We prove small data modified scattering for the Vlasov-Poisson system in dimension d = 3 using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamic related to the scattering mass.

No abstract

In this paper, we introduce a new set of vector fields for the relativistic transport equation, which is applicable for general Vlasov-Wave type coupled systems. By combining the strength of Klainerman vector field method and Fourier method, we prove global regularity and scattering for the 3D massive relativistic Vlasov-Nordström system for small initial data without any compact support assumption, which is widely used in the literature for the study of Vlasov solution.

No abstract

Background: Asymptomatic cerebral emboli (ACE) are commonly seen on cerebral magnetic resonance imaging (MRI) after atrial fibrillation ablation, but the incidence in previous studies varies widely. No data exists to compare the effects of different diffusion-weighted imaging (DWI) settings on detecting ablation-related ACE. This self-control study sought to compare the incidence and characteristics of ablation-related ACE between high-resolution DWI and conventional DWI. Methods: A total of 55 consecutive patients referred for atrial fibrillation ablation between December 2017 and September 2018 were enrolled. Patients underwent high-resolution DWI 1 day before ablation and repeated high-resolution DWI and conventional DWI within 48 hours post-ablation. The incidence, number, size, and location of ACE were compared between 2 DWI settings in the same patients. Results: The high-resolution DWI revealed a higher incidence of acute ACE compared with conventional DWI (67.3% versus 41.8% of patients, P <0.001) and significantly more ACE (106 versus 45 lesions, P =0.001). For ACE seen on both scans, the size measured by high-resolution DWI was larger (5.42 versus 4.21 mm, P <0.001). No patients had any impaired neurocognitive performance during follow-up. Impaired left ventricular ejection fraction ( P =0.012) and low intraoperative activated clotting time ( P =0.009) level were associated with the occurrence of ACE in a multivariate analysis. Conclusions: High-resolution DWI revealed a higher incidence and greater details of post-ablation ACE in patients with atrial fibrillation. MRI settings significantly impact the detection of ACE and should be considered when comparing incidence rates of ACE among different studies. Clinical Trial Registration: URL: https://www.clinicaltrials.gov . Unique identifier: NCT01761188.