Measures of non-compactness in Orlicz modular spaces

In this paper we show that the ball measure of non-compactness of a norm bounded subset of an Orlicz modular space $L^\psi$ is equal to the limit of its $n$-widths. We also obtain several inequalities between the measures of noncompactness and the limit of the $n$-widths for modular bounded subsets of $L^\psi$ which do not have $\Delta_2$-condition. Minimum conditions on $\psi$ to have such results are specified and an example of such a function $\psi$ is provided

Linear Superiorization for Infeasible Linear Programming

Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward feasible points that have lower (not necessarily minimal) values of the objective function than points that would have been reached by the same feasiblity-seeking iterative process without superiorization. Using a feasibility-seeking iterative process that converges even if the linear feasible set is empty, LinSup generates an iterative sequence that converges to a point that minimizes a proximity function which measures the linear constraints violation. In addition, due to LinSup's repeated objective function reduction steps such a point will most probably have a reduced objective function value. We present an exploratory experimental result that illustrates the behavior of LinSup on an infeasible LP problem.Comment: arXiv admin note: substantial text overlap with arXiv:1612.0653

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

Mrk 421, Mrk 501, and 1ES 1426+428 at 100 GeV with the CELESTE Cherenkov Telescope

We have measured the gamma-ray fluxes of the blazars Mrk 421 and Mrk 501 in the energy range between 50 and 350 GeV (1.2 to 8.3 x 10^25 Hz). The detector, called CELESTE, used first 40, then 53 heliostats of the former solar facility "Themis" in the French Pyrenees to collect Cherenkov light generated in atmospheric particle cascades. The signal from Mrk 421 is often strong. We compare its flux with previously published multi-wavelength studies and infer that we are straddling the high energy peak of the spectral energy distribution. The signal from Mrk 501 in 2000 was weak (3.4 sigma). We obtain an upper limit on the flux from 1ES 1426+428 of less than half that of the Crab flux near 100 GeV. The data analysis and understanding of systematic biases have improved compared to previous work, increasing the detector's sensitivity.Comment: 15 pages, 14 figures, accepted to A&A (July 2006) August 19 -- corrected error in author lis

From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

Classical novae from the POINT-AGAPE microlensing survey of M31 -- I. The nova catalogue

The POINT-AGAPE survey is an optical search for gravitational microlensing events towards the Andromeda Galaxy (M31). As well as microlensing, the survey is sensitive to many different classes of variable stars and transients. Here we describe the automated detection and selection pipeline used to identify M31 classical novae (CNe) and we present the resulting catalogue of 20 CN candidates observed over three seasons. CNe are observed both in the bulge region as well as over a wide area of the M31 disk. Nine of the CNe are caught during the final rise phase and all are well sampled in at least two colours. The excellent light-curve coverage has allowed us to detect and classify CNe over a wide range of speed class, from very fast to very slow. Among the light-curves is a moderately fast CN exhibiting entry into a deep transition minimum, followed by its final decline. We have also observed in detail a very slow CN which faded by only 0.01 mag day$^{-1}$ over a 150 day period. We detect other interesting variable objects, including one of the longest period and most luminous Mira variables. The CN catalogue constitutes a uniquely well-sampled and objectively-selected data set with which to study the statistical properties of classical novae in M31, such as the global nova rate, the reliability of novae as standard-candle distance indicators and the dependence of the nova population on stellar environment. The findings of this statistical study will be reported in a follow-up paper.Comment: 21 pages, 13 figures, re-submitted for publication in MNRAS, typos corrected, references updated, figures 5-9 made cleare

\pi\pi, K\pi and \pi N potential scattering and a prediction of a narrow \sigma meson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.Comment: 42 pages, 17 PS figures, REFTeX, epsfig.sty needed, submitted to Phys. Re

The CAT Imaging Telescope for Very-High-Energy Gamma-Ray Astronomy

The CAT (Cherenkov Array at Themis) imaging telescope, equipped with a very-high-definition camera (546 fast phototubes with 0.12 degrees spacing surrounded by 54 larger tubes in two guard rings) started operation in Autumn 1996 on the site of the former solar plant Themis (France). Using the atmospheric Cherenkov technique, it detects and identifies very high energy gamma-rays in the range 250 GeV to a few tens of TeV. The instrument, which has detected three sources (Crab nebula, Mrk 421 and Mrk 501), is described in detail.Comment: 24 pages, 15 figures. submitted to Elsevier Preprin

The POINT-AGAPE Survey: Comparing Automated Searches of Microlensing Events toward M31

Searching for microlensing in M31 using automated superpixel surveys raises a number of difficulties which are not present in more conventional techniques. Here we focus on the problem that the list of microlensing candidates is sensitive to the selection criteria or "cuts" imposed and some subjectivity is involved in this. Weakening the cuts will generate a longer list of microlensing candidates but with a greater fraction of spurious ones; strengthening the cuts will produce a shorter list but may exclude some genuine events. We illustrate this by comparing three analyses of the same data-set obtained from a 3-year observing run on the INT in La Palma. The results of two of these analyses have been already reported: Belokurov et al. (2005) obtained between 3 and 22 candidates, depending on the strength of their cuts, while Calchi Novati et al. (2005) obtained 6 candidates. The third analysis is presented here for the first time and reports 10 microlensing candidates, 7 of which are new. Only two of the candidates are common to all three analyses. In order to understand why these analyses produce different candidate lists, a comparison is made of the cuts used by the three groups...Comment: 28 pages, 24 figures, 9 table

Congested traffic equilibria and degenerate anisotropic PDEs

Congested traffic problems on very dense networks lead, at the limit, to minimization problems posed on measures on curves as shown in Baillon and Carlier (Netw. Heterogenous Media 7: 219--241, 2012). Here, we go one step further by showing that these problems can be reformulated in terms of the minimization of an integral functional over a set of vector fields with prescribed divergence. We prove a Sobolev regularity result for their minimizers despite the fact that the Euler-Lagrange equation of the dual is highly degenerate and anisotropic. This somehow extends the analysis of Brasco et al. (J. Math. Pures Appl. 93: 652--671, 2010) to the anisotropic case