Schwinger Terms and Cohomology of Pseudodifferential Operators

We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the ``twisted'' Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry. In the process we also show how the ordinary Radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component.Comment: 19 pages, plain te

History and Actuality of Galician Emigrants: A Galicia (Spain) Shared between Latin America and Europe

Despite the significant advances in path planning methods, problems involving highly constrained spaces are still challenging. In particular, in many situations the configuration space is a non-parametrizable variety implicitly defined by constraints, which complicates the successful generalization of sampling-based path planners. In this paper, we present a new path planning algorithm specially tailored for highly constrained systems. It builds on recently developed tools for Higher-dimensional Continuation, which provide numerical procedures to describe an implicitly defined variety using a set of local charts. We propose to extend these methods to obtain an efficient path planner on varieties, handling highly constrained problems. The advantage of this planner comes from that it directly operates into the configuration space and not into the higher-dimensional ambient space, as most of the existing methods do.Postprint (author’s final draft

The state of neuro-oncology during the COVID-19 pandemic: a worldwide assessment.

It remains unknown how the COVID-19 pandemic has changed neuro-oncology clinical practice, training, and research efforts. We performed an international survey of practitioners, scientists, and trainees from 21 neuro-oncology organizations across 6 continents, April 24-May 17, 2020. We assessed clinical practice and research environments, institutional preparedness and support, and perceived impact on patients. Of 582 respondents, 258 (45%) were US-based and 314 (55%) international. Ninety-four percent of participants reported changes in their clinical practice. Ninety-five percent of respondents converted at least some practice to telemedicine. Ten percent of practitioners felt the need to see patients in person, specifically because of billing concerns and pressure from their institutions. Sixty-seven percent of practitioners suspended enrollment for at least one clinical trial, including 62% suspending phase III trial enrollments. More than 50% believed neuro-oncology patients were at increased risk for COVID-19. Seventy-one percent of clinicians feared for their own personal safety or that of their families, specifically because of their clinical duties; 20% had inadequate personal protective equipment. While 69% reported increased stress, 44% received no psychosocial support from their institutions. Thirty-seven percent had salary reductions and 63% of researchers temporarily closed their laboratories. However, the pandemic created positive changes in perceived patient satisfaction, communication quality, and technology use to deliver care and mediate interactions with other practitioners. The pandemic has changed treatment schedules and limited investigational treatment options. Institutional lack of support created clinician and researcher anxiety. Communication with patients was satisfactory. We make recommendations to guide clinical and scientific infrastructure moving forward and address the personal challenges of providers and researchers