15,508 research outputs found
Wavevector-dependent spin filtering and spin transport through magnetic barriers in graphene
We study the spin-resolved transport through magnetic nanostructures in monolayer and bilayer graphene. We take into account both the orbital effect of the inhomogeneous perpendicular magnetic field as well as the in-plane spin splitting due to the Zeeman interaction and to the exchange coupling possibly induced by the proximity of a ferromagnetic insulator. We find that a single barrier exhibits a wavevector-dependent spin filtering effect at energies close to the transmission threshold. This effect is significantly enhanced in a resonant double barrier configuration, where the spin polarization of the outgoing current can be increased up to 100% by increasing the distance between the barriers
Effective Sample Size for Importance Sampling based on discrepancy measures
The Effective Sample Size (ESS) is an important measure of efficiency of
Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance
Sampling (IS) techniques. In the IS context, an approximation
of the theoretical ESS definition is widely applied, involving the inverse of
the sum of the squares of the normalized importance weights. This formula,
, has become an essential piece within Sequential Monte Carlo
(SMC) methods, to assess the convenience of a resampling step. From another
perspective, the expression is related to the Euclidean
distance between the probability mass described by the normalized weights and
the discrete uniform probability mass function (pmf). In this work, we derive
other possible ESS functions based on different discrepancy measures between
these two pmfs. Several examples are provided involving, for instance, the
geometric mean of the weights, the discrete entropy (including theperplexity
measure, already proposed in literature) and the Gini coefficient among others.
We list five theoretical requirements which a generic ESS function should
satisfy, allowing us to classify different ESS measures. We also compare the
most promising ones by means of numerical simulations
Magnetic confinement of massless Dirac fermions in graphene
Due to Klein tunneling, electrostatic potentials are unable to confine Dirac
electrons. We show that it is possible to confine massless Dirac fermions in a
monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to
design mesoscopic structures in graphene by magnetic barriers, e.g. quantum
dots or quantum point contacts.Comment: 4 pages, 3 figures, version to appear in PR
Group Importance Sampling for Particle Filtering and MCMC
Bayesian methods and their implementations by means of sophisticated Monte
Carlo techniques have become very popular in signal processing over the last
years. Importance Sampling (IS) is a well-known Monte Carlo technique that
approximates integrals involving a posterior distribution by means of weighted
samples. In this work, we study the assignation of a single weighted sample
which compresses the information contained in a population of weighted samples.
Part of the theory that we present as Group Importance Sampling (GIS) has been
employed implicitly in different works in the literature. The provided analysis
yields several theoretical and practical consequences. For instance, we discuss
the application of GIS into the Sequential Importance Resampling framework and
show that Independent Multiple Try Metropolis schemes can be interpreted as a
standard Metropolis-Hastings algorithm, following the GIS approach. We also
introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS.
The first one, named Group Metropolis Sampling method, produces a Markov chain
of sets of weighted samples. All these sets are then employed for obtaining a
unique global estimator. The second one is the Distributed Particle
Metropolis-Hastings technique, where different parallel particle filters are
jointly used to drive an MCMC algorithm. Different resampled trajectories are
compared and then tested with a proper acceptance probability. The novel
schemes are tested in different numerical experiments such as learning the
hyperparameters of Gaussian Processes, two localization problems in a wireless
sensor network (with synthetic and real data) and the tracking of vegetation
parameters given satellite observations, where they are compared with several
benchmark Monte Carlo techniques. Three illustrative Matlab demos are also
provided.Comment: To appear in Digital Signal Processing. Related Matlab demos are
provided at https://github.com/lukafree/GIS.gi
Parallel Metropolis chains with cooperative adaptation
Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) algorithms, have
become very popular in signal processing over the last years. In this work, we
introduce a novel MCMC scheme where parallel MCMC chains interact, adapting
cooperatively the parameters of their proposal functions. Furthermore, the
novel algorithm distributes the computational effort adaptively, rewarding the
chains which are providing better performance and, possibly even stopping other
ones. These extinct chains can be reactivated if the algorithm considers
necessary. Numerical simulations shows the benefits of the novel scheme
Topology-Induced Inverse Phase Transitions
Inverse phase transitions are striking phenomena in which an apparently more
ordered state disorders under cooling. This behavior can naturally emerge in
tricritical systems on heterogeneous networks and it is strongly enhanced by
the presence of disassortative degree correlations. We show it both
analytically and numerically, providing also a microscopic interpretation of
inverse transitions in terms of freezing of sparse subgraphs and coupling
renormalization.Comment: 4 pages, 4 figure
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