28,862 research outputs found
Cosmological constant and late transient acceleration of the universe in the Horava-Witten Heterotic M-Theory on S^{1}/Z_{2}
Orbifold branes are studied in the framework of the 11-dimensional
Horava-Witten heterotic M-Theory. It is found that the effective cosmological
constant can be easily lowered to its current observational value by the
mechanism of large extra dimensions. The domination of this constant over the
evolution of the universe is only temporarily. Due to the interaction of the
bulk and the branes, the universe will be in its decelerating expansion phase
again in the future, whereby all problems connected with a far future de Sitter
universe are resolved.Comment: latex4 file, one figure. Version to be published in Physics Letters
Hierarchical Theory of Quantum Adiabatic Evolution
Quantum adiabatic evolution is a dynamical evolution of a quantum system
under slow external driving. According to the quantum adiabatic theorem, no
transitions occur between non-degenerate instantaneous eigen-energy levels in
such a dynamical evolution. However, this is true only when the driving rate is
infinitesimally small. For a small nonzero driving rate, there are generally
small transition probabilities between the energy levels. We develop a
classical mechanics framework to address the small deviations from the quantum
adiabatic theorem order by order. A hierarchy of Hamiltonians are constructed
iteratively with the zeroth-order Hamiltonian being determined by the original
system Hamiltonian. The th-order deviations are governed by a th-order
Hamiltonian, which depends on the time derivatives of the adiabatic parameters
up to the th-order. Two simple examples, the Landau-Zener model and a
spin-1/2 particle in a rotating magnetic field, are used to illustrate our
hierarchical theory. Our analysis also exposes a deep, previously unknown
connection between classical adiabatic theory and quantum adiabatic theory.Comment: 10 pages, 6 figures, 29 reference
Learning Active Basis Models by EM-Type Algorithms
EM algorithm is a convenient tool for maximum likelihood model fitting when
the data are incomplete or when there are latent variables or hidden states. In
this review article we explain that EM algorithm is a natural computational
scheme for learning image templates of object categories where the learning is
not fully supervised. We represent an image template by an active basis model,
which is a linear composition of a selected set of localized, elongated and
oriented wavelet elements that are allowed to slightly perturb their locations
and orientations to account for the deformations of object shapes. The model
can be easily learned when the objects in the training images are of the same
pose, and appear at the same location and scale. This is often called
supervised learning. In the situation where the objects may appear at different
unknown locations, orientations and scales in the training images, we have to
incorporate the unknown locations, orientations and scales as latent variables
into the image generation process, and learn the template by EM-type
algorithms. The E-step imputes the unknown locations, orientations and scales
based on the currently learned template. This step can be considered
self-supervision, which involves using the current template to recognize the
objects in the training images. The M-step then relearns the template based on
the imputed locations, orientations and scales, and this is essentially the
same as supervised learning. So the EM learning process iterates between
recognition and supervised learning. We illustrate this scheme by several
experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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