7,197 research outputs found
Fast learning rates for plug-in classifiers under the margin condition
It has been recently shown that, under the margin (or low noise) assumption,
there exist classifiers attaining fast rates of convergence of the excess Bayes
risk, i.e., the rates faster than . The works on this subject
suggested the following two conjectures: (i) the best achievable fast rate is
of the order , and (ii) the plug-in classifiers generally converge
slower than the classifiers based on empirical risk minimization. We show that
both conjectures are not correct. In particular, we construct plug-in
classifiers that can achieve not only the fast, but also the {\it super-fast}
rates, i.e., the rates faster than . We establish minimax lower bounds
showing that the obtained rates cannot be improved.Comment: 36 page
The effect of dark strings on semilocal strings
Dark strings have recently been suggested to exist in new models of dark
matter that explain the excessive electronic production in the galaxy. We study
the interaction of these dark strings with semilocal strings which are
solutions of the bosonic sector of the Standard Model in the limit
, where is the Weinberg angle. While
embedded Abelian-Higgs strings exist for generic values of the coupling
constants, we show that semilocal solutions with non-vanishing condensate
inside the string core exist only above a critical value of the Higgs to gauge
boson mass ratio when interacting with dark strings. Above this critical value,
which is greater than unity, the energy per unit length of the semilocal-dark
string solutions is always smaller than that of the embedded Abelian-Higgs-dark
string solutions and we show that Abelian-Higgs-dark strings become unstable
above this critical value. Different from the non-interacting case, we would
thus expect semilocal strings to be stable for values of the Higgs to gauge
boson mass ratio larger than unity. Moreover, the one-parameter family of
solutions present in the non-interacting case ceases to exist when semilocal
strings interact with dark strings.Comment: 16 pages including 6 figures; stability analysis adde
The varying w spread spectrum effect for radio interferometric imaging
We study the impact of the spread spectrum effect in radio interferometry on
the quality of image reconstruction. This spread spectrum effect will be
induced by the wide field-of-view of forthcoming radio interferometric
telescopes. The resulting chirp modulation improves the quality of
reconstructed interferometric images by increasing the incoherence of the
measurement and sparsity dictionaries. We extend previous studies of this
effect to consider the more realistic setting where the chirp modulation varies
for each visibility measurement made by the telescope. In these first
preliminary results, we show that for this setting the quality of
reconstruction improves significantly over the case without chirp modulation
and achieves almost the reconstruction quality of the case of maximal, constant
chirp modulation.Comment: 1 page, 1 figure, Proceedings of the Biomedical and Astronomical
Signal Processing Frontiers (BASP) workshop 201
Remarks on the interaction between Born-Infeld solitons
We consider the Abelian Higgs model as well as the SU(2) Georgi-Glashow model
in which the gauge field action is replaced by a non linear Born-Infeld action.
We study soliton solutions arising in these models, namely the vortex and
monopole solutions, respectively. We construct formulas which provide good
approximations for the mass of the Born-Infeld deformed solitons using only the
data of the undeformed solutions. The results obtained indicate that in the
self-dual limit, the Born-Infeld interaction leads to bound vortices, while for
monopoles it gives rise to repulsion.Comment: 11 Revtex pages; some typos corrected, formular adde
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