Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting

Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem within Euclidean spaces of changing dimension. Recently, an alternative approach which first decomposes complex space using triangular decomposition before refining to real space has been introduced and implemented within the RegularChains Library of Maple. We here describe a freely available package ProjectionCAD which utilises the routines within the RegularChains Library to build CADs by projection and lifting. We detail how the projection and lifting algorithms were modified to allow this, discuss the motivation and survey the functionality of the package

QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average

In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions. With QuickWeakHeapsort and QuickMergesort we present two examples for the QuickXsort-construction. Both are efficient algorithms that incur approximately n log n - 1.26n +o(n) comparisons on the average. A worst case of n log n + O(n) comparisons can be achieved without significantly affecting the average case. Furthermore, we describe an implementation of MergeInsertion for small n. Taking MergeInsertion as a base case for QuickMergesort, we establish a worst-case efficient sorting algorithm calling for n log n - 1.3999n + o(n) comparisons on average. QuickMergesort with constant size base cases shows the best performance on practical inputs: when sorting integers it is slower by only 15% to STL-Introsort

Searching a bitstream in linear time for the longest substring of any given density

Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) reformulating the problem as a constrained walk through a sparse matrix, and then (ii) developing a data structure for this sparse matrix that allows us to perform each step of the walk in amortised constant time. We also give a linear time algorithm to find the longest substring whose ratio of ones to zeroes is bounded below by a given value. Both problems have practical relevance to cryptography and bioinformatics.Comment: 22 pages, 19 figures; v2: minor edits and enhancement

Generic meta-modelling with concepts, templates and mixin layers

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-16145-2_2Proceedings of 13th International Conference, MODELS 2010, Oslo, Norway, October 3-8, 2010.Meta-modelling is a key technique in Model Driven Engineering, where it is used for language engineering and domain modelling. However, mainstream approaches like the OMG’s Meta-Object Facility provide little support for abstraction, modularity, reusability and extendibility of (meta-)models, behaviours and transformations. In order to alleviate this weakness, we bring three elements of generic programming into meta-modelling: concepts, templates and mixin layers. Concepts permit an additional typing for models, enabling the definition of behaviours and transformations independently of meta-models, making specifications reusable. Templates use concepts to express requirements on their generic parameters, and are applicable to models and meta-models. Finally, we define functional layers by means of meta-model mixins which can extend other meta-models. As a proof of concept we also report on MetaDepth, a multi-level meta-modelling framework that implements these ideas.Work sponsored by the Spanish Ministry of Science, project TIN2008-02081 and mobility grants JC2009-00015 and PR2009-0019, and by the R&D programme of the Community of Madrid, project S2009/TIC-165

Xcd - Modular, Realizable Software Architectures

Connector-Centric Design (Xcd) is centred around a new formal architectural description language, focusing mainly on complex connectors. Inspired by Wright and BIP, Xcd aims to cleanly separate in a modular manner the high-level functional, interaction, and control system behaviours. This can aid in both increasing the understandability of architectural specifications and the reusability of components and connectors themselves. Through the independent specification of control behaviours, Xcd allows designers to experiment more easily with different design decisions early on, without having to modify the functional behaviour specifications (components) or the interaction ones(connectors). At the same time Xcd attempts to ease the architectural specification by following (and extending) a Design-by-Contract approach, which is more familiar to software developers than process algebras like CSP or languages like BIP that are closer to synchronous/hardware specification languages. Xcd extends Design-by-Contract (i) by separating component contracts into functional and interaction sub-contracts, and (ii) by allowing service consumers to specify their own contractual clauses. Xcd connector specifications are completely decentralized, foregoing Wright’s connector glue, to ensure their realizability by construction

Effect of Subcutaneous Casirivimab and Imdevimab Antibody Combination vs Placebo on Development of Symptomatic COVID-19 in Early Asymptomatic SARS-CoV-2 Infection: A Randomized Clinical Trial

