28,093 research outputs found
Computationally Efficient Nonparametric Importance Sampling
The variance reduction established by importance sampling strongly depends on
the choice of the importance sampling distribution. A good choice is often hard
to achieve especially for high-dimensional integration problems. Nonparametric
estimation of the optimal importance sampling distribution (known as
nonparametric importance sampling) is a reasonable alternative to parametric
approaches.In this article nonparametric variants of both the self-normalized
and the unnormalized importance sampling estimator are proposed and
investigated. A common critique on nonparametric importance sampling is the
increased computational burden compared to parametric methods. We solve this
problem to a large degree by utilizing the linear blend frequency polygon
estimator instead of a kernel estimator. Mean square error convergence
properties are investigated leading to recommendations for the efficient
application of nonparametric importance sampling. Particularly, we show that
nonparametric importance sampling asymptotically attains optimal importance
sampling variance. The efficiency of nonparametric importance sampling
algorithms heavily relies on the computational efficiency of the employed
nonparametric estimator. The linear blend frequency polygon outperforms kernel
estimators in terms of certain criteria such as efficient sampling and
evaluation. Furthermore, it is compatible with the inversion method for sample
generation. This allows to combine our algorithms with other variance reduction
techniques such as stratified sampling. Empirical evidence for the usefulness
of the suggested algorithms is obtained by means of three benchmark integration
problems. As an application we estimate the distribution of the queue length of
a spam filter queueing system based on real data.Comment: 29 pages, 7 figure
The Principal Axis of the Virgo Cluster
Using accurate distances to individual Virgo cluster galaxies obtained by the
method of Surface Brightness Fluctuations, we show that Virgo's brightest
ellipticals have a remarkably collinear arrangement in three dimensions. This
axis, which is inclined by 10 to 15 degrees from the line of sight, can be
traced to even larger scales where it appears to join a filamentary bridge of
galaxies connecting Virgo to the rich cluster Abell 1367. The orientations of
individual Virgo ellipticals also show some tendency to be aligned with the
cluster axis, as does the jet of the supergiant elliptical M87. These results
suggest that the formation of the Virgo cluster, and its brightest member
galaxies, have been driven by infall of material along the Virgo-A1367
filament.Comment: 8 pages, 4 figures, accepted for publication in ApJ Letter
E_11 and M Theory
We argue that eleven dimensional supergravity can be described by a
non-linear realisation based on the group E_{11}. This requires a formulation
of eleven dimensional supergravity in which the gravitational degrees of
freedom are described by two fields which are related by duality. We show the
existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde
E11, generalised space-time and equations of motion in four dimensions
We construct the non-linear realisation of the semi-direct product of E11 and
its first fundamental representation at low levels in four dimensions. We
include the fields for gravity, the scalars and the gauge fields as well as the
duals of these fields. The generalised space-time, upon which the fields
depend, consists of the usual coordinates of four dimensional space-time and
Lorentz scalar coordinates which belong to the 56-dimensional representation of
E7. We demand that the equations of motion are first order in derivatives of
the generalised space-time and then show that they are essentially uniquely
determined by the properties of the E11 Kac-Moody algebra and its first
fundamental representation. The two lowest equations correctly describe the
equations of motion of the scalars and the gauge fields once one takes the
fields to depend only on the usual four dimensional space-time
The Low-level Spectrum of the String
We investigate the spectrum of physical states in the string theory, up
to level 2 for a multi-scalar string, and up to level 4 for the two-scalar
string. The (open) string has a photon as its only massless state. By
using screening charges to study the null physical states in the two-scalar
string, we are able to learn about the gauge symmetries of the states in
the multi-scalar string.Comment: 31 pages, Plain Tex, CTP TAMU-70/92, Goteborg ITP 92-43,
Imperial/TP/91-92/22, KCL-TH-92-
Current-induced nuclear-spin activation in a two-dimensional electron gas
Electrically detected nuclear magnetic resonance was studied in detail in a
two-dimensional electron gas as a function of current bias and temperature. We
show that applying a relatively modest dc-current bias, I_dc ~ 0.5 microAmps,
can induce a re-entrant and even enhanced nuclear spin signal compared with the
signal obtained under similar thermal equilibrium conditions at zero current
bias. Our observations suggest that dynamic nuclear spin polarization by small
current flow is possible in a two-dimensional electron gas, allowing for easy
manipulation of the nuclear spin by simple switching of a dc current.Comment: 5 pages, 3 fig
Very Extended and at low levels, Gravity and Supergravity
We define a level for a large class of Lorentzian Kac-Moody algebras. Using
this we find the representation content of very extended and
(i.e. ) at low levels in terms of and
representations respectively. The results are consistent with the conjectured
very extended and symmetries of gravity and maximal supergravity
theories given respectively in hep-th/0104081 and hep-th/0107209. We explain
how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference
expanded
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