Abstract: Systems and methods are provided for performing a risk-measuring or risk-limiting audit of reported winner(s) from among two or more candidates or of a reported outcome of ballot measure(s) in one or more contests of an election based on one or more social choice functions from a plurality of ballot cards.

Abstract: Systems and methods for an analysis of clinical trial data using randomization tests that honors the randomized design of the clinical trial are provided herein. In particular, a non-parametric analyzer implementing randomization tests and associated methods for analyzing clinical data is provided. The non-parametric analyzer receives clinical trial data comprising a data structure containing data corresponding to subjects in the clinical trial, where the subjects have been organized into treatment groups, including at least one control group. The non-parametric analyzer generates multiple treatment allocations of the data structure by reorganizing, at random, the subjects along with corresponding data to generate further groups. In some embodiments, the non-parametric analyzer determines the statistical significance based on an overall probability and the multiple allocations of the data structure.

Abstract: A sandal including a sole having a front region and a back region and an interior side and an exterior side, having a first opening in or near the back region at the interior side and a second opening in or near the back region at the exterior side. A primary strap is threaded through the first opening, then looped around the back region, and threaded through the second opening, thereby defining a heel region of the primary strap between the first opening and the second opening. The sandal further includes an adjustable securement strap that attaches on one side to the interior side of the heel region of the primary strap and on the other side to the exterior side of the heel region of the primary strap.

Abstract: A sandal including a sole having a front region and a back region and an interior side and an exterior side, that includes a first opening located in said front region, a second opening in or near said back region at said interior side and a third opening in or near said back region at said exterior side, and a strap, which includes a plurality of sections, having a first end and a second end and wherein said first end is threaded upwardly through said front opening, through said second opening and looped around said back region, and through said third opening, thereby defining a heel region between said second opening and said third opening.