate the null distribution and speed up the estimation for larger sample
sizes is desirable.Comment: 17 pages, 12 figures, 1 tabl
A note on sewage sludge - risk assessments and fertilization value
A number of recent studies of risk related to agricultural use of sewage sludge are reviewed, as a contribution to the discussion of potential for use in organic agriculture. Furthermore a very tentative assessment of the fertilization value of sewage sludge and its derived products is developed
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