1,776 research outputs found
Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature
In this paper we study the problem of prescribing a fourth order conformal
invariant (the Paneitz curvature) on the -sphere, with . Using
tools from the theory of critical points at infinity, we provide some
topological conditions on the level sets of a given positive function under
which we prove the existene of a metric, conformally equivalent to the standard
metric, with prescribed Paneitz curvature.Comment: 20 page
The Paneitz Curvature Problem on Lower Dimensional Spheres
In this paper we prescribe a fourth order conformal invariant 9the Paneitz
Curvature) on five and six spheres. Using dynamical and topological methods
involving the study of critical points at infinity of the associated
variational problem, we prove some existence results.Comment: 34 page
DOPE: Distributed Optimization for Pairwise Energies
We formulate an Alternating Direction Method of Mul-tipliers (ADMM) that
systematically distributes the computations of any technique for optimizing
pairwise functions, including non-submodular potentials. Such discrete
functions are very useful in segmentation and a breadth of other vision
problems. Our method decomposes the problem into a large set of small
sub-problems, each involving a sub-region of the image domain, which can be
solved in parallel. We achieve consistency between the sub-problems through a
novel constraint that can be used for a large class of pair-wise functions. We
give an iterative numerical solution that alternates between solving the
sub-problems and updating consistency variables, until convergence. We report
comprehensive experiments, which demonstrate the benefit of our general
distributed solution in the case of the popular serial algorithm of Boykov and
Kolmogorov (BK algorithm) and, also, in the context of non-submodular
functions.Comment: Accepted at CVPR 201
Redesigning the Schedule Time Slots for Qatar University to Cope with Local Specificities
This study is concerned with the redesign of the class meeting pattern at Qatar University. It examines the existing meeting pattern based on its operational efficiency, its alignment with the strategic plan of the University, and its perception by the students and the faculty members. The analysis reveals serious limitations and shows the need for a new pattern with a full non-teaching day and no one-hour lectures. A capacity analysis proves the feasibility of such a pattern. Taking into consideration the specifications of the Qatari society, it was judged that the non-teaching day be split in two-half days. The present research recognizes the distinction between scheduling and class meeting patterns and aims to address the under-researched theme of having the meeting pattern as a variable rather than just an input to scheduling
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