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

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

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

On The Mx/G/1 Retrial Queue With Impatient Customers

In this work, we carry out a stochastic analysis of the M/G/1 retrial queue with batch arrivals and impatient customers. Our study includes: steady state joint distribution of the server state and the number of customers in retrial group, embedded Markov chain and stochastic decomposition for the number of customers in the system. We investigate also the asymptotic behaviour of the system under high and low retrial intensities.0.10.136

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

Théra, Variational sum of monotone operators

The sum of (nonlinear) maximal monotone operators is reconsidered from the Yosida approximation and graph-convergence point of view. This leads to a new concept, called variational sum, which coincides with the classical (pointwise) sum when the classical sum happens to be maximal monotone. In the case of subdifferentials of convex lower semicontinuous proper functions, the variational sum is equal to the subdifferential of the sum of the functions. A general feature of the variational sum is to involve not only the values of the two operators at the given point but also their values at nearby points

Informing, simulating experience, or both: A field experiment on phishing risks

Cybersecurity cannot be ensured with mere technical solutions. Hackers often use fraudulent emails to simply ask people for their password to breach into organizations. This technique, called phishing, is a major threat for many organizations. A typical prevention measure is to inform employees but is there a better way to reduce phishing risks? Experience and feedback have often been claimed to be effective in helping people make better decisions. In a large field experiment involving more than 10,000 employees of a Dutch ministry, we tested the effect of information provision, simulated experience, and their combination to reduce the risks of falling into a phishing attack. Both approaches substantially reduced the proportion of employees giving away their password. Combining both interventions did not have a larger impact

\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 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