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Algorithmic Probability-Guided Machine Learning on Non-Differentiable Spaces.
Hernández-Orozco S, Zenil H, Riedel J, Uccello A, Kiani NA, Tegnér J. Hernández-Orozco S, et al. Front Artif Intell. 2021 Jan 25;3:567356. doi: 10.3389/frai.2020.567356. eCollection 2020. Front Artif Intell. 2021. PMID: 33733213 Free PMC article.
We investigate the shape of a discrete algorithmic space when performing regression or classification using a loss function parametrized by algorithmic complexity, demonstrating that the property of differentiation is not required to achieve results similar to those obtained usin …
We investigate the shape of a discrete algorithmic space when performing regression or classification using a loss function parametrized by …
Reformulating scalar-tensor field theories as scalar-scalar field theories using a novel geometry.
Horndeski GW. Horndeski GW. Philos Trans A Math Phys Eng Sci. 2022 May 2;380(2222):20210183. doi: 10.1098/rsta.2021.0183. Epub 2022 Mar 14. Philos Trans A Math Phys Eng Sci. 2022. PMID: 35282686
In this paper, I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold M. This will enable me to use the second vertical derivatives of f, along with t …
In this paper, I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, f, on the …
Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems.
Kowalczyk P, Glendinning P. Kowalczyk P, et al. Chaos. 2011 Jun;21(2):023126. doi: 10.1063/1.3596708. Chaos. 2011. PMID: 21721768
The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the differentiability is lost across the switching surface. In the full system the slow manifold is no longer continuous, and there is an O(e) discontinuity across the swit …
The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the differentiability is lost across th …
Flows with cross sections.
Verjovsky A. Verjovsky A. Proc Natl Acad Sci U S A. 1970 Aug;66(4):1154-6. doi: 10.1073/pnas.66.4.1154. Proc Natl Acad Sci U S A. 1970. PMID: 16591849 Free PMC article.
Let M be a compact connected C(infinity)-manifold, of dimension n, without boundary. Let f(t): M --> M be a C(r)-flow with cross section. Let D(r)(M) be the topological group of diffeomorphisms of M with C(r)-topology (1 </= r </= infinity) and let D(o) (r) …
Let M be a compact connected C(infinity)-manifold, of dimension n, without boundary. Let f(t): M --> M be a C(r)-flow with cross s …