317,630 research outputs found
A density result in vector optimization
We study a class of vector minimization problems
on a complete metric space such that all its bounded closed
subsets are compact. We show that a subclass of minimization
problems with a nonclosed set of minimal values is dense in
the whole class of minimization problems
Geometry of Log-Concave Density Estimation
Shape-constrained density estimation is an important topic in mathematical
statistics. We focus on densities on that are log-concave, and
we study geometric properties of the maximum likelihood estimator (MLE) for
weighted samples. Cule, Samworth, and Stewart showed that the logarithm of the
optimal log-concave density is piecewise linear and supported on a regular
subdivision of the samples. This defines a map from the space of weights to the
set of regular subdivisions of the samples, i.e. the face poset of their
secondary polytope. We prove that this map is surjective. In fact, every
regular subdivision arises in the MLE for some set of weights with positive
probability, but coarser subdivisions appear to be more likely to arise than
finer ones. To quantify these results, we introduce a continuous version of the
secondary polytope, whose dual we name the Samworth body. This article
establishes a new link between geometric combinatorics and nonparametric
statistics, and it suggests numerous open problems.Comment: 22 pages, 3 figure
Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization
We assume that a finite set of moments of a random vector is given. Its
underlying density is unknown. An algorithm is proposed for efficiently
calculating Dirac mixture densities maintaining these moments while providing a
homogeneous coverage of the state space.Comment: 18 pages, 6 figure
On the extrapolation of magneto-hydro-static equilibria on the sun
Modeling the interface region between solar photosphere and corona is
challenging, because the relative importance of magnetic and plasma forces
change by several orders of magnitude. While the solar corona can be modeled by
the force-free assumption, we need to take care about plasma forces (pressure
gradient and gravity) in photosphere and chromosphere, here within the
magneto-hydro-static (MHS) model. We solve the MHS equations with the help of
an optimization principle and use vector magnetogram as boundary condition.
Positive pressure and density are ensured by replacing them with two new basic
variables. The Lorentz force during optimization is used to update the plasma
pressure on the bottom boundary, which makes the new extrapolation works even
without pressure measurement on the photosphere. Our code is tested by using a
linear MHS model as reference. From the detailed analyses, we find that the
newly developed MHS extrapolation recovers the reference model at high
accuracy. The MHS extrapolation is, however, numerically more expensive than
the nonlinear force-free field (NLFFF) extrapolation and consequently one
should limit their application to regions where plasma forces become important,
e.g. in a layer of about 2 Mm above the photosphere.Comment: accepted for publication in Ap
3-D topology optimization of single-pole-type head by using design sensitivity analysis
It is necessary to develop a write head having a large recording field and small stray field in adjacent tracks and adjacent bits in perpendicular magnetic recording systems. In this paper, a practical three-dimensional topology optimization technique combined with the edge-based finite-element method is proposed. A technique for obtaining a smooth topology is also shown. The optimization of single-pole-type head having a magnetic shield is performed by using the topology optimization technique so that the leakage flux in the adjacent bit can be reduced. A useful shape of the magnetic shield obtained by the proposed technique is illustrated.</p
- …