66,898 research outputs found
Multitask Learning for Fine-Grained Twitter Sentiment Analysis
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
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
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
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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