Importance: Easy-to-administer anti-SARS-CoV-2 treatments may be used to prevent progression from asymptomatic infection to symptomatic disease and to reduce viral carriage. Objective: To evaluate the effect of combination subcutaneous casirivimab and imdevimab on progression from early asymptomatic SARS-CoV-2 infection to symptomatic COVID-19. Design, Setting, and Participants: Randomized, double-blind, placebo-controlled, phase 3 trial of close household contacts of a SARS-CoV-2-infected index case at 112 sites in the US, Romania, and Moldova enrolled July 13, 2020-January 28, 2021; follow-up ended March 11, 2021. Asymptomatic individuals (aged ≥12 years) were eligible if identified within 96 hours of index case positive test collection. Results from 314 individuals positive on SARS-CoV-2 reverse transcriptase-quantitative polymerase chain reaction (RT-qPCR) testing are reported. Interventions: Individuals were randomized 1:1 to receive 1 dose of subcutaneous casirivimab and imdevimab, 1200 mg (600 mg of each; n = 158), or placebo (n = 156). Main Outcomes and Measures: The primary end point was the proportion of seronegative participants who developed symptomatic COVID-19 during the 28-day efficacy assessment period. The key secondary efficacy end points were the number of weeks of symptomatic SARS-CoV-2 infection and the number of weeks of high viral load (>4 log10copies/mL). Results: Among 314 randomized participants (mean age, 41.0 years; 51.6% women), 310 (99.7%) completed the efficacy assessment period; 204 were asymptomatic and seronegative at baseline and included in the primary efficacy analysis. Subcutaneous casirivimab and imdevimab, 1200 mg, significantly prevented progression to symptomatic disease (29/100 [29.0%] vs 44/104 [42.3%] with placebo; odds ratio, 0.54 [95% CI, 0.30-0.97]; P =.04; absolute risk difference, -13.3% [95% CI, -26.3% to -0.3%]). Casirivimab and imdevimab reduced the number of symptomatic weeks per 1000 participants (895.7 weeks vs 1637.4 weeks with placebo; P =.03), an approximately 5.6-day reduction in symptom duration per symptomatic participant. Treatment with casirivimab and imdevimab also reduced the number of high viral load weeks per 1000 participants (489.8 weeks vs 811.9 weeks with placebo; P =.001). The proportion of participants receiving casirivimab and imdevimab who had 1 or more treatment-emergent adverse event was 33.5% vs 48.1% for placebo, including events related (25.8% vs 39.7%) or not related (11.0% vs 16.0%) to COVID-19. Conclusions and Relevance: Among asymptomatic SARS-CoV-2 RT-qPCR-positive individuals living with an infected household contact, treatment with subcutaneous casirivimab and imdevimab antibody combination vs placebo significantly reduced the incidence of symptomatic COVID-19 over 28 days. Trial Registration: ClinicalTrials.gov Identifier: NCT04452318

Subcutaneous REGEN-COV Antibody Combination to Prevent Covid-19

BACKGROUND REGEN-COV (previously known as REGN-COV2), a combination of the monoclonal antibodies casirivimab and imdevimab, has been shown to markedly reduce the risk of hospitalization or death among high-risk persons with coronavirus disease 2019 (Covid-19). Whether subcutaneous REGEN-COV prevents severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and subsequent Covid-19 in persons at high risk for infection because of household exposure to a person with SARS-CoV-2 infection is unknown. METHODS We randomly assigned, in a 1:1 ratio, participants (=12 years of age) who were enrolled within 96 hours after a household contact received a diagnosis of SARSCoV- 2 infection to receive a total dose of 1200 mg of REGEN-COV or matching placebo administered by means of subcutaneous injection. At the time of randomization, participants were stratified according to the results of the local diagnostic assay for SARS-CoV-2 and according to age. The primary efficacy end point was the development of symptomatic SARS-CoV-2 infection through day 28 in participants who did not have SARS-CoV-2 infection (as measured by reverse-transcriptase- quantitative polymerase-chain-reaction assay) or previous immunity (seronegativity). RESULTS Symptomatic SARS-CoV-2 infection developed in 11 of 753 participants in the REGEN-COV group (1.5%) and in 59 of 752 participants in the placebo group (7.8%) (relative risk reduction [1 minus the relative risk], 81.4%; P104 copies per milliliter) was shorter (0.4 weeks and 1.3 weeks, respectively). No dose-limiting toxic effects of REGEN-COV were noted. CONCLUSIONS Subcutaneous REGEN-COV prevented symptomatic Covid-19 and asymptomatic SARS-CoV-2 infection in previously uninfected household contacts of infected persons. Among the participants who became infected, REGEN-COV reduced the duration of symptomatic disease and the duration of a high viral load