FORM Matters: Fast Symbolic Computation under UNIX

We give a brief introduction to FORM, a symbolic programming language for massive batch operations, designed by J.A.M. Vermaseren. In particular, we stress various methods to efficiently use FORM under the UNIX operating system. Several scripts and examples are given, and suggestions on how to use the vim editor as development platform.Comment: 10 pages, PDF document (PDFLaTeX source available upon request) with 2 JPG figures; submitted to Computers & Mathematics with Application

Self force on a scalar charge in the spacetime of a stationary, axisymmetric black hole

We study the self force acting on a particle endowed with scalar charge, which is held static (with respect to an undragged, static observer at infinity) outside a stationary, axially-symmetric black hole. We find that the acceleration due to the self force is in the same direction as the black hole's spin, and diverges when the particle approaches the outer boundary of the black hole's ergosphere. This acceleration diverges more rapidly approaching the ergosphere's boundary than the particle's acceleration in the absence of the self force. At the leading order this self force is a (post)$^2$-Newtonian effect. For scalar charges with high charge-to-mass ratio, the acceleration due to the self force starts dominating over the regular acceleration already far from the black hole. The self force is proportional to the rate at which the black hole's rotational energy is dissipated. This self force is local (i.e., only the Abraham-Lorentz-Dirac force and the local coupling to Ricci curvature contribute to it). The non-local, tail part of the self force is zero.Comment: 28 pages, 9 figure

Combinatorial species and graph enumeration

In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the distinction between labeled and unlabeled structures. The cycle index series of a species encodes the labeled and unlabeled enumerative data of that species. Moreover, by using species operations, we are able to solve for the cycle index series of one species in terms of other, known cycle indices of other species. Section 3 is an exposition of species theory and Section 4 is an enumeration of point-determining bipartite graphs using this toolset. In Section 5, we extend a result about point-determining graphs to a similar result for point-determining {\Phi}-graphs, where {\Phi} is a class of graphs with certain properties. Finally, Appendix A is an expository on species computation using the software Sage [9] and Appendix B uses Sage to calculate the cycle index series of point-determining bipartite graphs.Comment: 39 pages, 16 figures, senior comprehensive project at Carleton Colleg

Towards Assume-Guarantee Profiles for Autonomous Vehicles

Rules or specifications for autonomous vehicles are currently formulated on a case-by-case basis, and put together in a rather ad-hoc fashion. As a step towards eliminating this practice, we propose a systematic procedure for generating a set of supervisory specifications for self-driving cars that are 1) associated with a distributed assume-guarantee structure and 2) characterizable by the notion of consistency and completeness. Besides helping autonomous vehicles make better decisions on the road, the assume-guarantee contract structure also helps address the notion of blame when undesirable events occur. We give several game-theoretic examples to demonstrate applicability of our framework