An exact approach for the bilevel knapsack problem with interdiction constraints and extensions

We consider the bilevel knapsack problem with interdiction constraints, an extension of the classic 0–1 knapsack problem formulated as a Stackelberg game with two agents, a leader and a follower, that choose items from a common set and hold their own private knapsacks. First, the leader selects some items to be interdicted for the follower while satisfying a capacity constraint. Then the follower packs a set of the remaining items according to his knapsack constraint in order to maximize the profits. The goal of the leader is to minimize the follower’s total profit. We derive effective lower bounds for the bilevel knapsack problem and present an exact method that exploits the structure of the induced follower’s problem. The approach strongly outperforms the current state-of-the-art algorithms designed for the problem. We extend the same algorithmic framework to the interval min–max regret knapsack problem after providing a novel bilevel programming reformulation. Also for this problem, the proposed approach outperforms the exact algorithms available in the literature

Rotating Electromagnetic Waves in Toroid-Shaped Regions

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.Comment: 27 pages, 40 figure

Comparing league formats with respect to match importance in Belgian football

Recently, most clubs in the highest Belgian football division have become convinced that the format of their league should be changed. Moreover, the TV station that broadcasts the league is pleading for a more attractive competition. However, the clubs have not been able to agree on a new league format, mainly because they have conflicting interests. In this paper, we compare the current league format, and three other formats that have been considered by the Royal Belgian Football Association. We simulate the course of each of these league formats, based on historical match results. We assume that the attractiveness of a format is determined by the importance of its games; our importance measure for a game is based on the number of teams for which this game can be decisive to reach a given goal. Furthermore, we provide an overview of how each league format aligns with the expectations and interests of each type of club

Effect of Lactoferrin on Clinical Outcomes of Hospitalized Patients with COVID-19: The LAC Randomized Clinical Trial

As lactoferrin is a nutritional supplement with proven antiviral and immunomodulatory abilities, it may be used to improve the clinical course of COVID-19. The clinical efficacy and safety of bovine lactoferrin were evaluated in the LAC randomized double-blind placebo-controlled trial. A total of 218 hospitalized adult patients with moderate-to-severe COVID-19 were randomized to receive 800 mg/die oral bovine lactoferrin (n = 113) or placebo (n = 105), both given in combination with standard COVID-19 therapy. No differences in lactoferrin vs. placebo were observed in the primary outcomes: the proportion of death or intensive care unit admission (risk ratio of 1.06 (95% CI 0.63–1.79)) or proportion of discharge or National Early Warning Score 2 (NEWS2) ≤ 2 within 14 days from enrollment (RR of 0.85 (95% CI 0.70–1.04)). Lactoferrin showed an excellent safety and tolerability profile. Even though bovine lactoferrin is safe and tolerable, our results do not support its use in hospitalized patients with moderate-to-severe COVID-19

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum