5,046 research outputs found
Efficient generation of random derangements with the expected distribution of cycle lengths
We show how to generate random derangements efficiently by two different
techniques: random restricted transpositions and sequential importance
sampling. The algorithm employing restricted transpositions can also be used to
generate random fixed-point-free involutions only, a.k.a. random perfect
matchings on the complete graph. Our data indicate that the algorithms generate
random samples with the expected distribution of cycle lengths, which we
derive, and for relatively small samples, which can actually be very large in
absolute numbers, we argue that they generate samples indistinguishable from
the uniform distribution. Both algorithms are simple to understand and
implement and possess a performance comparable to or better than those of
currently known methods. Simulations suggest that the mixing time of the
algorithm based on random restricted transpositions (in the total variance
distance with respect to the distribution of cycle lengths) is
with and the length of the
derangement. We prove that the sequential importance sampling algorithm
generates random derangements in time with probability of
failing.Comment: This version corrected and updated; 14 pages, 2 algorithms, 2 tables,
4 figure
Two-stream instability in quasi-one-dimensional Bose-Einstein condensates
We apply a kinetic model to predict the existence of an instability mechanism in elongated Bose-Einstein condensates. Our kinetic description, based on the Wigner formalism, is employed to highlight the existence of unstable Bogoliubov waves that may be excited in the counterpropagation configuration. We identify a dimensionless parameter, the Mach number at T=0, that tunes different regimes of stability. We also estimate the magnitude of the main parameters at which two-stream instability is expected to be observed under typical experimental conditions
Driven collective instabilities in magneto-optical traps: a fluid-dynamical approach
We present a theoretical model to describe an instability mechanism in
ultra-cold gases, where long-range interactions are taken into account.
Focusing on the nonlinear coupling between the collective (plasma-like) and the
center-of-mass modes, we show that the resulting dynamics is governed by a
parametric equation of the generalized Mathieu type and compute the
corresponding stability chart. We apply our model to typical ranges of
magneto-optical traps (MOT) parameters and find a good agreement with previous
experimental observations.Comment: 4 pages, 3 figures. Some minor changes in the published version
Cascaded Nondegenerate Four-Wave Mixing Technique for High-Power Single-Cycle Pulse Synthesis in the Visible and Ultraviolet Ranges
We present a new technique to synthesize high-power single-cycle pulses in
the visible and ultraviolet ranges by coherent superposition of a multiband
octave-spanning spectrum obtained by highly-nondegenerate cascaded four-wave
mixing of femtosecond pulses in bulk isotropic nonresonant media. The
generation of coherent spectra spanning over two octaves in bandwidth is
experimentally demonstrated using a thin fused silica slide. Full
characterization of the intervening multicolored fields using
frequency-resolved optical gating, where multiple cascaded orders have been
measured simultaneously for the first time, supports the possibility of direct
synthesis of near-single-cycle 2.2 fs visible-UV pulses without recurring to
complex amplitude or phase control, which should enable many applications in
science and technology.Comment: 13 pages, 4 figures. Submitted to Physical Review
Massive "spin-2" theories in arbitrary dimensions
Here we show that in arbitrary dimensions there are two families of
second order Lagrangians describing massive "spin-2" particles via a
nonsymmetric rank-2 tensor. They differ from the usual Fierz-Pauli theory in
general. At zero mass one of the families is Weyl invariant. Such massless
theory has no particle content in and gives rise, via master action, to a
dual higher order (in derivatives) description of massive spin-2 particles in
where both the second and the fourth order terms are Weyl invariant,
contrary to the linearized New Massive Gravity. However, only the fourth order
term is invariant under arbitrary antisymmetric shifts. Consequently, the
antisymmetric part of the tensor propagates at large momentum as
instead of . So, the same kind of obstacle for the
renormalizability of the New Massive Gravity reappears in this nonsymmetric
higher order description of massive spin-2 particles.Comment: 11 pages, 0 figure
Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion
Here we obtain alternative descriptions of massive spin-2 particles by an
embedding procedure of the Fierz-Pauli equations of motion. All models are free
of ghosts at quadratic level although most of them are of higher order in
derivatives. The models that we obtain can be nonlinearly completed in terms of
a dynamic and a fixed metric. They include some massive gravities
recently considered in the literature. In some cases there is an infrared (no
derivative) modification of the Fierz-Pauli mass term altogether with higher
order terms in derivatives. The analytic structure of the propagator of the
corresponding free theories is not affected by the extra terms in the action as
compared to the usual second order Fierz-Pauli theory.Comment: 13 page
Detection of Polyps via Shape and Appearance Modeling
Presented at the MICCAI 2008 Workshop on Computational and Visualization Challenges in the New Era of Virtual Colonoscopy, September 6, 2008, New York, USA.This paper describes a CAD system for the detection of colorectal polyps in CT. It is based on stochastic shape and appearance modeling of structures of the colon and rectum, in contrast to the data-driven approaches more commonly found in the literature it derives predictive stochastic models for the features used for classification. The method makes extensive use of medical domain knowledge in the design of the models and in the setting of their parameters. The proposed approach was successfully tested on challenging datasets acquired under a protocol with little colonic preparation; such protocol reduces patient discomfort and potentially improves compliance
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