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

Group decision rules and group rationality under risk

This paper investigates the rationality of group decisions versus individual decisions under risk. We study two group decision rules, majority and unanimity, in stochastic dominance and Allais paradox tasks. We distinguish communication effects (the effects of group discussions and interactions) from aggregation effects (mere impact of the voting procedure), which makes it possible to better understand the complex dynamics of group decision making. In an experiment, both effects occurred for intellective tasks whereas there were only aggregation effects in judgmental tasks. Communication effects always led to more rational choices; aggregation effects did so sometimes but not always. Groups violated stochastic dominance less often than individuals did, which was due to both aggregation and communication effects. In the Allais paradox tasks, there were almost no communication effects, and aggregation effects made groups deviate more from expected utility than individuals

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]

First measurement of the cross section for top-quark pair production in proton–proton collisions at √s = 7 TeV

20 páginas, 3 figuras, 1 tabla.-- This article is published Open Access at sciencedirect.com. It is distributed under the terms of the Creative Commons Attribution License 3.0.-- CMS Collaboration: et al.The first measurement of the cross section for top-quark pair production in pp collisions at the Large Hadron Collider at center-of-mass energy √s = 7 TeV has been performed using a data sample corresponding to an integrated luminosity of 3.1 ± 0.3 pb−1 recorded by the CMS detector. This result utilizes the final state with two isolated, highly energetic charged leptons, large missing transverse energy, and two or more jets. Backgrounds from Drell–Yan and non-W/Z boson production are estimated from data. Eleven events are observed in the data with 2.1 ± 1.0 events expected from background. The measured cross section is 194±72(stat.)±24(syst.)±21(lumi.) pb, consistent with next-to-leading order predictions.Acknowledge support from: FMSR (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); Academy of Sciences and NICPB (Estonia); Academy of Finland, ME, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLPFAI (Mexico); PAEC (Pakistan); SCSR (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MST and MAE (Russia); MSTD (Serbia); MICINN and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); TUBITAK and TAEK (Turkey); STFC (United Kingdom); DOE and NSF (USA).Peer reviewe

Search for supersymmetry in pp collisions at 7 TeV in events with jets and missing transverse energy

Acknowledge support from: FMSR (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); Academy of Sciences and NICPB (Estonia); Academy of Finland, ME, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); PAEC (Pakistan); SCSR (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MST and MAE (Russia); MSTD (Serbia); MICINN and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); TUBITAK and TAEK (Turkey); STFC (United Kingdom); DOE and NSF (USA).A search for supersymmetry with R-parity conservation in proton–proton collisions at a centre-of-mass energy of 7 TeV is presented. The data correspond to an integrated luminosity of 35 pb−1 collected by the CMS experiment at the LHC. The search is performed in events with jets and significant missing transverse energy, characteristic of the decays of heavy, pair-produced squarks and gluinos. The primary background, from standard model multijet production, is reduced by several orders of magnitude to a negligible level by the application of a set of robust kinematic requirements. With this selection, the data are consistent with the standard model backgrounds, namely t¯t, W + jet and Z + jet production, which are estimated from data control samples. Limits are set on the parameters of the constrained minimal supersymmetric extension of the standard model. These limits extend those set previously by experiments at the Tevatron and LEP colliders.23 páginas, 5 figuras, 2 tablas.-- Open access: This article is distributed under the terms of the Creative Commons Attribution License 3.0.-- CMS Collaboration: et al.Peer reviewe