6,757 research outputs found
There is no variational characterization of the cycles in the method of periodic projections
The method of periodic projections consists in iterating projections onto
closed convex subsets of a Hilbert space according to a periodic sweeping
strategy. In the presence of sets, a long-standing question going
back to the 1960s is whether the limit cycles obtained by such a process can be
characterized as the minimizers of a certain functional. In this paper we
answer this question in the negative. Projection algorithms that minimize
smooth convex functions over a product of convex sets are also discussed
Microlensing Surveys of M31 in the Wide Field Imaging Era
The Andromeda Galaxy (M31) is the closest large galaxy to the Milky Way, thus
it is an important laboratory for studying massive dark objects in galactic
halos (MACHOs) by gravitational microlensing. Such studies strongly complement
the studies of the Milky Way halo using the the Large and Small Magellanic
Clouds. We consider the possibilities for microlensing surveys of M31 using the
next generation of wide field imaging telescopes with fields of view in the
square degree range. We consider proposals for such imagers both on the ground
and in space. For concreteness, we specialize to the SNAP proposal for a space
telescope and the LSST proposal for a ground based telescope. We find that a
modest space-based survey of 50 visits of one hour each is considerably better
than current ground based surveys covering 5 years. Crucially, systematic
effects can be considerably better controlled with a space telescope because of
both the infrared sensitivity and the angular resolution. To be competitive, 8
meter class wide-field ground based imagers must take exposures of several
hundred seconds with several day cadence.Comment: 10 pages, 4 figures, 2 table
Optimal Microlensing Observations
One of the major limitations of microlensing observations toward the Large
Magellanic Cloud (LMC) is the low rate of event detection. What can be done to
improve this rate? Is it better to invest telescope time in more frequent
observations of the inner high surface-brightness fields, or in covering new,
less populated outer fields? How would a factor 2 improvement in CCD
sensitivity affect the detection efficiency? Would a series of major (factor
2--4) upgrades in telescope aperture, seeing, sky brightness, camera size, and
detector efficiency increase the event rate by a huge factor, or only
marginally? I develop a simplified framework to address these questions. With
observational resources fixed at the level of the MACHO and EROS experiments,
the biggest improvement (factor ~2) would come by reducing the time spent on
the inner ~25 deg^2 and applying it to the outer ~100 deg^2. By combining this
change with the characteristics of a good medium-size telescope (2.5 m mirror,
1" point spread function, thinned CCD chips, 1 deg^2 camera, and dark sky), it
should be possible to increase the detection of LMC events to more than 100 per
year (assuming current estimates of the optical depth apply to the entire LMC).Comment: Submitted to ApJ, 13 pages plus 3 figure
Asymptotic behavior of compositions of under-relaxed nonexpansive operators
In general there exists no relationship between the fixed point sets of the
composition and of the average of a family of nonexpansive operators in Hilbert
spaces. In this paper, we establish an asymptotic principle connecting the
cycles generated by under-relaxed compositions of nonexpansive operators to the
fixed points of the average of these operators. In the special case when the
operators are projectors onto closed convex sets, we prove a conjecture by De
Pierro which has so far been established only for projections onto affine
subspaces
The Anomaly in the Candidate Microlensing Event PA-99-N2
The lightcurve of PA-99-N2, one of the recently announced microlensing
candidates towards M31, shows small deviations from the standard Paczynski
form. We explore a number of possible explanations, including correlations with
the seeing, the parallax effect and a binary lens. We find that the
observations are consistent with an unresolved RGB or AGB star in M31 being
microlensed by a binary lens. We find that the best fit binary lens mass ratio
is about one hundredth, which is one of most extreme values found for a binary
lens so far. If both the source and lens lie in the M31 disk, then the standard
M31 model predicts the probable mass range of the system to be 0.02-3.6 solar
masses (95 % confidence limit). In this scenario, the mass of the secondary
component is therefore likely to be below the hydrogen-burning limit. On the
other hand, if a compact halo object in M31 is lensing a disk or spheroid
source, then the total lens mass is likely to lie between 0.09-32 solar masses,
which is consistent with the primary being a stellar remnant and the secondary
a low mass star or brown dwarf. The optical depth (or alternatively the
differential rate) along the line of sight toward the event indicates that a
halo lens is more likely than a stellar lens provided that dark compact objects
comprise no less than 15 per cent (or 5 per cent) of haloes.Comment: Latex, 23 pages, 9 figures, in press at The Astrophysical Journa
AGAPE, an experiment to detect MACHO's in the direction of the Andromeda galaxy
The status of the Agape experiment to detect Machos in the direction of the
andromeda galaxy is presented.Comment: 4 pages, 1 figure in a separate compressed, tarred, uuencoded uufile.
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Measuring ambiguity attitude: (Extended) multiplier preferences for the American and the Dutch population
Empirical studies of ambiguity aversion often use measures that are not grounded in theory. This paper shows how a theoretically-founded measure of ambiguity aversion can be derived from Hansen and Sargentâs theory of multiplier preferences. Multiplier preferences are used in macroeconomics to capture model uncertainty. At the micro level, they have not been applied yet, because they do not permit ambiguity seeking, which is usually observed for a substantial proportion of subjects. We give a preference foundation for (extended) multiplier preferences accommodating both ambiguity aversion and ambiguity seeking and we propose a simple method to measure them using matching probabilities. We illustrate our method in two large representative samples (Dutch and American) and obtain the first micro estimates of multiplier preferences
AgapeZ1: a Large Amplification Microlensing Event or an Odd Variable Star Towards the Inner Bulge of M31
AgapeZ1 is the brightest and the shortest duration microlensing candidate
event found in the Agape data. It occured only 42" from the center of M31. Our
photometry shows that the half intensity duration of the event6 is 4.8 days and
at maximum brightness we measure a stellar magnitude of R=18.0 with B-R=0.80
mag color. A search on HST archives produced a single resolved star within the
projected event position error box. Its magnitude is R=22.Comment: 4 pages with 5 figure
Event rates and timescale distributions from realistic microlensing models of M31
We provide a set of microlensing event rate maps for M31, the Andromeda
Galaxy. Rates for M31 microlensing were calculated on the basis of a four
component model of the lens and source populations: disk and bulge sources
lensed by bulge, disk, M31 halo and Galactic halo lenses. We confirm the high
rate gradient along the minor axis of M31 due to a dark halo of lenses.
Furthermore, we compute the timescale distributions of events, for both
Einstein times and full-width at half-maximum times. We explore how the rate
contours and the timescale distributions can be used to measure the shape and
extent of the microlensing halo. With one year of twice--weekly sampling, or
three observing seasons, a halo MACHO fraction as small as 5% can be detected
with modest ground based telescopes.Comment: 11 pages, 6 figures, matches published versio
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