The Chapel Hill Linux Lab: A Case Study in the Use of Linux and Other Open Source Applications in the High School Setting

This case study describes the design, installation, and maintenance of a small, Linux-based computer lab consisting of a console-server and four thin-client terminals at Chapel Hill High School in Chapel Hill, North Carolina. The project further involved the development of a 12-hour course in basic Linux system administration and its presentation to a self-selected group of high school students. Despite some early difficulties with the high school's hardware, the lab was successfully installed and remained in place with little call for maintenance throughout the fall. The course was taught during these months to seven students. Although the project was not without setbacks and minor failures, each of these suggested not overall deficiency, but a way in which such a project could be more profitably deployed n an enterprise, rather than an experimental, setting

Quantum-limited estimation of the axial separation of two incoherent point sources

Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cram\'er-Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require neither activation of fluorophores nor sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful to a variety of applications such as far-field fluorescence microscopy.Comment: Comments are welcom

An extremal effective survey about extremal effective cycles in moduli spaces of curves

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.Comment: Submitted to the Proceedings of the Abel Symposium 2017. Comments are welcom

Quantum-limited estimation of the axial separation of two incoherent point sources

Improving axial resolution is crucial for three-dimensional optical imaging systems. Here we present a scheme of axial superresolution for two incoherent point sources based on spatial mode demultiplexing. A radial mode sorter is used to losslessly decompose the optical fields into a radial mode basis set to extract the phase information associated with the axial positions of the point sources. We show theoretically and experimentally that, in the limit of a zero axial separation, our scheme allows for reaching the quantum Cramér–Rao lower bound and thus can be considered as one of the optimal measurement methods. Unlike other superresolution schemes, this scheme does not require either activation of fluorophores or sophisticated stabilization control. Moreover, it is applicable to the localization of a single point source in the axial direction. Our demonstration can be useful for a variety of applications such as far-field fluorescence microscopy

Hyperbolicity of varieties of log general type

These notes provide an overview of various notions of hyperbolicity for varieties of log general type from the viewpoint of both arithmetic and birational geometry. The main results are based on our paper entitled "Hyperbolicity and uniformity of varieties of log general type." They are expanded notes from a minicourse the authors gave as part of the Geometry and arithmetic of orbifolds workshop at UQ\'AM.Comment: Addressed some inaccuracies and typos pointed out by the referees and some readers. Slight change of title. To appear in CRM short courses (Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces: Hyperbolicity in Montr\'eal