Related papers: Hyperbolic Cross Approximation
It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the error estimate of hyperbolic cross (HC) approximations with…
Mathematical oncology is an interdisciplinary research field where the mathematical sciences meet cancer research. Being situated at the intersection of these two fields makes mathematical oncology highly dynamic, as practicing researchers…
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…
Accurately measuring the translations of objects between images is essential in many fields, including biology, medicine, chemistry, and physics. One important application is tracking one or more particles by measuring their apparent…
Molecular dynamics (MD) simulations are used in biochemistry, physics, and other fields to study the motions, thermodynamic properties, and the interactions between molecules. Computational limitations and the complexity of these problems,…
We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and limited) by the theme of the author's interests. Thus we will…
Hyperbolic polynomials are real polynomials whose real hypersurfaces are nested ovaloids, the inner most of which is convex. These polynomials appear in many areas of mathematics, including optimization, combinatorics and differential…
A significant amount of high-impact contemporary scientific research occurs where biology, computer science, engineering and chemistry converge. Although programmes have been put in place to support such work, the complex dynamics of…
Crosslinking mass spectrometry (Crosslinking MS) has substantially matured as a method over the last two decades through parallel development in multiple labs, demonstrating its applicability for protein structure determination,…
Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen…
Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
This paper presents the principal challenges and opportunities associated with computational biomechanics research. The underlying cognitive control involved in the process of human motion is inherently complex, dynamic, multidimensional,…
A mixture of joint generalized hyperbolic distributions (MJGHD) is introduced for asymmetric clustering for high-dimensional data. The MJGHD approach takes into account the cluster-specific subspace, thereby limiting the number of…
The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport…
Polymer materials have the characteristic feature that they are multiscale systems by definition. Already the description of a single molecules involves a multitude of different scales, and cooperative processes in polymer assemblies are…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
A large number of applications such as querying sensor networks, and analyzing protein-protein interaction (PPI) networks, rely on mining uncertain graph and hypergraph databases. In this work we study the following problem: given an…