1,079 research outputs found
Polyhedral Predictive Regions For Power System Applications
Despite substantial improvement in the development of forecasting approaches,
conditional and dynamic uncertainty estimates ought to be accommodated in
decision-making in power system operation and market, in order to yield either
cost-optimal decisions in expectation, or decision with probabilistic
guarantees. The representation of uncertainty serves as an interface between
forecasting and decision-making problems, with different approaches handling
various objects and their parameterization as input. Following substantial
developments based on scenario-based stochastic methods, robust and
chance-constrained optimization approaches have gained increasing attention.
These often rely on polyhedra as a representation of the convex envelope of
uncertainty. In the work, we aim to bridge the gap between the probabilistic
forecasting literature and such optimization approaches by generating forecasts
in the form of polyhedra with probabilistic guarantees. For that, we see
polyhedra as parameterized objects under alternative definitions (under
and norms), the parameters of which may be modelled and predicted.
We additionally discuss assessing the predictive skill of such multivariate
probabilistic forecasts. An application and related empirical investigation
results allow us to verify probabilistic calibration and predictive skills of
our polyhedra.Comment: 8 page
Convex Hulls of Random Walks in Higher Dimensions: A Large Deviation Study
The distribution of the hypervolume and surface of convex
hulls of (multiple) random walks in higher dimensions are determined
numerically, especially containing probabilities far smaller than to estimate large deviation properties. For arbitrary dimensions
and large walk lengths , we suggest a scaling behavior of the distribution
with the length of the walk similar to the two-dimensional case, and
behavior of the distributions in the tails. We underpin both with numerical
data in and dimensions. Further, we confirm the analytically known
means of those distributions and calculate their variances for large .Comment: 9 pages, 8 figures, 3 table
Finding Convex Hulls Using Quickhull on the GPU
We present a convex hull algorithm that is accelerated on commodity graphics
hardware. We analyze and identify the hurdles of writing a recursive divide and
conquer algorithm on the GPU and divise a framework for representing this class
of problems. Our framework transforms the recursive splitting step into a
permutation step that is well-suited for graphics hardware. Our convex hull
algorithm of choice is Quickhull. Our parallel Quickhull implementation (for
both 2D and 3D cases) achieves an order of magnitude speedup over standard
computational geometry libraries.Comment: 11 page
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