14,474 research outputs found
Do Convolutional Networks need to be Deep for Text Classification ?
We study in this work the importance of depth in convolutional models for
text classification, either when character or word inputs are considered. We
show on 5 standard text classification and sentiment analysis tasks that deep
models indeed give better performances than shallow networks when the text
input is represented as a sequence of characters. However, a simple
shallow-and-wide network outperforms deep models such as DenseNet with word
inputs. Our shallow word model further establishes new state-of-the-art
performances on two datasets: Yelp Binary (95.9\%) and Yelp Full (64.9\%)
Two-loop self-energy diagrams worked out with NDIM
In this work we calculate two two-loop massless Feynman integrals pertaining
to self-energy diagrams using NDIM (Negative Dimensional Integration Method).
We show that the answer we get is 36-fold degenerate. We then consider special
cases of exponents for propagators and the outcoming results compared with
known ones obtained via traditional methods.Comment: LaTeX, 10 pages, 2 figures, styles include
Prescriptionless light-cone integrals
Perturbative quantum gauge field theory seen within the perspective of
physical gauge choices such as the light-cone entails the emergence of
troublesome poles of the type in the Feynman integrals,
and these come from the boson field propagator, where and
is the external arbitrary four-vector that defines the gauge proper.
This becomes an additional hurdle to overcome in the computation of Feynman
diagrams, since any graph containing internal boson lines will inevitably
produce integrands with denominators bearing the characteristic gauge-fixing
factor. How one deals with them has been the subject of research for over
decades, and several prescriptions have been suggested and tried in the course
of time, with failures and successes.
However, a more recent development in this front which applies the negative
dimensional technique to compute light-cone Feynman integrals shows that we can
altogether dispense with prescriptions to perform the calculations. An
additional bonus comes attached to this new technique in that not only it
renders the light-cone prescriptionless, but by the very nature of it, can also
dispense with decomposition formulas or partial fractioning tricks used in the
standard approach to separate pole products of the type , .
In this work we demonstrate how all this can be done.Comment: 6 pages, no figures, Revtex style, reference [2] correcte
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
As a continuation of our series works on the Boltzmann equation without
angular cutoff assumption, in this part, the global existence of solution to
the Cauchy problem in the whole space is proved in some suitable weighted
Sobolev spaces for hard potential when the solution is a small perturbation of
a global equilibrium
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