44,912 research outputs found
Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning
Multilevel partitioning methods that are inspired by principles of
multiscaling are the most powerful practical hypergraph partitioning solvers.
Hypergraph partitioning has many applications in disciplines ranging from
scientific computing to data science. In this paper we introduce the concept of
algebraic distance on hypergraphs and demonstrate its use as an algorithmic
component in the coarsening stage of multilevel hypergraph partitioning
solvers. The algebraic distance is a vertex distance measure that extends
hyperedge weights for capturing the local connectivity of vertices which is
critical for hypergraph coarsening schemes. The practical effectiveness of the
proposed measure and corresponding coarsening scheme is demonstrated through
extensive computational experiments on a diverse set of problems. Finally, we
propose a benchmark of hypergraph partitioning problems to compare the quality
of other solvers
Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures
The QR factorization and the SVD are two fundamental matrix decompositions
with applications throughout scientific computing and data analysis. For
matrices with many more rows than columns, so-called "tall-and-skinny
matrices," there is a numerically stable, efficient, communication-avoiding
algorithm for computing the QR factorization. It has been used in traditional
high performance computing and grid computing environments. For MapReduce
environments, existing methods to compute the QR decomposition use a
numerically unstable approach that relies on indirectly computing the Q factor.
In the best case, these methods require only two passes over the data. In this
paper, we describe how to compute a stable tall-and-skinny QR factorization on
a MapReduce architecture in only slightly more than 2 passes over the data. We
can compute the SVD with only a small change and no difference in performance.
We present a performance comparison between our new direct TSQR method, a
standard unstable implementation for MapReduce (Cholesky QR), and the classic
stable algorithm implemented for MapReduce (Householder QR). We find that our
new stable method has a large performance advantage over the Householder QR
method. This holds both in a theoretical performance model as well as in an
actual implementation
Orbital and Maxillofacial Computer Aided Surgery: Patient-Specific Finite Element Models To Predict Surgical Outcomes
This paper addresses an important issue raised for the clinical relevance of
Computer-Assisted Surgical applications, namely the methodology used to
automatically build patient-specific Finite Element (FE) models of anatomical
structures. From this perspective, a method is proposed, based on a technique
called the Mesh-Matching method, followed by a process that corrects mesh
irregularities. The Mesh-Matching algorithm generates patient-specific volume
meshes from an existing generic model. The mesh regularization process is based
on the Jacobian matrix transform related to the FE reference element and the
current element. This method for generating patient-specific FE models is first
applied to Computer-Assisted maxillofacial surgery, and more precisely to the
FE elastic modelling of patient facial soft tissues. For each patient, the
planned bone osteotomies (mandible, maxilla, chin) are used as boundary
conditions to deform the FE face model, in order to predict the aesthetic
outcome of the surgery. Seven FE patient-specific models were successfully
generated by our method. For one patient, the prediction of the FE model is
qualitatively compared with the patient's post-operative appearance, measured
from a Computer Tomography scan. Then, our methodology is applied to
Computer-Assisted orbital surgery. It is, therefore, evaluated for the
generation of eleven patient-specific FE poroelastic models of the orbital soft
tissues. These models are used to predict the consequences of the surgical
decompression of the orbit. More precisely, an average law is extrapolated from
the simulations carried out for each patient model. This law links the size of
the osteotomy (i.e. the surgical gesture) and the backward displacement of the
eyeball (the consequence of the surgical gesture)
Projection-Based and Look Ahead Strategies for Atom Selection
In this paper, we improve iterative greedy search algorithms in which atoms
are selected serially over iterations, i.e., one-by-one over iterations. For
serial atom selection, we devise two new schemes to select an atom from a set
of potential atoms in each iteration. The two new schemes lead to two new
algorithms. For both the algorithms, in each iteration, the set of potential
atoms is found using a standard matched filter. In case of the first scheme, we
propose an orthogonal projection strategy that selects an atom from the set of
potential atoms. Then, for the second scheme, we propose a look ahead strategy
such that the selection of an atom in the current iteration has an effect on
the future iterations. The use of look ahead strategy requires a higher
computational resource. To achieve a trade-off between performance and
complexity, we use the two new schemes in cascade and develop a third new
algorithm. Through experimental evaluations, we compare the proposed algorithms
with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201
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