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

Use of three-dimensional computed tomography overlay for real-time cryoballoon ablation in atrial fibrillation reduces radiation dose and contrast dye

AIMS: Cryoballoon pulmonary vein (PV) isolation in patients with atrial fibrillation has proven to be effective in short-term and long-term follow-up. To visualise the PV anatomy, pre-ablation contrast pulmonary venography is commonly performed. Three-dimensional (3D) computed tomography (CT) overlay is a new technique creating a live 3D image of the left atrium by integrating a previously obtained CT scan during fluoroscopy. To evaluate the benefits of 3D CT overlay during cryoballoon ablation, we studied the use of 3D CT overlay versus contrast pulmonary venography in a randomised fashion in patients with paroxysmal atrial fibrillation undergoing cryoballoon PV isolation. METHODS AND RESULTS: Between October 2012 and June 2013, 30 patients accepted for PV isolation were randomised to cryoballoon PV isolation using either 3D CT overlay or contrast pulmonary venography. All patients underwent a pre-procedural cardiac CT for evaluation of the anatomy of the left atrium (LA) and the PVs. In the 3D CT overlay group, a 3D reconstruction of the LA and PVs was made. An overlay of the CT reconstruction was then projected over live fluoroscopy. Patients in the contrast pulmonary venography group received significantly more contrast agent (77.1 ± 21.2 cc vs 40.1 ± 17.6 cc, p < 0.001) and radiation (43.0 ± 21.9 Gy.cm2 vs 28.41 ± 11.7 Gy.cm2, p = 0.04) than subjects in the 3D CT overlay group. There was no difference in total procedure time, fluoroscopy time and the amount of cryoapplications between the two groups. CONCLUSION: The use of 3D CT overlay decreases radiation and contrast dye exposure and can assist in guiding cryoballoon-based PV isolation

The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

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

Complications in pulmonary vein isolation in the Netherlands Heart Registration differ with sex and ablation technique

Aims Pulmonary vein isolation (PVI) has become a cornerstone of the invasive treatment of atrial fibrillation. Severe complications are reported in 1-3% of patients. This study aims to compare complications and follow-up outcome of PVI in patients with atrial fibrillation. Methods and results The data were extracted from the Netherlands Heart Registration. Procedural and follow-up outcomes in patients treated with conventional radiofrequency (C-RF), multielectrode phased RF (Ph-RF), or cryoballoon (CB) ablation from 2012 to 2017 were compared. Subgroup analysis was performed to identify variables associated with complications and repeat ablations. In total, 13 823 patients (69% male) were included. The reported complication incidence was 3.6%. Patients treated with C-RF developed more cardiac tamponades (C-RF 0.8% vs. Ph-RF 0.3% vs. CB 0.3%, P Conclusion The reported complication rate during PVI was low. Patients treated with C-RF ablation were more likely to develop cardiac tamponades and vascular complications. Female sex was associated with more cardiac tamponade and bleeding complications

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