Reclaiming our Assumptions at the Intersection of Technology, Learning and Equity

Educatio

The Hyperplane is the Only Stable, Smooth Solution to the Isoperimetric Problem in Gaussian Space

We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $\Sigma^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize Gaussian weighted area and preserve Gaussian weighted volume. We show that such $\Sigma$ satisfy a curvature condition, and derive the Jacobi operator $L$ for the second variation of such $\Sigma$. Our first main result is that for non-planar $\Sigma$, bounds on the index of $L$, acting on volume preserving variations, gives us that $\Sigma$ splits off a linear space. A corollary of this result is that hyperplanes are the only stable smooth complete solutions to this Gaussian isoperimetric type problem, and that there are no hypersurfaces of index one. Finally, we show that for the case of $\Sigma^2 \subset \mathbb R^3$, there is a gradient decay estimate depending on bounds for the curvature condition and an appropriate area growth bound. This shows that, in the limit as $R \to \infty$, stable $(\Sigma, \partial\Sigma) \subset (B_{2R}(0), \partial B_{2R}(0))$ with good area growth bounds approach hyperplanes.Comment: 20 page

Visualisation techniques for users and designers of layout algorithms

Visualisation systems consisting of a set of components through which data and interaction commands flow have been explored by a number of researchers. Such hybrid and multistage algorithms can be used to reduce overall computation time, and to provide views of the data that show intermediate results and the outputs of complementary algorithms. In this paper we present work on expanding the range and variety of such components, with two new techniques for analysing and controlling the performance of visualisation processes. While the techniques presented are quite different, they are unified within HIVE: a visualisation system based upon a data-flow model and visual programming. Embodied within this system is a framework for weaving together our visualisation components to better afford insight into data and also deepen understanding of the process of the data's visualisation. We describe the new components and offer short case studies of their application. We demonstrate that both analysts and visualisation designers can benefit from a rich set of components and integrated tools for profiling performance

Tracking the Economy of the City of Atlanta: Past Trends and Future Prospects

This report explores the changes in the level and composition of employment in the City of Atlanta over the last 25 years. FRC Report 17

Evaluating cultural competency and patient satisfaction in an urban dermatology clinic.

Cultural competency continues to gain increased attention in medicine. Not only does it play a significant role in the delivery of health care and patient outcomes, but it also remains a major determinant of patient satisfaction. This study investigated how patients in an urban dermatology clinic rated their satisfaction with cultural competency. Compared to White patients, satisfaction scores were greater for Hispanic or Latino patients and less for Asian patients, while there was no significant difference for Black or African American patients. There were clear differences in patient satisfaction rates of various dimensions of cultural competency. A follow-up study with a larger sample size is needed for closer examination into the conclusions

Rapid-Setting Non-Portland Cement Concrete Applications

CSA (calcium sulfoaluminate) cement was engineered to overcome the performance challenges of traditional portland cement while producing high early strength, allowing large reductions in lane closure time and dangerous exposure to construction personnel and the traveling public. We will look at examples from the 2,500 lane miles of pavement that have been replaced since the early 1980s, with very few failures and long-term durability

Biometrics-as-a-Service: A Framework to Promote Innovative Biometric Recognition in the Cloud

Biometric recognition, or simply biometrics, is the use of biological attributes such as face, fingerprints or iris in order to recognize an individual in an automated manner. A key application of biometrics is authentication; i.e., using said biological attributes to provide access by verifying the claimed identity of an individual. This paper presents a framework for Biometrics-as-a-Service (BaaS) that performs biometric matching operations in the cloud, while relying on simple and ubiquitous consumer devices such as smartphones. Further, the framework promotes innovation by providing interfaces for a plurality of software developers to upload their matching algorithms to the cloud. When a biometric authentication request is submitted, the system uses a criteria to automatically select an appropriate matching algorithm. Every time a particular algorithm is selected, the corresponding developer is rendered a micropayment. This creates an innovative and competitive ecosystem that benefits both software developers and the consumers. As a case study, we have implemented the following: (a) an ocular recognition system using a mobile web interface providing user access to a biometric authentication service, and (b) a Linux-based virtual machine environment used by software developers for algorithm development and submission