Similar to ordinary differential equations, rough paths and equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when approximate space-valued weakly geometric $\alpha$-rough by signatures of curves bounded variation, given some tuning the H\"older parameter. We show that these are satisfied on Hilbert spaces. As an application, obtain Wong-Zaka...

abstract this study addresses two dimensional infiltration from irrigated furrows. the basic approach is to develop a two-dimensional infiltration as a combination of the corresponding one-dimensional vertical and an edge effect. the edge effect is the difference between the cumulative infiltration per unit of adjusted wetting perimeter and the corresponding one-dimensional infiltration. this a...

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length differ from those for the planar Ising model. The quantitative alternation of these exponents originates from the difference ...

Nativists have postulated fundamental geometric knowledge that predates linguistic and symbolic thought. Central to these claims is the proposal for an isolated cognitive system dedicated to processing geometric information. Testing such hypotheses presents challenges due to difficulties in eliminating the combination of geometric and non-geometric information through language. We present evide...

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian ...