Related papers: Two-Scale Geometric Modelling for Defective Media

A similarity structure on a connected manifold M is a Riemannian metric on its universal cover such that the fundamental group of M acts by similarities. If the manifold M is compact, we show that the universal cover admits a de Rham…

The addition of mass terms in general breaks gauge symmetries which can be recovered usually via Stueckelberg fields. The massive BF model describes massive spin-1 particles while preserving the $U(1)$ symmetry without Stueckelberg fields.…

We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group $G$. The invariants are constructed from any right $G$-modules $M$ and any $G$-invariant bilinear function on $M$, and are of bilinear forms. For…

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…

We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction…

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data…

The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a K\"ahler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A…

Let (M, g) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g: two almost complex and two almost product structures satisfying additionally certain integrability conditions. For instance, if r is a…

Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…

We construct stable minimal hypersurfaces with simple topology in certain compact $4$-manifolds $X$ with boundary, where $X$ embeds into a smooth manifold homeomorphic to $S^4$. For example, if $X$ is equipped with a Riemannian metric $g$…

We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…

It is challenging to directly estimate the human geometry from a single image due to the high diversity and complexity of body shapes with the various clothing styles. Most of model-based approaches are limited to predict the shape and pose…

We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the…

Considering a theory space consisting of a large number of five-dimensional Dirac fermion field theories including background abelian gauge fields, we can construct a theory similar to a continuous six-dimensional theory compactified with…

This paper presents an analytical study about the behavior of arbitrary shaped and sized non-cohesive two-dimensional granular materials. Several mechanical properties and relations are unraveled by connecting micro and macro scales in an…

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…

We address the problem of determining the hypersurfaces $f\colon M^{n} \to \mathbb{Q}_s^{n+1}(c)$ with dimension $n\geq 3$ of a pseudo-Riemannian space form of dimension $n+1$, constant curvature $c$ and index $s\in \{0, 1\}$ for which…

Emergent modified gravity is a post-Einsteinian gravitational theory where spacetime geometry is not fundamental but rather emerges from the gravitational degrees of freedom in a non-trivial way. The specific relationship between geometry…

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$…