66,898 research outputs found

    Multitask Learning for Fine-Grained Twitter Sentiment Analysis

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    Traditional sentiment analysis approaches tackle problems like ternary (3-category) and fine-grained (5-category) classification by learning the tasks separately. We argue that such classification tasks are correlated and we propose a multitask approach based on a recurrent neural network that benefits by jointly learning them. Our study demonstrates the potential of multitask models on this type of problems and improves the state-of-the-art results in the fine-grained sentiment classification problem.Comment: International ACM SIGIR Conference on Research and Development in Information Retrieval 201

    Ideal Submodules versus Ternary Ideals versus Linking Ideals

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    We show that ideal submodules and closed ternary ideals in Hilbert modules are the same; this contradicts the result of [Kol17]. We use this insight as a little peg on which to hang a little note about interrelations with other notions regarding Hilbert modules. In Section 1, we show (to our knowledge for the first time) that the ternary ideals (and equivalent notions) merit fully, in terms of homomorphisms and quotients, to be called ideals of (not necessarily full) Hilbert modules. The properties to be checked are intrinsically formulated for the modules (without any reference to the algebra over which they are modules) in terms of their ternary structure. The proofs, instead, are motivated from a third equivalent notion, linking ideals (Section 0), and a Theorem (Section 1) that all extends nicely to (reduced) linking algebras. As an application, in Section 2, we reprove most of the basic statements about extensions of Hilbert modules, by reducing their proof to the well-know analogue theorems about extensions of C*-algebras. Finally, in Section 3, we propose several new open problems that our method naturally suggests.Comment: 24 pages; corrected typos and minor cosmetics; new abstract; details added to the proof of Theorem 2.

    Fluctuating hydrodynamics of multi-species, non-reactive mixtures

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    In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of non-equilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multi-species fluids. The extension to include chemical reactions will be treated in a sequel paper

    Ternary expansions of powers of 2

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    Paul Erdos asked how frequently the ternary expansion of 2^n omits the digit 2. He conjectured this happens only for finitely many values of n. We generalize this question to consider iterates of two discrete dynamical systems. The first is over the real numbers, and considers the integer part of lambda 2^n for a real input lambda. The second is over the 3-adic integers, and considers the sequence lambda 2^n for a 3-adic integer input lambda. We show that the number of input values that have infinitely many iterates omitting the digit 2 in their ternary expansion is small in a suitable sense. For each nonzero input we give an asymptotic upper bound on the number of the first k iterates that omit the digit 2, as k goes to infinity. We also study auxiliary problems concerning the Hausdorff dimension of intersections of multiplicative translates of 3-adic Cantor sets.Comment: 28 pages latex; v4 major revision, much more detail to proofs, added material on intersections of Cantor set
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