In this paper we establish a one-to-one correspondence between S1-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This result is a higher-order analogue of the familiar equivalence between bundles with connections and their holonomies for connected manifolds. The holonomy of a g...

Introduction The concept of parallelism may significantly increase the performance of transport subsystems [1, 2, 3, etc.]. A transport subsystem covers a subset of a complete transport system, which combines the functions of the four lower layers according to the OSI Reference Model. Because parallelising standard protocols like OSI TP4/CLNP or TCP/IP suffers from their inherent sequential str...

We propose an algorithm for generating a moving coordinate frame on a space curve based on the concept of parallel transport. Such algorithms can be used for creating ribbons, tubes, and camera orientations that are smoothly varying and controlled by the curve geometry itself. The more familiar Frenet frame approach su ers from ambiguity and sudden orientation changes when the curve straightens...

This paper presents a fast parallel method to compute the solution of the radiative transport equation in inhomogeneous participating media. The efficiency of the method comes from different factors. First, we use a novel approximation scheme to find a good guess for both the direct and the scattered component. This scheme is based on the analytic solution for homogeneous media, which is modula...

This paper describes the parallel implementation of a transport network model. A ‘SingleProgram, Multiple Data’ (SPMD) paradigm is employed using a simple data decomposition approach where each processor runs the same program but acts on a different subset of the data. The objective is to reduce the execution time of the model. The computationally intensive part of the model is within the assig...

Given connection ∇ on a smooth vector bundle E → M , with connected base space M , the set of the parallel transport maps (associated to ∇) along closed loops based at x ∈M form a subgroup, Hol(∇), of the general linear group on the fibre Ex, GL(Ex). The group Hol(∇) is known as the holonomy group of the connection and it is independent of the base point x under conjugation of elements of the g...

This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus particularly on a one-dimensional lattice—a ring—of entangled rebits, which are binary quantum objects confined to a real state space. We consider states of...

Geometry representations in production Monte Carlo radiation transport codes used for linear-transport simulations are traditionally limited to combinatorial geometry (CG) topologies. While CG representations of input geometries are efficient to query, they are difficult to construct. In the Integrated-TIGER-Series (ITS) Monte Carlo code suite, a new approach for radiation transport geometry en...

Data flow acyclic directed graphs (digraphs) can be applied to accurately describe the data dependency for a wide range of grid-based scientific computing applications ranging from numerical algebra to realistic applications of radiation or neutron transport. The parallel computing of these applications is equivalent to the parallel execution of digraphs. This paper presents a framework of scal...

Increasing application demands together with the modern network technology towards gigabit speeds require new adequate transport systems. The transport subsystem PATROCLOS (parallel transport subsystem for cell based high speed networks) is based on a modular protocol architecture with a high degree of inherent parallelism. The primary goal of PATROCLOS was to allow efficient implementations of...