80,324 research outputs found
On pole-swapping algorithms for the eigenvalue problem
Pole-swapping algorithms, which are generalizations of the QZ algorithm for
the generalized eigenvalue problem, are studied. A new modular (and therefore
more flexible) convergence theory that applies to all pole-swapping algorithms
is developed. A key component of all such algorithms is a procedure that swaps
two adjacent eigenvalues in a triangular pencil. An improved swapping routine
is developed, and its superiority over existing methods is demonstrated by a
backward error analysis and numerical tests. The modularity of the new
convergence theory and the generality of the pole-swapping approach shed new
light on bi-directional chasing algorithms, optimally packed shifts, and bulge
pencils, and allow the design of novel algorithms
Optimal Gaussian Entanglement Swapping
We consider entanglement swapping with general mixed two-mode Gaussian states
and calculate the optimal gains for a broad class of such states including
those states most relevant in communication scenarios. We show that for this
class of states, entanglement swapping adds no additional mixedness, that is
the ensemble average output state has the same purity as the input states. This
implies that, by using intermediate entanglement swapping steps, it is, in
principle, possible to distribute entangled two-mode Gaussian states of higher
purity as compared to direct transmission. We then apply the general results on
optimal Gaussian swapping to the problem of quantum communication over a lossy
fiber and demonstrate that, contrary to negative conclusions in the literature,
swapping-based schemes in fact often perform better than direct transmission
for high input squeezing. However, an effective transmission analysis reveals
that the hope for improved performance based on optimal Gaussian entanglement
swapping is spurious since the swapping does not lead to an enhancement of the
effective transmission. This implies that the same or better results can always
be obtained using direct transmission in combination with, in general, less
squeezing.Comment: 10 pages, 2 figures, minor corrections in version 2 with one
reference added (ref.9
Macroscopic Entanglement by Entanglement Swapping
We present a scheme for entangling two micromechanical oscillators. The
scheme exploits the quantum effects of radiation pressure and it is based on a
novel application of entanglement swapping, where standard optical measurements
are used to generate purely mechanical entanglement. The scheme is presented by
first solving the general problem of entanglement swapping between arbitrary
bipartite Gaussian states, for which simple input-output formulas are provided.Comment: 4 pages, 2 figures, RevTe
Complexity of Token Swapping and its Variants
In the Token Swapping problem we are given a graph with a token placed on
each vertex. Each token has exactly one destination vertex, and we try to move
all the tokens to their destinations, using the minimum number of swaps, i.e.,
operations of exchanging the tokens on two adjacent vertices. As the main
result of this paper, we show that Token Swapping is -hard parameterized
by the length of a shortest sequence of swaps. In fact, we prove that, for
any computable function , it cannot be solved in time where is the number of vertices of the input graph, unless the ETH
fails. This lower bound almost matches the trivial -time algorithm.
We also consider two generalizations of the Token Swapping, namely Colored
Token Swapping (where the tokens have different colors and tokens of the same
color are indistinguishable), and Subset Token Swapping (where each token has a
set of possible destinations). To complement the hardness result, we prove that
even the most general variant, Subset Token Swapping, is FPT in nowhere-dense
graph classes.
Finally, we consider the complexities of all three problems in very
restricted classes of graphs: graphs of bounded treewidth and diameter, stars,
cliques, and paths, trying to identify the borderlines between polynomial and
NP-hard cases.Comment: 23 pages, 7 Figure
Fast Face-swap Using Convolutional Neural Networks
We consider the problem of face swapping in images, where an input identity
is transformed into a target identity while preserving pose, facial expression,
and lighting. To perform this mapping, we use convolutional neural networks
trained to capture the appearance of the target identity from an unstructured
collection of his/her photographs.This approach is enabled by framing the face
swapping problem in terms of style transfer, where the goal is to render an
image in the style of another one. Building on recent advances in this area, we
devise a new loss function that enables the network to produce highly
photorealistic results. By combining neural networks with simple pre- and
post-processing steps, we aim at making face swap work in real-time with no
input from the user
An Infinite Swapping Approach to the Rare-Event Sampling Problem
We describe a new approach to the rare-event Monte Carlo sampling problem.
This technique utilizes a symmetrization strategy to create probability
distributions that are more highly connected and thus more easily sampled than
their original, potentially sparse counterparts. After discussing the formal
outline of the approach and devising techniques for its practical
implementation, we illustrate the utility of the technique with a series of
numerical applications to Lennard-Jones clusters of varying complexity and
rare-event character.Comment: 24 pages, 16 figure
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