The cyclic-routing UAV problem is PSPACE-complete

© 2015, Springer-Verlag Berlin Heidelberg. Consider a finite set of targets, with each target assigned a relative deadline, and each pair of targets assigned a fixed transit flight time. Given a flock of identical UAVs, can one ensure that every target is repeatedly visited by some UAV at intervals of duration at most the target’s relative deadline? The Cyclic-Routing UAV Problem (cr-uav) is the question of whether this task has a solution. This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata. The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the cr-uav Problem is in fact PSPACE-complete even in the single-UAV case

Combined scanning probe microscopy and x-ray scattering instrument for in situ catalysis investigations

Catalysis and Surface Chemistr

Error bounds for monomial convexification in polynomial optimization

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately. Our main error bounds depend primarily on the degree of the monomial, making them easy to compute. Since monomial convexification studies depend on the bounds on the associated variables, in the second part, we conduct an error analysis for a multilinear monomial over two different types of box constraints. As part of this analysis, we also derive the convex hull of a multilinear monomial over $[-1,1]^n$.Comment: 33 pages, 2 figures, to appear in journa

Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components

Ternary erbium chromium sulfides : structural relationships and magnetic properties

Single crystals of four erbium-chromium sulfides have been grown by chemical vapor transport using iodine as the transporting agent. Single-crystal X-ray diffraction reveals that in Er(3)CrS(6) octahedral sites are occupied exclusively by Cr(3+) cations, leading to one-dimensional CrS(4)(5-) chains of edge-sharing octahedra, while in Er(2)CrS(4), Er(3+), and Cr(2+) cations occupy the available octahedral sites in an ordered manner. By contrast, in Er(6)Cr(2)S(11) and Er(4)CrS(7), Er(3+) and Cr(2+) ions are disordered over the octahedral sites. In Er(2)CrS(4), Er(6)Cr(2)S(11), and Er(4)CrS(7), the network of octahedra generates an anionic framework constructed from M(2)S(5) slabs of varying thickness, linked by one-dimensional octahedral chains. This suggests that these three phases belong to a series in which the anionic framework may be described by the general formula [M(2n+1)S(4n+3)](x-), with charge balancing provided by Er(3+) cations located in sites of high-coordination number within one-dimensional channels defined by the framework. Er(4)CrS(7), Er(6)Cr(2)S(11), and Er(2)CrS(4) may thus be considered as the n = 1, 2, and infinity members of this series. While Er(4)CrS(7) is paramagnetic, successive magnetic transitions associated with ordering of the chromium and erbium sub-lattices are observed on cooling Er(3)CrS(6) (T(C)(Cr) = 30 K; T(C)(Er) = 11 K) and Er(2)CrS(4) (T(N)(Cr) = 42 K, T(N)(Er) = 10 K) whereas Er(6)Cr(2)S(11) exhibits ordering of the chromium sub-lattice only (T(N) = 11.4 K)

Improved Outcomes with Heavy Silicone Oil in Complex Primary Retinal Detachment: A Large Multicenter Matched Cohort Study

\ua9 2023 American Academy of OphthalmologyPurpose: To establish whether Densiron 68, a heavier-than-water endotamponade agent, is an effective alternative to conventional light silicone oil in primary rhegmatogenous retinal detachment (RD) surgery for eyes with inferior breaks in the detached retina and severe proliferative vitreoretinopathy (PVR). Design: Cohort study of routinely collected data from the European Society of Retina Specialists and British and Eire Association of Vitreoretinal Surgeons vitreoretinal database between 2015 and 2022. Participants: All consecutive eyes that underwent primary rhegmatogenous RD surgery using Densiron 68 or light silicone oil as an internal tamponade agent. Methods: To minimize confounding bias, we undertook 2:1 nearest-neighbor matching on inferior breaks, large inferior rhegmatogenous RDs, PVR, and, for visual analyses, baseline visual acuity (VA) between treatment groups. We fit regression models including prognostically relevant covariates, treatment–covariate interactions, and matching weights. We used g-computation with cluster-robust methods to estimate marginal effects. For nonlinear models, we calculated confidence intervals (CIs) using bias-corrected cluster bootstrapping with 9999 replications. Main Outcome Measures: Presence of a fully attached retina and VA at least 2 months after oil removal. Results: Of 1061 eyes enrolled, 426 and 239 were included in our matched samples for anatomic and visual outcome analyses, respectively. The primary success rate was higher in the Densiron 68 group (113 of 142; 80%) compared with the light silicone oil group (180 of 284; 63%), with an adjusted odds ratio of 1.90 (95% CI, 1.63–2.23, P < 0.001). We also observed a significant improvement favoring Densiron 68 of –0.26 logarithm of the minimum angle of resolution (logMAR) in postoperative VA between the 2 groups (95% CI, –0.43 to –0.10, P = 0.002). The anatomic benefit of using Densiron 68 in eyes with inferior retinal breaks and large detachments was more pronounced among eyes with PVR grade C. We found no evidence of visual effect moderation by anatomic outcome or foveal attachment. Conclusions: Densiron achieved higher anatomic success rates and improved visual outcomes compared with conventional light silicone oil in eyes with inferior retinal pathology and severe PVR. Financial Disclosure(s): Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article