A Trichotomy for Regular Trail Queries

Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice

Evaluation and Enumeration Problems for Regular Path Queries

Regular path queries (RPQs) are a central component of graph databases. We investigate decision- and enumeration problems concerning the evaluation of RPQs under several semantics that have recently been considered: arbitrary paths, shortest paths, and simple paths. Whereas arbitrary and shortest paths can be enumerated in polynomial delay, the situation is much more intricate for simple paths. For instance, already the question if a given graph contains a simple path of a certain length has cases with highly non-trivial solutions and cases that are long-standing open problems. We study RPQ evaluation for simple paths from a parameterized complexity perspective and define a class of simple transitive expressions that is prominent in practice and for which we can prove a dichotomy for the evaluation problem. We observe that, even though simple path semantics is intractable for RPQs in general, it is feasible for the vast majority of RPQs that are used in practice. At the heart of our study on simple paths is a result of independent interest: the two disjoint paths problem in directed graphs is W[1]-hard if parameterized by the length of one of the two paths

Efficacy and safety of two neutralising monoclonal antibody therapies, sotrovimab and BRII-196 plus BRII-198, for adults hospitalised with COVID-19 (TICO): a randomised controlled trial

We aimed to assess the efficacy and safety of two neutralising monoclonal antibody therapies (sotrovimab [Vir Biotechnology and GlaxoSmithKline] and BRII-196 plus BRII-198 [Brii Biosciences]) for adults admitted to hospital for COVID-19 (hereafter referred to as hospitalised) with COVID-19. In this multinational, double-blind, randomised, placebo-controlled, clinical trial (Therapeutics for Inpatients with COVID-19 [TICO]), adults (aged ≥18 years) hospitalised with COVID-19 at 43 hospitals in the USA, Denmark, Switzerland, and Poland were recruited. Patients were eligible if they had laboratory-confirmed SARS-CoV-2 infection and COVID-19 symptoms for up to 12 days. Using a web-based application, participants were randomly assigned (2:1:2:1), stratified by trial site pharmacy, to sotrovimab 500 mg, matching placebo for sotrovimab, BRII-196 1000 mg plus BRII-198 1000 mg, or matching placebo for BRII-196 plus BRII-198, in addition to standard of care. Each study product was administered as a single dose given intravenously over 60 min. The concurrent placebo groups were pooled for analyses. The primary outcome was time to sustained clinical recovery, defined as discharge from the hospital to home and remaining at home for 14 consecutive days, up to day 90 after randomisation. Interim futility analyses were based on two seven-category ordinal outcome scales on day 5 that measured pulmonary status and extrapulmonary complications of COVID-19. The safety outcome was a composite of death, serious adverse events, incident organ failure, and serious coinfection up to day 90 after randomisation. Efficacy and safety outcomes were assessed in the modified intention-to-treat population, defined as all patients randomly assigned to treatment who started the study infusion. This study is registered with ClinicalTrials.gov, NCT04501978. Between Dec 16, 2020, and March 1, 2021, 546 patients were enrolled and randomly assigned to sotrovimab (n=184), BRII-196 plus BRII-198 (n=183), or placebo (n=179), of whom 536 received part or all of their assigned study drug (sotrovimab n=182, BRII-196 plus BRII-198 n=176, or placebo n=178; median age of 60 years [IQR 50–72], 228 [43%] patients were female and 308 [57%] were male). At this point, enrolment was halted on the basis of the interim futility analysis. At day 5, neither the sotrovimab group nor the BRII-196 plus BRII-198 group had significantly higher odds of more favourable outcomes than the placebo group on either the pulmonary scale (adjusted odds ratio sotrovimab 1·07 [95% CI 0·74–1·56]; BRII-196 plus BRII-198 0·98 [95% CI 0·67–1·43]) or the pulmonary-plus complications scale (sotrovimab 1·08 [0·74–1·58]; BRII-196 plus BRII-198 1·00 [0·68–1·46]). By day 90, sustained clinical recovery was seen in 151 (85%) patients in the placebo group compared with 160 (88%) in the sotrovimab group (adjusted rate ratio 1·12 [95% CI 0·91–1·37]) and 155 (88%) in the BRII-196 plus BRII-198 group (1·08 [0·88–1·32]). The composite safety outcome up to day 90 was met by 48 (27%) patients in the placebo group, 42 (23%) in the sotrovimab group, and 45 (26%) in the BRII-196 plus BRII-198 group. 13 (7%) patients in the placebo group, 14 (8%) in the sotrovimab group, and 15 (9%) in the BRII-196 plus BRII-198 group died up to day 90. Neither sotrovimab nor BRII-196 plus BRII-198 showed efficacy for improving clinical outcomes among adults hospitalised with COVID-19. US National Institutes of Health and Operation Warp Spee