Fall 2016¶

11 / 4 Prof. Chris Fox¶

LogicBench: Web Tools for Learning Logic

There are many tools for helping students learn logic. Most tend to be rather clunky and restricted to classical propositional and predicate logic. The LogicBench project is an effort to make more elegant pedagogical tools for a wide range of logics, including modal and temporal logics.

10 / 21 Prof. David Bernstein¶

Finding Alternatives to the Best Path

This talk considers several different ways of thinking about alternatives to the best (e.g., shortest, minimum cost) path. It then defines the notion of the Best k-Similar Path and considers a linear optimization formulation of the problem of finding such paths. Next it considers a Lagrangian Relaxation heuristic for solving this problem (and other related problems). Finally, it concludes with some empirical results. Along the way it provides some background (for those who need it) on multivariate calculus and linear optimization.

10 / 7 Prof. Mike Lam¶

Office Space and Salami - Automated Floating-Point Program Analysis

Most computers use floating-point arithmetic to perform non-integer computations. However, floating-point representations provide limited precision and it can be difficult to quantify the resulting loss of accuracy. Because of this, computer programmers tend to use the highest available precision and "hope for the best." My research addresses this situation by providing automated techniques for analyzing and providing insights about the floating-point behavior of computer programs. Most of these techniques operate at the assembly and machine code level, adding instrumentation to detect problems or simulate alternative representations. In this talk, I will describe past efforts as well as my current research, including concrete projects that I would like to work on with undergraduate students.

9 / 22 Prof. John C. Bowers¶

Cauchy Rigidity of convex c-Polyhedra

A c-polyhedron is a generalization of circle packings on the sphere to circle patterns with specified inversive distances between adjacent circles where the underlying 1-skeleton need not be a triangulation. In this talk we prove that any two convex c-polyhedra with inversive congruent faces are inversive congruent. The proof follows the pattern of Cauchy’s proof o f his celebrated rigidity theorem for convex Euclidean polyhedra. The trick in applying Cauchy’s argument in this setting is in constructing hyperbolic polygons around each vertex in a c-polyhedron on which a variant of Cauchy’s arm lemma can be applied.