28,513 research outputs found
Spectral Optimization Problems
In this survey paper we present a class of shape optimization problems where
the cost function involves the solution of a PDE of elliptic type in the
unknown domain. In particular, we consider cost functions which depend on the
spectrum of an elliptic operator and we focus on the existence of an optimal
domain. The known results are presented as well as a list of still open
problems. Related fields as optimal partition problems, evolution flows,
Cheeger-type problems, are also considered.Comment: 42 pages with 8 figure
A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
We consider the multiphase shape optimization problem
where
is a given constant and is a bounded open set
with Lipschitz boundary. We give some new results concerning the qualitative
properties of the optimal sets and the regularity of the corresponding
eigenfunctions. We also provide numerical results for the optimal partitions
Cube-Cut: Vertebral Body Segmentation in MRI-Data through Cubic-Shaped Divergences
In this article, we present a graph-based method using a cubic template for
volumetric segmentation of vertebrae in magnetic resonance imaging (MRI)
acquisitions. The user can define the degree of deviation from a regular cube
via a smoothness value Delta. The Cube-Cut algorithm generates a directed graph
with two terminal nodes (s-t-network), where the nodes of the graph correspond
to a cubic-shaped subset of the image's voxels. The weightings of the graph's
terminal edges, which connect every node with a virtual source s or a virtual
sink t, represent the affinity of a voxel to the vertebra (source) and to the
background (sink). Furthermore, a set of infinite weighted and non-terminal
edges implements the smoothness term. After graph construction, a minimal
s-t-cut is calculated within polynomial computation time, which splits the
nodes into two disjoint units. Subsequently, the segmentation result is
determined out of the source-set. A quantitative evaluation of a C++
implementation of the algorithm resulted in an average Dice Similarity
Coefficient (DSC) of 81.33% and a running time of less than a minute.Comment: 23 figures, 2 tables, 43 references, PLoS ONE 9(4): e9338
Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined Networks
The performance of computer networks relies on how bandwidth is shared among
different flows. Fair resource allocation is a challenging problem particularly
when the flows evolve over time. To address this issue, bandwidth sharing
techniques that quickly react to the traffic fluctuations are of interest,
especially in large scale settings with hundreds of nodes and thousands of
flows. In this context, we propose a distributed algorithm based on the
Alternating Direction Method of Multipliers (ADMM) that tackles the multi-path
fair resource allocation problem in a distributed SDN control architecture. Our
ADMM-based algorithm continuously generates a sequence of resource allocation
solutions converging to the fair allocation while always remaining feasible, a
property that standard primal-dual decomposition methods often lack. Thanks to
the distribution of all computer intensive operations, we demonstrate that we
can handle large instances at scale
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