相关论文: Hyperbolic reflections as fundamental building blo…

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

Metamaterials are nano-engineered media with designed properties beyond those available in nature with applications in all aspects of materials science. In particular, metamaterials have shown promise for next generation of optical…

A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…

A hyperbolic reflection group is a discrete group generated by reflections in the faces of an $n$-dimensional hyperbolic polyhedron. This survey article is dedicated to the study of arithmetic hyperbolic reflection groups with an emphasis…

Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…

Label inventories for fine-grained entity typing have grown in size and complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic spaces offer a mathematically appealing approach for learning hierarchical representations of…

According to the holographic principle, the description of a volume of space can be thought of as encoded on its boundary. Holographic principle establishes equivalence, or duality, between theoretical description of volume physics, which…

Deep representation learning is a ubiquitous part of modern computer vision. While Euclidean space has been the de facto standard manifold for learning visual representations, hyperbolic space has recently gained rapid traction for learning…

We show that any metallo-dielectric multilayer with a hyperbolic dispersion relation can actually be characterized by a complex effective index. This refractive index, extracted from the complex Bloch band diagram, can be directly linked to…

By using Klein's model for hyperbolic geometry, hyperbolic structures on orbifolds or manifolds provide examples of real projective structures. By Andreev's theorem, many 3-dimensional reflection orbifolds admit a finite volume hyperbolic…

In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…

Motivated by an experimental study of groups generated by reflections in planar patterns of tangent circles, we describe some methods for constructing and studying representation spaces of holonomy groups of infinite volume hyperbolic…

This paper is an introduction to the hyperbolic geometry of noncommutative polyballs B_n of bounded linear operators on Hilbert spaces. We use the theory of free pluriharmonic functions on polyballs and noncommutative Poisson kernels on…

Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…

In this paper, we study a problem related to geometry of bisectors in quaternionic hyperbolic geometry. We develop some of the basic theory of bisectors in quaternionic hyperbolic space $H^n_Q$. In particular, we show that quaternionic…

The implementation of hyperbolic metamaterials as component in optical waveguides, semiconductor light emitters and solar cells has been limited by the inherent loss in the metallic layers. The features of a hyperbolic metamaterial arise by…

Inspired by non-Hermitian systems, we study reflection and transmission in a stack of thin films composed by the repetition of a bipartite unit cell. We aim for controlled reflection and transmission using lossless and lossy materials in…

Motivated by recent breakthrough studies of wave hyperbolicity in extremely anisotropic natural materials and artificial composites, we investigate the radiation pattern of a localized emitter in a hyperbolic medium. Since the emission of a…

Auxiliary nanostructures introduce additional flexibility into optomechanical manipulation schemes. Metamaterials and metasurfaces capable to control electromagnetic interactions at the near-field regions are especially beneficial for…