Related papers: New tools in hierarchical hyperbolicity: A survey
The first part of this survey is a heuristic, non-technical discussion of what an HHS is, and the aim is to provide a good mental picture both to those actively doing research on HHSs and to those who only seek a basic understanding out of…
This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer…
Statistical tools have been developed to quantify the agreement between a hypothesis or a model and the observed data for probabilistic phenomena. In this work, we define statistical methods used to measure the properties of the higgs boson…
Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of…
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…
We introduce a number of tools for finding and studying \emph{hierarchically hyperbolic spaces (HHS)}, a rich class of spaces including mapping class groups of surfaces, Teichm\"{u}ller space with either the Teichm\"{u}ller or…
This paper evaluates methods of hierarchical skill analysis developed in aerospace to the problem of surgical skill assessment and modeling. The analysis employs tool motion data of Fundamental of Laparoscopic Skills (FLS) tasks collected…
Learning in hyperbolic spaces has attracted increasing attention due to its superior ability to model hierarchical structures of data. Most existing hyperbolic learning methods use fixed distance measures for all data, assuming a uniform…
The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.
Hierarchical semantic structures, naturally existing in real-world datasets, can assist in capturing the latent distribution of data to learn robust hash codes for retrieval systems. Although hierarchical semantic structures can be simply…
In this conference paper I introduce a selection of BSM tools and describe their most recent developments. I choose to focus on tools for the reinterpretation of LHC searches, tools that compute dark matter constraints,…
The goal of this survey is to present combinatorial modulus that have been recently used to study quasi-conformal properties of boundaries of hyperbolic groups. First, we will recall well known rigidity results and questions that motivated…
With the prevalence of online social media, users' social connections have been widely studied and utilized to enhance the performance of recommender systems. In this paper, we explore the use of hyperbolic geometry for social…
This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group.…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
The number of tools for dynamics simulation has grown in the last years. It is necessary for the robotics community to have elements to ponder which of the available tools is the best for their research. As a complement to an objective and…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…