Transformations of Heun's equation and its integral relations

We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011) 07520

Prepose: privacy, security, and reliability for gesture-based programming

With the rise of sensors such as Microsoft Kinect, gesture-based interfaces have become practical. However, to recognize such gestures, applications need access to users' depth and video, exposing sensitive data about individuals and their environment. Prepose, a domain-specific language for building gesture recognizers, combined with a system architecture that protects privacy, security, and reliability with untrusted applications, addresses these threats