831 research outputs found

    A tool for subjective and interactive visual data exploration

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    We present SIDE, a tool for Subjective and Interactive Visual Data Exploration, which lets users explore high dimensional data via subjectively informative 2D data visualizations. Many existing visual analytics tools are either restricted to specific problems and domains or they aim to find visualizations that align with user’s belief about the data. In contrast, our generic tool computes data visualizations that are surprising given a user’s current understanding of the data. The user’s belief state is represented as a set of projection tiles. Hence, this user-awareness offers users an efficient way to interactively explore yet-unknown features of complex high dimensional datasets

    CSNE: Conditional Signed Network Embedding

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    Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations (embeddings) of these networks for the prediction of missing relations or signs. Existing embedding methods for sign prediction generally enforce different notions of status or balance theories in their optimization function. These theories, however, are often inaccurate or incomplete, which negatively impacts method performance. In this context, we introduce conditional signed network embedding (CSNE). Our probabilistic approach models structural information about the signs in the network separately from fine-grained detail. Structural information is represented in the form of a prior, while the embedding itself is used for capturing fine-grained information. These components are then integrated in a rigorous manner. CSNE's accuracy depends on the existence of sufficiently powerful structural priors for modelling signed networks, currently unavailable in the literature. Thus, as a second main contribution, which we find to be highly valuable in its own right, we also introduce a novel approach to construct priors based on the Maximum Entropy (MaxEnt) principle. These priors can model the \emph{polarity} of nodes (degree to which their links are positive) as well as signed \emph{triangle counts} (a measure of the degree structural balance holds to in a network). Experiments on a variety of real-world networks confirm that CSNE outperforms the state-of-the-art on the task of sign prediction. Moreover, the MaxEnt priors on their own, while less accurate than full CSNE, achieve accuracies competitive with the state-of-the-art at very limited computational cost, thus providing an excellent runtime-accuracy trade-off in resource-constrained situations

    Introductory clifford analysis

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    In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

    On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix

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    The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all Rothstein contributions known as Efetov-Wegner terms in physics was quite cumbersome. We derive the supermatrix Bessel function with all Efetov-Wegner terms for an arbitrary rotation invariant probability density function. As applications we consider representations of generating functions for Hermitian random matrices with and without an external field as integrals over eigenvalues of Hermitian supermatrices. All results are obtained with all Efetov-Wegner terms which were unknown before in such an explicit and compact representation.Comment: 23 pages, PACS: 02.30.Cj, 02.30.Fn, 02.30.Px, 05.30.Ch, 05.30.-d, 05.45.M

    De Noordzee: een waardevol archief onder water. Meer dan 100 jaar onderzoek van strandvondsten en vondsten uit zee in België: een overzicht

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    De Noordzee kan beschouwd worden als een waardevol en speciaal archief, met heel wat interessante informatie over het verleden. De zone beneden de laagwaterlijn behoort tot het domein van de subtidale archeologie of de archeologie van het subgetijdengebied van de Noordzee. De zone tussen de hoog- en de laagwaterlijn behoort tot de intertidale archeologie of de archeologie van het intergetijdengebied van de Noordzee. In het eerste deel van deze studie wordt kort de geschiedenis van het onderzoek in deze beide zones geschetst. Daarna wordt in een tweede deel een chronologisch overzicht gegeven van de resultaten van het onderzoek en dit vanaf het ontstaan van de archeologie als wetenschappelijke discipline. In dit tweede deel wordt ook een klein aantal tot nu toe ongepubliceerde vondsten opgenomen van buiten het Belgische deel van de Noordzee. De reden hiervoor is zowel pragmatisch als inhoudelijk. Enerzijds worden deze vondsten geregistreerd samen met de andere vondsten, ze bevinden zich immers samen in de bestudeerde collecties. Anderzijds dragen ze ook inhoudelijk bij tot een beter inzicht in de genese van het hele zuidelijke Noordzeegebied, waarvan de zone onder Belgisch toezicht deel uitmaakt. Verder dienen in dit tweede deel ook een aantal vraagstellingen en onderzoeksstrategieën als basis voor de globale discussie in het derde deel van deze bijdrage. De bijdrage wordt ten slotte afgesloten met een zo volledig mogelijke bibliografie over het onderzoek in het Belgische deel van de Noordzee inclusief de stranden

    Fast Gaussian Pairwise Constrained Spectral Clustering

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    International audienceWe consider the problem of spectral clustering with partial supervision in the form of must-link and cannot-link constraints. Such pairwise constraints are common in problems like coreference resolution in natural language processing. The approach developed in this paper is to learn a new representation space for the data together with a dis-tance in this new space. The representation space is obtained through a constraint-driven linear transformation of a spectral embedding of the data. Constraints are expressed with a Gaussian function that locally reweights the similarities in the projected space. A global, non-convex optimization objective is then derived and the model is learned via gradi-ent descent techniques. Our algorithm is evaluated on standard datasets and compared with state of the art algorithms, like [14,18,31]. Results on these datasets, as well on the CoNLL-2012 coreference resolution shared task dataset, show that our algorithm significantly outperforms related approaches and is also much more scalable

    q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials

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    We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows to construct q-deformed Schroedinger equations in higher dimensions. The equivalence of these Schroedinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an su_q(1|1)-representation
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