Related papers: New tools in hierarchical hyperbolicity: A survey
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.
We present a collection of new, open-source computational tools for numerically modeling recent large-scale observational data sets using modern cosmology theory. Specifically, these tools will allow both students and researchers to…
This is a lightning introduction to some modern techniques used in the study of the statistical properties of hyperbolic dynamical systems. The emphasis is not in presenting a comprehensive theory but rather in fleshing out the main ideas…
This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on size of the object and the wave length. To this end, two…
The HL-LHC presents significant challenges for the HEP analysis community. The number of events in each analysis is expected to increase by an order of magnitude and new techniques are expected to be required; both challenges necessitate…
The HyperCarte research group wishes to offer a new cartographic tool for spatial analysis of social data, using the potential smoothing method. The purpose of this method is to view the spreading of phenomena's in a continuous way, at a…
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
These are lecture notes of a course held at IMPA, Rio de Janiero, in september 2010: the purpose was to present recent results on Kobayashi hyperbolicity in complex geometry. Our ultimate goal is to describe the results obtained on…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
Unsupervised summarization is a powerful technique that enables training summarizing models without requiring labeled datasets. This survey covers different recent techniques and models used for unsupervised summarization. We cover…
The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…
Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and…
Metaheuristic search methods have proven to be essential tools for tackling complex optimization challenges, but their full potential is often constrained by conventional algorithmic frameworks. In this paper, we introduce a novel approach…
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
Context. In the current era of multi-wavelength and multi-messenger astronomy, international organisations are actively working on the definition of new standards for the publication of astronomical data, and substantial effort is devoted…
Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce…
We derive geometric formulas for the mass of asymptotically hyperbolic manifolds using coordinate horospheres. As an application, we obtain a new rigidity result of hyperbolic space: if a complete asymptotically hyperbolic manifold has…
Hyperbolic geometry has been successfully applied in modeling brain cortical and subcortical surfaces with general topological structures. However such approaches, similar to other surface based brain morphology analysis methods, usually…