114 research outputs found
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
The geometry of syntax and semantics for directed file transformations
We introduce a conceptual framework that associates syntax and semantics with
vertical and horizontal directions in principal bundles and related
constructions. This notion of geometry corresponds to a mechanism for
performing goal-directed file transformations such as "eliminate unsafe syntax"
and suggests various engineering practices
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