There is no variational characterization of the cycles in the method of periodic projections

The method of periodic projections consists in iterating projections onto $m$ closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of $m\geq 3$ 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. In case ofproblem contact [email protected]

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 Sargent’s 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