168,919 research outputs found
Unambiguous comparison of the states of multiple quantum systems
We consider N quantum systems initially prepared in pure states and address
the problem of unambiguously comparing them. One may ask whether or not all
systems are in the same state. Alternatively, one may ask whether or not the
states of all N systems are different. We investigate the possibility of
unambiguously obtaining this kind of information. It is found that some
unambiguous comparison tasks are possible only when certain linear independence
conditions are satisfied. We also obtain measurement strategies for certain
comparison tasks which are optimal under a broad range of circumstances, in
particular when the states are completely unknown. Such strategies, which we
call universal comparison strategies, are found to have intriguing connections
with the problem of quantifying the distinguishability of a set of quantum
states and also with unresolved conjectures in linear algebra. We finally
investigate a potential generalisation of unambiguous state comparison, which
we term unambiguous overlap filtering.Comment: 20 pages, no figure
The evolution of classical doubles: clues from complete samples
We describe the inter-dependence of four properties of classical double radio
sources - spectral index, linear size, luminosity and redshift - from an
extensive study based on spectroscopically-identified complete samples. We use
these relationships to discuss aspects of strategies for searching for radio
galaxies at extreme redshifts, in the context of possible capabilities of the
new generation of proposed radio telescopes.Comment: To appear in `Perspectives in Radio Astronomy: scientific imperatives
at cm and m wavelengths.' eds: M.P. van Haarlem and J.M. van der Hulst
Version with colour figures available at
http://www-astro.physics.ox.ac.uk/~km
Optimal Transport for Domain Adaptation
Domain adaptation from one data space (or domain) to another is one of the
most challenging tasks of modern data analytics. If the adaptation is done
correctly, models built on a specific data space become more robust when
confronted to data depicting the same semantic concepts (the classes), but
observed by another observation system with its own specificities. Among the
many strategies proposed to adapt a domain to another, finding a common
representation has shown excellent properties: by finding a common
representation for both domains, a single classifier can be effective in both
and use labelled samples from the source domain to predict the unlabelled
samples of the target domain. In this paper, we propose a regularized
unsupervised optimal transportation model to perform the alignment of the
representations in the source and target domains. We learn a transportation
plan matching both PDFs, which constrains labelled samples in the source domain
to remain close during transport. This way, we exploit at the same time the few
labeled information in the source and the unlabelled distributions observed in
both domains. Experiments in toy and challenging real visual adaptation
examples show the interest of the method, that consistently outperforms state
of the art approaches
Community detection in networks via nonlinear modularity eigenvectors
Revealing a community structure in a network or dataset is a central problem
arising in many scientific areas. The modularity function is an established
measure quantifying the quality of a community, being identified as a set of
nodes having high modularity. In our terminology, a set of nodes with positive
modularity is called a \textit{module} and a set that maximizes is thus
called \textit{leading module}. Finding a leading module in a network is an
important task, however the dimension of real-world problems makes the
maximization of unfeasible. This poses the need of approximation techniques
which are typically based on a linear relaxation of , induced by the
spectrum of the modularity matrix . In this work we propose a nonlinear
relaxation which is instead based on the spectrum of a nonlinear modularity
operator . We show that extremal eigenvalues of
provide an exact relaxation of the modularity measure , however at the price
of being more challenging to be computed than those of . Thus we extend the
work made on nonlinear Laplacians, by proposing a computational scheme, named
\textit{generalized RatioDCA}, to address such extremal eigenvalues. We show
monotonic ascent and convergence of the method. We finally apply the new method
to several synthetic and real-world data sets, showing both effectiveness of
the model and performance of the method
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
In the framework of large deformation diffeomorphic metric mapping (LDDMM),
we develop a multi-scale theory for the diffeomorphism group based on previous
works. The purpose of the paper is (1) to develop in details a variational
approach for multi-scale analysis of diffeomorphisms, (2) to generalise to
several scales the semidirect product representation and (3) to illustrate the
resulting diffeomorphic decomposition on synthetic and real images. We also
show that the approaches presented in other papers and the mixture of kernels
are equivalent.Comment: 21 pages, revised version without section on evaluatio
Strict bounding of quantities of interest in computations based on domain decomposition
This paper deals with bounding the error on the estimation of quantities of
interest obtained by finite element and domain decomposition methods. The
proposed bounds are written in order to separate the two errors involved in the
resolution of reference and adjoint problems : on the one hand the
discretization error due to the finite element method and on the other hand the
algebraic error due to the use of the iterative solver. Beside practical
considerations on the parallel computation of the bounds, it is shown that the
interface conformity can be slightly relaxed so that local enrichment or
refinement are possible in the subdomains bearing singularities or quantities
of interest which simplifies the improvement of the estimation. Academic
assessments are given on 2D static linear mechanic problems.Comment: Computer Methods in Applied Mechanics and Engineering, Elsevier,
2015, online previe
- …