Smooth slopes can be displayed on treadmills through tilt mechanisms , but these mechanisms are typically too slow to present sudden slope changes. The Sarcos Treadport utilizes a mechanical tether that can apply horizontal forces to the user to simulate gravity forces. Psychophys-ical results are presented to show that slope display via tether forces is a reasonable facsimile for treadmill slo...

We give a “second generation” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.

In this paper, we determine geometric information on slope lengths of a large class of knots in the 3–sphere, based only on dia-grammatical properties of the knots. In particular, we show such knots have meridian length strictly less than 4, and we find infinitely many families with meridian length approaching 4 from below. Finally, we present an example to show that, in contrast to the case of...