10,498 research outputs found
High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation
The ratio between two probability density functions is an important component
of various tasks, including selection bias correction, novelty detection and
classification. Recently, several estimators of this ratio have been proposed.
Most of these methods fail if the sample space is high-dimensional, and hence
require a dimension reduction step, the result of which can be a significant
loss of information. Here we propose a simple-to-implement, fully nonparametric
density ratio estimator that expands the ratio in terms of the eigenfunctions
of a kernel-based operator; these functions reflect the underlying geometry of
the data (e.g., submanifold structure), often leading to better estimates
without an explicit dimension reduction step. We show how our general framework
can be extended to address another important problem, the estimation of a
likelihood function in situations where that function cannot be
well-approximated by an analytical form. One is often faced with this situation
when performing statistical inference with data from the sciences, due the
complexity of the data and of the processes that generated those data. We
emphasize applications where using existing likelihood-free methods of
inference would be challenging due to the high dimensionality of the sample
space, but where our spectral series method yields a reasonable estimate of the
likelihood function. We provide theoretical guarantees and illustrate the
effectiveness of our proposed method with numerical experiments.Comment: With supplementary materia
On the structure of framed vertex operator algebras and their pointwise frame stabilizers
In this paper, we study the structure of a general framed vertex operator
algebra. We show that the structure codes (C,D) of a framed VOA V satisfy
certain duality conditions. As a consequence, we prove that every framed VOA is
a simple current extension of the associated binary code VOA V_C. This result
would give a prospect on the classification of framed vertex operator algebras.
In addition, the pointwise frame stabilizer of V is studied. We completely
determine all automorphisms in this pointwise stabilizer, which are of order 1,
2 or 4. The 4A-twisted sector and the 4A-twisted orbifold theory of the famous
Moonshine VOA are also constructed explicitly. We verify that the top module of
this twisted sector is of dimension 1 and of weight 3/4 and the VOA obtained by
4A-twisted orbifold construction of the moonshine VOA is isomorphic to the
moonshine VOA itself.Comment: Version 3: 59 pages. Corrected version. 54 pages on my LaTeX system
version 2: We add Theorem 5.16 in which we give a necessary and sufficient
condtion for a code to be a structure code of a holomorphic framed VOA.
"hyperref" style is also introduce
Quantum interference in attosecond transient absorption of laser-dressed helium atoms
We calculate the transient absorption of an isolated attosecond pulse by
helium atoms subject to a delayed infrared (\ir) laser pulse. With the central
frequency of the broad attosecond spectrum near the ionization threshold, the
absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given
that the absorption spectrum results from a time-integrated measurement, we
investigate the extent to which the delay-dependence of the absorption yields
information about the attosecond dynamics of the atom-field energy exchange. We
find two configurations in which this is possible. The first involves multi
photon transitions between bound states that result in interference between
different excitation pathways. The other involves the modification of the bound
state absorption lines by the IR field, which we find can result in a sub-cycle
time dependence only when ionization limits the duration of the strong field
interaction
Oblique and curved D-branes in IIB plane-wave string theory
Oblique Dp-branes in the maximally supersymmetric type IIB plane-wave
background are constructed in terms of boundary states, as well as from the
open string point of view. These Dp-branes, whose existence was anticipated by
Hikida and Yamaguchi from general supersymmetry arguments, have an isometry
that is a subgroup of the diagonal SO(4) symmetry of the background. The
oblique D3-brane is found to preserve four dynamical and four kinematical
supersymmetries while the oblique D5-brane preserves one half of both the
dynamical and kinematical supersymmetries. We also discuss the open-string
boundary conditions for curved D7- and D5-branes, and analyze their
supersymmetry.Comment: 27 page
Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra
We study the influence of phase matching on interference minima in high
harmonic spectra. We concentrate on structures in atoms due to interference of
different angular momentum channels during recombination. We use the Cooper
minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure
2d harmonic spectra in argon as a function of wavelength and angular
divergence. While we identify a clear CM in the spectrum when the target gas
jet is placed after the laser focus, we find that the appearance of the CM
varies with angular divergence and can even be completely washed out when the
gas jet is placed closer to the focus. We also show that the argon CM appears
at different wavelengths in harmonic and photo-absorption spectra measured
under conditions independent of any wavelength calibration. We model the
experiment with a simulation based on coupled solutions of the time-dependent
Schr\"odinger equation and the Maxwell wave equation, including both the single
atom response and macroscopic effects of propagation. The single atom
calculations confirm that the ground state of argon can be represented by its
field free symmetry, despite the strong laser field used in high harmonic
generation. Because of this, the CM structure in the harmonic spectrum can be
described as the interference of continuum and channels, whose relative
phase jumps by at the CM energy, resulting in a minimum shifted from the
photoionization result. We also show that the full calculations reproduce the
dependence of the CM on the macroscopic conditions. We calculate simple phase
matching factors as a function of harmonic order and explain our experimental
and theoretical observation in terms of the effect of phase matching on the
shape of the harmonic spectrum. Phase matching must be taken into account to
fully understand spectral features related to HHG spectroscopy
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