12,475 research outputs found
On the use of reproducing kernel Hilbert spaces in functional classification
The H\'ajek-Feldman dichotomy establishes that two Gaussian measures are
either mutually absolutely continuous with respect to each other (and hence
there is a Radon-Nikodym density for each measure with respect to the other
one) or mutually singular. Unlike the case of finite dimensional Gaussian
measures, there are non-trivial examples of both situations when dealing with
Gaussian stochastic processes. This paper provides:
(a) Explicit expressions for the optimal (Bayes) rule and the minimal
classification error probability in several relevant problems of supervised
binary classification of mutually absolutely continuous Gaussian processes. The
approach relies on some classical results in the theory of Reproducing Kernel
Hilbert Spaces (RKHS).
(b) An interpretation, in terms of mutual singularity, for the "near perfect
classification" phenomenon described by Delaigle and Hall (2012). We show that
the asymptotically optimal rule proposed by these authors can be identified
with the sequence of optimal rules for an approximating sequence of
classification problems in the absolutely continuous case.
(c) A new model-based method for variable selection in binary classification
problems, which arises in a very natural way from the explicit knowledge of the
RN-derivatives and the underlying RKHS structure. Different classifiers might
be used from the selected variables. In particular, the classical, linear
finite-dimensional Fisher rule turns out to be consistent under some standard
conditions on the underlying functional model
Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections
Motivated by recent scanning tunneling microscopy experiments on single
magnetic impurities on superconducting surfaces, we present here a
comprehensive theoretical study of the interplay between Yu-Shiba-Rusinov bound
states and (multiple) Andreev reflections. Our theory is based on a combination
of an Anderson model with broken spin degeneracy and nonequilibrium Green's
function techniques that allows us to describe the electronic transport through
a magnetic impurity coupled to superconducting leads for arbitrary junction
transparency. Using this combination we are able to elucidate the different
tunneling processes that give a significant contribution to the subgap
transport. In particular, we predict the occurrence of a large variety of
Andreev reflections mediated by Yu-Shiba-Rusinov bound states that clearly
differ from the standard Andreev processes in non-magnetic systems. Moreover,
we provide concrete guidelines on how to experimentally identify the subgap
features originating from these tunneling events. Overall, our work provides
new insight into the role of the spin degree of freedom in Andreev transport
physics.Comment: 15 pages, 10 figure
Field enhancement in subnanometer metallic gaps
Motivated by recent experiments [Ward et al., Nature Nanotech. 5, 732
(2010)], we present here a theoretical analysis of the optical response of
sharp gold electrodes separated by a subnanometer gap. In particular, we have
used classical finite difference time domain simulations to investigate the
electric field distribution in these nanojunctions upon illumination. Our
results show a strong confinement of the field within the gap region, resulting
in a large enhancement compared to the incident field. Enhancement factors
exceeding 1000 are found for interelectrode distances on the order of a few
angstroms, which are fully compatible with the experimental findings. Such huge
enhancements originate from the coupling of the incident light to the
evanescent field of hybrid plasmons involving charge density oscillations in
both electrodes.Comment: 4 pages, 3 figures, to appear in Physical Review
Interaction of moving breathers with an impurity
We analyze the influence of an impurity in the evolution of moving discrete
breathers in a Klein--Gordon chain with non-weak nonlinearity. Three different
behaviours can be observed when moving breathers interact with the impurity:
they pass through the impurity continuing their direction of movement; they are
reflected by the impurity; they are trapped by the impurity, giving rise to
chaotic breathers. Resonance with a breather centred at the impurity site is
conjectured to be a necessary condition for the appearance of the trapping
phenomenon.Comment: 4 pages, 2 figures, Proceedings of the Third Conference, San Lorenzo
De El Escorial, Spain 17-21 June 200
Vibrational Instabilities in Resonant Electron Transport through Single-Molecule Junctions
We analyze various limits of vibrationally coupled resonant electron
transport in single-molecule junctions. Based on a master equation approach, we
discuss analytic and numerical results for junctions under a high bias voltage
or weak electronic-vibrational coupling. It is shown that in these limits the
vibrational excitation of the molecular bridge increases indefinitely, i.e. the
junction exhibits a vibrational instability. Moreover, our analysis provides
analytic results for the vibrational distribution function and reveals that
these vibrational instabilities are related to electron-hole pair creation
processes.Comment: 19 pages, 3 figure
Effect of the Introduction of Impurities on the Stability Properties of Multibreathers at Low Coupling
sing a theorem dubbed the {\em Multibreather Stabiliy Theorem} [Physica D 180
(2003) 235-255] we have obtained the stability properties of multibreathers in
systems of coupled oscillators with on-site potentials, with an inhomogeneity.
Analytical results are obtained for 2-site, 3-site breathers, multibreathers,
phonobreathers and dark breathers. The inhomogeneity is considered both at the
on-site potential and at the coupling terms. All the results have been checked
numerically with excellent agreement. The main conclusion is that the
introduction of a impurity does not alter the stability properties.Comment: 20 pages, 9 figure
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