Related papers: A brief survey on local holomorphic dynamics in hi…
We propose a new image representation for texture categorization and facial analysis, relying on the use of higher-order local differential statistics as features. It has been recently shown that small local pixel pattern distributions can…
We describe the variation of the Minkowski, packing and Hausdorff dimensions of a set moving under a holomorphic motion, as well as the variation of its area. Our method provides a new, unified approach to various celebrated theorems about…
The motion of the charged particles in graphen in the frame of the quantum non-local hydrodynamic description is considered. It is shown as results of the mathematical modeling that the mentioned motion is realizing in the soliton forms.…
Hydrodynamic surfaces are solutions of hydrodynamic type systems viewed as non-parametrized submanifolds of the hodograph space. We propose an invariant differential-geometric characterization of hydrodynamic surfaces by expressing the…
The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…
The relations and differences between various classification problems arising in the context of local two-dimensional conformal QFT, modular invariants, and subfactors are discussed. The extent to which locality implies modular invariance,…
The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological…
Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical for numerous applications, including the computation of chemical reaction rates and transport of objects in the solar system. Many…
The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…
We show that the dynamics between inherent structures in glass forming systems can be understood in purely dynamical terms, without any reference to ``topographic'' features of the potential energy landscape. This ``non-topographic''…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
The purpose of this work is the development and determination of higher-order continuum-like kinematic measures which characterize discrete kinematic data obtained from experimental measurement (e.g., digital image correlation) or kinematic…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
This work studies two dimensional local skew fields and their automorphisms.
We provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regularity, H\"older continuity of the inverse mapping,…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
We describe all the dynamical degrees of automorphisms of hyperk\"ahler manifolds in terms of the first dynamical degree. We also present two explicit examples of different geometric flavours.
The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient…
Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…