Effective temperature for finite systems

Under the Ansatz that the occupation times of a system with finitely many states are given by the Gibbs distribution, an effective temperature is uniquely determined (up to a choice of scale), and may be computed de novo, without any reference to a Hamiltonian for empirically accessible systems. As an example, the calculation of the effective temperature for a classical Bose gas is outlined and applied to the analysis of computer network traffic.Comment: 9 pages, 10 figure

Quality-diversity in dissimilarity spaces

The theory of magnitude provides a mathematical framework for quantifying and maximizing diversity. We apply this framework to formulate quality-diversity algorithms in generic dissimilarity spaces. In particular, we instantiate and demonstrate a very general version of Go-Explore with promising performance.Comment: Minor bug fix: see new appendix J for details. Only small quantitative effects; no significant changes to results (but all redone

Magnitude and Topological Entropy of Digraphs

Magnitude and (co)weightings are quite general constructions in enriched categories, yet they have been developed almost exclusively in the context of Lawvere metric spaces. We construct a meaningful notion of magnitude for flow graphs based on the observation that topological entropy provides a suitable map into the max-plus semiring, and we outline its utility. Subsequently, we identify a separate point of contact between magnitude and topological entropy in digraphs that yields an analogue of volume entropy for geodesic flows. Finally, we sketch the utility of this construction for feature engineering in downstream applications with generic digraphs.Comment: In Proceedings ACT 2022, arXiv:2307.1551

Greybox fuzzing time-intensive programs

We examine (directed) greybox fuzzing from a geometrical perspective, viewing dissimilarities on inputs and on control flow graphs (with dynamical statistics) as primitive objects of interest. We prototype and evaluate GoExploreFuzz, a greybox fuzzer for time-intensive programs that incorporates this perspective. The results indicate useful capabilities for greybox fuzzing that have hitherto been underutilized, notably quantifying the diversity of paths and autonomously tuning the "bandwidth" of mutations