Arithmetic purity of strong approximation for homogeneous spaces

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given

Automating Carotid Intima-Media Thickness Video Interpretation with Convolutional Neural Networks

Cardiovascular disease (CVD) is the leading cause of mortality yet largely preventable, but the key to prevention is to identify at-risk individuals before adverse events. For predicting individual CVD risk, carotid intima-media thickness (CIMT), a noninvasive ultrasound method, has proven to be valuable, offering several advantages over CT coronary artery calcium score. However, each CIMT examination includes several ultrasound videos, and interpreting each of these CIMT videos involves three operations: (1) select three end-diastolic ultrasound frames (EUF) in the video, (2) localize a region of interest (ROI) in each selected frame, and (3) trace the lumen-intima interface and the media-adventitia interface in each ROI to measure CIMT. These operations are tedious, laborious, and time consuming, a serious limitation that hinders the widespread utilization of CIMT in clinical practice. To overcome this limitation, this paper presents a new system to automate CIMT video interpretation. Our extensive experiments demonstrate that the suggested system significantly outperforms the state-of-the-art methods. The superior performance is attributable to our unified framework based on convolutional neural networks (CNNs) coupled with our informative image representation and effective post-processing of the CNN outputs, which are uniquely designed for each of the above three operations.Comment: J. Y. Shin, N. Tajbakhsh, R. T. Hurst, C. B. Kendall, and J. Liang. Automating carotid intima-media thickness video interpretation with convolutional neural networks. CVPR 2016, pp 2526-2535; N. Tajbakhsh, J. Y. Shin, R. T. Hurst, C. B. Kendall, and J. Liang. Automatic interpretation of CIMT videos using convolutional neural networks. Deep Learning for Medical Image Analysis, Academic Press, 201

Liquid rocket combustor computer code development

The Advanced Rocket Injector/Combustor Code (ARICC) that has been developed to model the complete chemical/fluid/thermal processes occurring inside rocket combustion chambers are highlighted. The code, derived from the CONCHAS-SPRAY code originally developed at Los Alamos National Laboratory incorporates powerful features such as the ability to model complex injector combustion chamber geometries, Lagrangian tracking of droplets, full chemical equilibrium and kinetic reactions for multiple species, a fractional volume of fluid (VOF) description of liquid jet injection in addition to the gaseous phase fluid dynamics, and turbulent mass, energy, and momentum transport. Atomization and droplet dynamic models from earlier generation codes are transplated into the present code. Currently, ARICC is specialized for liquid oxygen/hydrogen propellants, although other fuel/oxidizer pairs can be easily substituted

Optical Resonator Analog of a Two-Dimensional Topological Insulator

A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes.Comment: 10 pages, 9 figure