Ten years ago A. Zorich discovered, by computer experiments on interval exchange transformations, some striking new power laws for the ergodic integrals of generic non-exact Hamiltonian flows on higher genus surfaces. In Zorich’s later work and in a joint paper authored by M. Kontsevich, Zorich and Kontsevich were able to explain conjecturally most of Zorich’s discoveries by relating them to th...

Studied are the moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows. It is actually shown that they are homeomorphic to those on dual modules associated with dual noncommutative flows. Moreover the method is also applicable to the case of noncommutative multi-flows. As an important application, computed are the the moduli spaces ...

The web can be regarded as an ecosystem of digital resources connected and shaped by collective successive behaviors of users. Knowing how people allocate limited attention on different resources is of great importance. To answer this, we embed the most popular Chinese web sites into a high dimensional Euclidean space based on the open flow network model of a large number of Chinese users' coll...

Abstract Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that routinely generated. In applications constrained by memory intensity, excessively large datasets may hinder discovery, making reduction a critical component data-driven methods. Datasets growing two directions: number points their dimensionality. Whereas dimension typic...

We show that the solutions to the non-stationary Navier–Stokes equations in R (d = 2, 3) which are left invariant under the action of discrete subgroups of the orthogonal group O(d) decay much faster as |x| → ∞ or t → ∞ than in generic case and we compute, for each subgroup, the precise decay rates in space-time of the velocity field.

Renormalisation Group (RG) flows in theory space (the space of couplings) are generated by a vector field – the β function. Using a specific metric ansatz in theory space and certain methods employed largely in the context of General Relativity, we examine the nature of the expansion, shear and rotation of geodesic RG flows. The expansion turns out to be a negative quantity inversely related to...