6,262 research outputs found
Orthogonal complex structures on domains in R^4
An orthogonal complex structure on a domain in R^4 is a complex structure
which is integrable and is compatible with the Euclidean metric. This gives
rise to a first order system of partial differential equations which is
conformally invariant. We prove two Liouville-type uniqueness theorems for
solutions of this system, and use these to give an alternative proof of the
classification of compact locally conformally flat Hermitian surfaces first
proved by Pontecorvo. We also give a classification of non-degenerate quadrics
in CP^3 under the action of the conformal group. Using this classification, we
show that generic quadrics give rise to orthogonal complex structures defined
on the complement of unknotted solid tori which are smoothly embedded in R^4.Comment: 42 pages. Version 2 contains several improvements and simplifications
throughout. Material from the first version on more general branched
coverings has been removed in order to make the article more focused, and
will appear elsewher
New Curves from Branes
We consider configurations of Neveu-Schwarz fivebranes, Dirichlet fourbranes
and an orientifold sixplane in type IIA string theory. Upon lifting the
configuration to M-theory and proposing a description of how to include the
effects of the orientifold sixplane we derive the curves describing the Coulomb
branch of N=2 gauge theories with orthogonal and symplectic gauge groups,
product gauge groups of the form SU(k_1)...SU(k_i) x SO(N) and
SU(k_1)...SU(k_i) x Sp(N). We also propose new curves describing theories with
unitary gauge groups and matter in the symmetric or antisymmetric
representation.Comment: 29 pages (harvmac b-mode), 2 figure
Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data
The Shape Interaction Matrix (SIM) is one of the earliest approaches to
performing subspace clustering (i.e., separating points drawn from a union of
subspaces). In this paper, we revisit the SIM and reveal its connections to
several recent subspace clustering methods. Our analysis lets us derive a
simple, yet effective algorithm to robustify the SIM and make it applicable to
realistic scenarios where the data is corrupted by noise. We justify our method
by intuitive examples and the matrix perturbation theory. We then show how this
approach can be extended to handle missing data, thus yielding an efficient and
general subspace clustering algorithm. We demonstrate the benefits of our
approach over state-of-the-art subspace clustering methods on several
challenging motion segmentation and face clustering problems, where the data
includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape
Search via Quantum Walk
We propose a new method for designing quantum search algorithms for finding a
"marked" element in the state space of a classical Markov chain. The algorithm
is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of
the Markov chain. The main new idea is to apply quantum phase estimation to the
quantum walk in order to implement an approximate reflection operator. This
operator is then used in an amplitude amplification scheme. As a result we
considerably expand the scope of the previous approaches of Ambainis (2004) and
Szegedy (2004). Our algorithm combines the benefits of these approaches in
terms of being able to find marked elements, incurring the smaller cost of the
two, and being applicable to a larger class of Markov chains. In addition, it
is conceptually simple and avoids some technical difficulties in the previous
analyses of several algorithms based on quantum walk.Comment: 21 pages. Various modifications and improvements, especially in
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