Related papers: Parallel Transport on Kendall Shape Spaces
Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel…
In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the…
Motion planning is an important and well-studied field of robotics. A typical approach to finding a route is to construct a {\em cell graph} representing a scene and then to find a path in such a graph. In this paper we present and analyze…
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…
In this paper, we introduce PASGAL (Parallel And Scalable Graph Algorithm Library), a parallel graph library that scales to a variety of graph types, many processors, and large graph sizes. One special focus of PASGAL is the efficiency on…
We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate…
In the present paper we study normal transport surfaces in four-dimensional Euclidean space $\mathbb{E}^{4}$ which are the generalization of surface offsets in $\mathbb{E}^{3}$. We find some results of normal transport surfaces in…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches…
We present a methodology for parallel acceleration of learning in the presence of matrix orthogonality and unitarity constraints of interest in several branches of machine learning. We show how an apparently sequential elementary rotation…
We present a heterogeneous localization framework for solving radar global localization and pose tracking on pre-built lidar maps. To bridge the gap of sensing modalities, deep neural networks are constructed to create shared embedding…
In robotics, structural design and behavior optimization have long been considered separate processes, resulting in the development of systems with limited capabilities. Recently, co-design methods have gained popularity, where bi-level…
We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
A Parallel Self-Organizing Map (Parallel-SOM) is proposed to modify Kohonen's SOM in parallel computing environment. In this model, two separate layers of neurons are connected together. The number of neurons in both layers and connections…
Car-hailing services have become a prominent data source for urban traffic studies. Extracting useful information from car-hailing trace data is essential for effective traffic management, while discrepancies between car-hailing vehicles…
Pairwise association measure is an important operation in data analytics. Kendall's tau coefficient is one widely used correlation coefficient identifying non-linear relationships between ordinal variables. In this paper, we investigated a…
Evaluating how well a whole system or set of subsystems performs is one of the primary objectives of performance testing. We can tell via performance assessment if the architecture implementation meets the design objectives. Performance…
We determine the topology of the moduli space of periodic tilings of the plane by parallelograms. To each such tiling, we associate combinatorial data via the zone curves of the tiling. We show that all tilings with the same combinatorial…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…