Singular values of some modular functions

We study the properties of special values of the modular functions obtained from Weierstrass P-function at imaginary quadratic points.Comment: 19 pages,corrected typo

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

COMPARE LAAO: Rationale and design of the randomized controlled trial "COMPARing Effectiveness and safety of Left Atrial Appendage Occlusion to standard of care for atrial fibrillation patients at high stroke risk and ineligible to use oral anticoagulation therapy"

Contains fulltext : 252137.pdf (Publisher’s version ) (Open Access)BACKGROUND: Left atrial appendage occlusion (LAAO) provides an alternative to oral anticoagulation (OAC) for stroke prevention in patients with atrial fibrillation (AF). In patients with a long-term or permanent contraindication for OAC randomized controlled trial (RCT) data is lacking. STUDY OBJECTIVES: To assess the efficacy and safety of LAAO in AF patients who are ineligible to use OAC. The co-primary efficacy endpoint is (1) time to first occurrence of stroke (ischemic, hemorrhagic, or undetermined) and (2) time to first occurrence of the composite of stroke, transient ischemic attack (TIA), and systemic embolism (SE). The primary safety endpoint is the 30-day rate of peri-procedural complications. STUDY DESIGN: This is a multicenter, investigator-initiated, open-label, blinded endpoint (PROBE), superiority-driven RCT. Patients with AF, a CHA₂DS₂-VASc score ≥2 for men and ≥3 for women and a long-term or permanent contraindication for OAC will be randomized in a 2:1 fashion to the device- or control arm. Patients in the device arm will undergo percutaneous LAAO and will receive post-procedural dual antiplatelet therapy (DAPT) per protocol, while those in the control arm will continue their current treatment consisting of no antithrombotic therapy or (D)APT as deemed appropriate by the primary responsible physician. In this endpoint-driven trial design, assuming a 50% lower stroke risk of LAAO compared to conservative treatment, 609 patients will be followed for a minimum of 1 and a maximum of 5 years. Cost-effectiveness and budget impact analyses will be performed to allow decision-making on reimbursement of LAAO for the target population in the Netherlands. SUMMARY: The COMPARE LAAO trial will investigate the clinical superiority in preventing thromboembolic events and cost-effectiveness of LAAO in AF patients with a high thromboembolic risk and a contraindication for OAC use. NCT TRIAL NUMBER: NCT04676880

A New Family of Pairing-Friendly elliptic curves

International audienceThere have been recent advances in solving the finite extension field discrete logarithm problem as it arises in the context of pairing-friendly elliptic curves. This has lead to the abandonment of approaches based on supersingular curves of small characteristic, and to the reconsideration of the field sizes required for implementation based on non-supersingular curves of large characteristic. This has resulted in a revision of recommendations for suitable curves, particularly at a higher level of security. Indeed for a security level of 256 bits, the BLS48 curves have been suggested, and demonstrated to be superior to other candidates. These curves have an embedding degree of 48. The well known taxonomy of Freeman, Scott and Teske only considered curves with embedding degrees up to 50. Given some uncertainty around the constants that apply to the best discrete logarithm algorithm, it would seem to be prudent to push a little beyond 50. In this note we announce the discovery of a new family of pairing friendly elliptic curves which includes a new construction for a curve with an embedding degree of 54