4,035 research outputs found
Adiabatic Floquet model for the optical response in femtosecond filaments
The standard model of femtosecond filamentation is based on phenomenological
assumptions which suggest that the ionization-induced carriers can be treated
as free according to the Drude model, while the nonlinear response of the bound
carriers follows the all-optical Kerr effect. Here, we demonstrate that the
additional plasma generated at a multiphoton resonance dominates the saturation
of the nonlinear refractive index. Since resonances are not captured by the
standard model, we propose a modification of the latter in which ionization
enhancements can be accounted for by an ionization rate obtained from
non-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes,
this augmented standard model is in excellent agreement with direct quantum
mechanical simulations. Since our proposal maintains the structure of the
standard model, it can be easily incorporated into existing codes of filament
simulation.Comment: 14 pages, 6 figures, submitted to New Journal of Physic
Probing nonlinear adiabatic paths with a universal integrator
We apply a flexible numerical integrator to the simulation of adiabatic
quantum computation with nonlinear paths. We find that a nonlinear path may
significantly improve the performance of adiabatic algorithms versus the
conventional straight-line interpolations. The employed integrator is suitable
for solving the time-dependent Schr\"odinger equation for any qubit
Hamiltonian. Its flexible storage format significantly reduces cost for storage
and matrix-vector multiplication in comparison to common sparse matrix schemes.Comment: 8 pages, 6 figure
Building suitable sets for locally compact groups by means of continuous selections
If a discrete subset S of a topological group G with the identity 1 generates
a dense subgroup of G and S \cup {1} is closed in G, then S is called a
suitable set for G. We apply Michael's selection theorem to offer a direct,
self-contained, purely topological proof of the result of Hofmann and Morris on
the existence of suitable sets in locally compact groups. Our approach uses
only elementary facts from (topological) group theory.Comment: No changes except page layout. 11 pages. To appear in: Topology and
its Application
The multivariate Piecing-Together approach revisited
The univariate Piecing-Together approach (PT) fits a univariate generalized
Pareto distribution (GPD) to the upper tail of a given distribution function in
a continuous manner. A multivariate extension was established by Aulbach et al.
(2012a): The upper tail of a given copula C is cut off and replaced by a
multivariate GPD-copula in a continuous manner, yielding a new copula called a
PT-copula. Then each margin of this PT-copula is transformed by a given
univariate distribution function. This provides a multivariate distribution
function with prescribed margins, whose copula is a GPD-copula that coincides
in its central part with C. In addition to Aulbach et al. (2012a), we achieve
in the present paper an exact representation of the PT-copula's upper tail,
giving further insight into the multivariate PT approach. A variant based on
the empirical copula is also added. Furthermore our findings enable us to
establish a functional PT version as well.Comment: 12 pages, 1 figure. To appear in the Journal of Multivariate Analysi
A stochastic model for multivariate surveillance of infectious diseases
We describe a stochastic model based on a branching process for analyzing surveillance data of infectious diseases that allows to make forecasts of the future development of the epidemic. The model is based on a Poisson branching process with immigration with additional adjustment for possible overdispersion. An extension to a space-time model for the multivariate case is described. The model is estimated in a Bayesian context using Markov Chain Monte Carlo (MCMC) techniques. We illustrate the applicability of the model through analyses of simulated and real data
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