Related papers: Hyperbolic Cross Approximation
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…
Continuum Approximation (CA) is an efficient and parsimonious technique for modeling complex logistics problems. In this paper,we review recent studies that develop CA models for transportation, distribution and logistics problems with the…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabatic sources in the equations, due to radiation for example.…
Various scaling relations of the entanglement entropy are reviewed. Based on the scaling, I would like to point out similarity of mathematical formulation among recent topics in wide research area. In particular, the scaling plays crucial…
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…
Crochet models of a hyperbolic plane is a popular educational tool as they help to visualize complicated objets in hyperbolic geometry. We present another way how to make crochet models when we view them as a part of a triangulated…
A mixture of multiple scaled generalized hyperbolic distributions (MMSGHDs) is introduced. Then, a coalesced generalized hyperbolic distribution (CGHD) is developed by joining a generalized hyperbolic distribution with a multiple scaled…
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…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive…
We introduce hyperbolic attention networks to endow neural networks with enough capacity to match the complexity of data with hierarchical and power-law structure. A few recent approaches have successfully demonstrated the benefits of…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
In recent years, there has been a growing trend of incorporating hyperbolic geometry methods into computer vision. While these methods have achieved state-of-the-art performance on various metric learning tasks using hyperbolic distance…
Variational Bayes (VB) has shown itself to be a powerful approximation method in many application areas. This paper describes some diagnostics methods which can assess how well the VB approximates the true posterior, particularly with…
Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…
Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…