168,919 research outputs found

    Unambiguous comparison of the states of multiple quantum systems

    Full text link
    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 NN 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

    Get PDF
    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

    Get PDF
    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

    Get PDF
    Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function QQ 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 QQ 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 QQ unfeasible. This poses the need of approximation techniques which are typically based on a linear relaxation of QQ, induced by the spectrum of the modularity matrix MM. In this work we propose a nonlinear relaxation which is instead based on the spectrum of a nonlinear modularity operator M\mathcal M. We show that extremal eigenvalues of M\mathcal M provide an exact relaxation of the modularity measure QQ, however at the price of being more challenging to be computed than those of MM. 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

    Full text link
    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

    Full text link
    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
    • …
    corecore