7,718 research outputs found

    Rebels Lead to the Doctrine of the Mean: Opinion Dynamic in a Heterogeneous DeGroot Model

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    We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors' opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updates her opinion by taking another weighted average between that value and her own opinion in the last round. We find that the effect of rebels is rather significant: as long as there is at least one rebel in every closed and strongly connected group, under very weak conditions, the opinion of each player in the whole society will eventually tend to 0.5.Comment: 7 pages, Proceedings of The 6th International Conference on Knowledge, Information and Creativity Support Systems, Beijing, 201

    (E)-3-Bromo-N′-(2-chloro­benzyl­idene)benzohydrazide

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    The title compound, C14H10BrClN2O, was synthesized by the reaction of 2-chloro­benzaldehyde with an equimolar quantity of 3-bromo­benzohydrazide in methanol. The mol­ecule displays an E configuration about the C=N bond. The dihedral angle between the two benzene rings is 13.0 (2)°. In the crystal structure, mol­ecules are linked through inter­molecular N—H⋯O hydrogen bonds, forming chains propagating along the c axis

    Cutting the traintracks: Cauchy, Schubert and Calabi-Yau

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    In this note we revisit the maximal-codimension residues, or leading singularities, of four-dimensional LL-loop traintrack integrals with massive legs, both in Feynman parameter space and in momentum (twistor) space. We identify a class of "half traintracks" as the most general degenerations of traintracks with conventional (0-form) leading singularities, although the integrals themselves still have rigidity L12\lfloor\frac{L-1}2\rfloor due to lower-loop "full traintrack'' subtopologies. As a warm-up exercise, we derive closed-form expressions for their leading singularities both via (Cauchy's) residues in Feynman parameters, and more geometrically using the so-called Schubert problems in momentum twistor space. For LL-loop full traintracks, we compute their leading singularities as integrals of (L1)(L{-}1)-forms, which proves that the rigidity is L1L{-}1 as expected; the form is given by an inverse square root of an irreducible polynomial quartic with respect to each variable, which characterizes an (L1)(L{-}1)-dim Calabi-Yau manifold (elliptic curve, K3 surface, etc.) for any LL. We also briefly comment on the implications for the "symbology" of these traintrack integrals.Comment: refs updated; 36 pages, 12 figure

    A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

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    Abstract In this paper, the common solution problem (P1) of generalized equilibrium problems for a system of inverse-strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed-point problem (P2) for a family of uniformly quasi-&#981;-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly H&#246;lder continuous mappings are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved on approximating a common solution of (P1) and (P2) in Banach space. 2000 MSC: 26B25, 40A05</p

    On constructibility of AdS supergluon amplitudes

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    We prove that all tree-level nn-point supergluon (scalar) amplitudes in AdS5_5 can be recursively constructed, using factorization and flat-space limit. Our method is greatly facilitated by a natural R-symmetry basis for planar color-ordered amplitudes, which reduces the latter to "partial amplitudes" with simpler pole structures and factorization properties. Given the nn-point scalar amplitude, we first extract spinning amplitudes with n2n{-}2 scalars and one gluon by imposing "gauge invariance", and then use a special "no-gluon kinematics" to determine the (n+1)(n{+}1)-point scalar amplitude completely (which in turn contains the nn-point single-gluon amplitude). Explicit results of up to 8-point scalar amplitudes and up to 6-point single-gluon amplitudes are included as supplemental materials.Comment: 5 pages, 4 figures, major revision from v2 including new ancillary fil

    Understanding Hidden Memories of Recurrent Neural Networks

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    Recurrent neural networks (RNNs) have been successfully applied to various natural language processing (NLP) tasks and achieved better results than conventional methods. However, the lack of understanding of the mechanisms behind their effectiveness limits further improvements on their architectures. In this paper, we present a visual analytics method for understanding and comparing RNN models for NLP tasks. We propose a technique to explain the function of individual hidden state units based on their expected response to input texts. We then co-cluster hidden state units and words based on the expected response and visualize co-clustering results as memory chips and word clouds to provide more structured knowledge on RNNs' hidden states. We also propose a glyph-based sequence visualization based on aggregate information to analyze the behavior of an RNN's hidden state at the sentence-level. The usability and effectiveness of our method are demonstrated through case studies and reviews from domain experts.Comment: Published at IEEE Conference on Visual Analytics Science and Technology (IEEE VAST 2017
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