Computing rotation and self-linking numbers in contact surgery diagrams

We give an explicit formula to compute the rotation number of a nullhomologous Legendrian knot in contact (1/n)-surgery diagrams along Legendrian links and obtain a corresponding result for the self-linking number of transverse knots. Moreover, we extend the formula by Ding-Geiges-Stipsicz for computing the d3-invariant to (1/n)-surgeries.Comment: 19 pages, 6 figures; V2: Added the section on the d3-invariant and fixed a few misprints; V3: Minor corrections and clarifications; V4: Added a missing "n" in the formula for computing the Euler class of the contact structure in Theorem 5.

SkelCL - A Portable Skeleton Library for High-Level GPU Programming

While CUDA and OpenCL made general-purpose programming for Graphics Processing Units (GPU) popular, using these programming approaches remains complex and error-prone because they lack high-level abstractions. The especially challenging systems with multiple GPU are not addressed at all by these low-level programming models. We propose SkelCL – a library providing so-called algorithmic skeletons that capture recurring patterns of parallel computation and communication, together with an abstract vector data type and constructs for specifying data distribution. We demonstrate that SkelCL greatly simplifies programming GPU systems. We report the competitive performance results of SkelCL using both a simple Mandelbrot set computation and an industrial-strength medical imaging application. Because the library is implemented using OpenCL, it is portable across GPU hardware of different vendors

Peer-to-Peer Communication Across Network Address Translators

Network Address Translation (NAT) causes well-known difficulties for peer-to-peer (P2P) communication, since the peers involved may not be reachable at any globally valid IP address. Several NAT traversal techniques are known, but their documentation is slim, and data about their robustness or relative merits is slimmer. This paper documents and analyzes one of the simplest but most robust and practical NAT traversal techniques, commonly known as "hole punching." Hole punching is moderately well-understood for UDP communication, but we show how it can be reliably used to set up peer-to-peer TCP streams as well. After gathering data on the reliability of this technique on a wide variety of deployed NATs, we find that about 82% of the NATs tested support hole punching for UDP, and about 64% support hole punching for TCP streams. As NAT vendors become increasingly conscious of the needs of important P2P applications such as Voice over IP and online gaming protocols, support for hole punching is likely to increase in the future.Comment: 8 figures, 1 tabl

dOpenCL: Towards a Uniform Programming Approach for Distributed Heterogeneous Multi-/Many-Core Systems

Modern computer systems are becoming increasingly heterogeneous by comprising multi-core CPUs, GPUs, and other accelerators. Current programming approaches for such systems usually require the application developer to use a combination of several programming models (e. g., MPI with OpenCL or CUDA) in order to exploit the full compute capability of a system. In this paper, we present dOpenCL (Distributed OpenCL) – a uniform approach to programming distributed heterogeneous systems with accelerators. dOpenCL extends the OpenCL standard, such that arbitrary computing devices installed on any node of a distributed system can be used together within a single application. dOpenCL allows moving data and program code to these devices in a transparent, portable manner. Since dOpenCL is designed as a fully-fledged implementation of the OpenCL API, it allows running existing OpenCL applications in a heterogeneous distributed environment without any modifications. We describe in detail the mechanisms that are required to implement OpenCL for distributed systems, including a device management mechanism for running multiple applications concurrently. Using three application studies, we compare the performance of dOpenCL with MPI+OpenCL and a standard OpenCL implementation

Towards High-Level Programming of Multi-GPU Systems Using the SkelCL Library

Application programming for GPUs (Graphics Processing Units) is complex and error-prone, because the popular approaches — CUDA and OpenCL — are intrinsically low-level and offer no special support for systems consisting of multiple GPUs. The SkelCL library presented in this paper is built on top of the OpenCL standard and offers preimplemented recurring computation and communication patterns (skeletons) which greatly simplify programming for multiGPU systems. The library also provides an abstract vector data type and a high-level data (re)distribution mechanism to shield the programmer from the low-level data transfers between the system’s main memory and multiple GPUs. In this paper, we focus on the specific support in SkelCL for systems with multiple GPUs and use a real-world application study from the area of medical imaging to demonstrate the reduced programming effort and competitive performance of SkelCL as compared to OpenCL and CUDA. Besides, we illustrate how SkelCL adapts to large-scale, distributed heterogeneous systems in order to simplify their programming