Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

Support Vectors Based Groundwater Head Observations Networks Design

This study presents a methodology for designing long-term groundwater head monitoring networks in order to reduce spatial redundancy. A spatially redundant well does not change the potentiometric surface estimation error appreciably, if not sampled. This methodology, based on Support Vector Machines, makes use of a uniquely solvable quadratic optimization problem that minimizes the bound on generalized risk, rather than just the mean square error of differences between measured and “predicted” groundwater head values. The nature of the optimization problem results in sparse approximation of the function defining the potentiometric surface that was utilized to select the number and locations of long-term monitoring wells and guide future data collection efforts, which is a prerequisite in building and calibrating regional flow and transport models. The methodology is applied to the design of regional groundwater monitoring networks in the Water Resources Inventory Area (WRIA) 1, Whatcom County, northern Washington State, USA

Effectiveness of the combination elvitegravir/cobicistat/tenofovir/emtricitabine (EVG/COB/TFV/FTC) plus darunavir among treatment-experienced patients in clinical practice : A multicentre cohort study

Background: The aim of this study was to investigate the effectiveness and tolerability of the combination elvitegravir/cobicistat/tenofovir/emtricitabine plus darunavir (EVG/COB/TFV/FTC + DRV) in treatment-experienced patients from the cohort of the Spanish HIV/AIDS Research Network (CoRIS). Methods: Treatment-experienced patients starting treatment with EVG/COB/TFV/FTC + DRV during the years 2014-2018 and with more than 24 weeks of follow-up were included. TFV could be administered either as tenofovir disoproxil fumarate or tenofovir alafenamide. We evaluated virological response, defined as viral load (VL) < 50 copies/ml and < 200 copies/ml at 24 and 48 weeks after starting this regimen, stratified by baseline VL (< 50 or ≥ 50 copies/ml at the start of the regimen). Results: We included 39 patients (12.8% women). At baseline, 10 (25.6%) patients had VL < 50 copies/ml and 29 (74.4%) had ≥ 50 copies/ml. Among patients with baseline VL < 50 copies/ml, 85.7% and 80.0% had VL < 50 copies/ml at 24 and 48 weeks, respectively, and 100% had VL < 200 copies/ml at 24 and 48 weeks. Among patients with baseline VL ≥ 50 copies/ml, 42.3% and 40.9% had VL < 50 copies/ml and 69.2% and 68.2% had VL < 200 copies/ml at 24 and 48 weeks. During the first 48 weeks, no patients changed their treatment due to toxicity, and 4 patients (all with baseline VL ≥ 50 copies/ml) changed due to virological failure. Conclusions: EVG/COB/TFV/FTC + DRV was well tolerated and effective in treatment-experienced patients with undetectable viral load as a simplification strategy, allowing once-daily, two-pill regimen with three antiretroviral drug classes. Effectiveness was low in patients with detectable viral loads

The Realm of the Pairings

Abstract. Bilinear maps, or pairings, initially proposed in a crypto-logic context for cryptanalytic purposes, proved afterward to be an amazingly flexible and useful tool for the construction of cryptosystems with unique features. Yet, they are notoriously hard to implement efficiently, so that their effective deployment requires a careful choice of parameters and algorithms. In this paper we review the evolution of pairing-based cryptosystems, the development of efficient algorithms and the state of the art in pairing computation, and the challenges yet to be addressed on the subject, while also presenting some new algorith-mic and implementation refinements in affine and projective coordinates

Efficacy, safety, and immunogenicity of a booster regimen of Ad26.COV2.S vaccine against COVID-19 (ENSEMBLE2) : results of a randomised, double-blind, placebo-controlled, phase 3 trial

Background Despite the availability of effective vaccines against COVID-19, booster vaccinations are needed to maintain vaccine-induced protection against variant strains and breakthrough infections. This study aimed to investigate the efficacy, safety, and immunogenicity of the Ad26.COV2.S vaccine (Janssen) as primary vaccination plus a booster dose. Methods ENSEMBLE2 is a randomised, double-blind, placebo-controlled, phase 3 trial including crossover vaccination after emergency authorisation of COVID-19 vaccines. Adults aged at least 18 years without previous COVID-19 vaccination at public and private medical practices and hospitals in Belgium, Brazil, Colombia, France, Germany, the Philippines, South Africa, Spain, the UK, and the USA were randomly assigned 1:1 via a computer algorithm to receive intramuscularly administered Ad26.COV2.S as a primary dose plus a booster dose at 2 months or two placebo injections 2 months apart. The primary endpoint was vaccine efficacy against the first occurrence of molecularly confirmed moderate to severe–critical COVID-19 with onset at least 14 days after booster vaccination, which was assessed in participants who received two doses of vaccine or placebo, were negative for SARS-CoV-2 by PCR at baseline and on serology at baseline and day 71, had no major protocol deviations, and were at risk of COVID-19 (ie, had no PCR-positive result or discontinued the study before day 71). Safety was assessed in all participants; reactogenicity, in terms of solicited local and systemic adverse events, was assessed as a secondary endpoint in a safety subset (approximately 6000 randomly selected participants). The trial is registered with ClinicalTrials.gov, NCT04614948, and is ongoing. Findings Enrolment began on Nov 16, 2020, and the primary analysis data cutoff was June 25, 2021. From 34 571 participants screened, the double-blind phase enrolled 31 300 participants, 14 492 of whom received two doses (7484 in the Ad26.COV2.S group and 7008 in the placebo group) and 11 639 of whom were eligible for inclusion in the assessment of the primary endpoint (6024 in the Ad26.COV2.S group and 5615 in the placebo group). The median (IQR) follow-up post-booster vaccination was 36·0 (15·0–62·0) days. Vaccine efficacy was 75·2% (adjusted 95% CI 54·6–87·3) against moderate to severe–critical COVID-19 (14 cases in the Ad26.COV2.S group and 52 cases in the placebo group). Most cases were due to the variants alpha (B.1.1.7) and mu (B.1.621); endpoints for the primary analysis accrued from Nov 16, 2020, to June 25, 2021, before the global dominance of delta (B.1.617.2) or omicron (B.1.1.529). The booster vaccine exhibited an acceptable safety profile. The overall frequencies of solicited local and systemic adverse events (evaluated in the safety subset, n=6067) were higher among vaccine recipients than placebo recipients after the primary and booster doses. The frequency of solicited adverse events in the Ad26.COV2.S group were similar following the primary and booster vaccinations (local adverse events, 1676 [55·6%] of 3015 vs 896 [57·5%] of 1559, respectively; systemic adverse events, 1764 [58·5%] of 3015 vs 821 [52·7%] of 1559, respectively). Solicited adverse events were transient and mostly grade 1–2 in severity. Interpretation A homologous Ad26.COV2.S booster administered 2 months after primary single-dose vaccination in adults had an acceptable safety profile and was efficacious against moderate to severe–critical COVID-19. Studies assessing efficacy against newer variants and with longer follow-up are needed