Systems and methods are provided for maintaining performance of an integrated circuit at a reduced power. The system includes a computer system and a billing error detection engine capable of detecting billing errors using predictive modeling techniques. The interval signal generator outputs a plurality of interval signals which are evenly or approximately evenly distributed over a time interval. A linear motion of the primary piston is converted to a rotational motion through engagement between the sensor pin and the sensor arm and is transmitted to the rotation angle detector. Methods of making and using the compounds of Formulas are also within the scope of the invention.