We'll discuss the Bayesian statistical paradigm and Markov Chain Monte Carlo (MCMC) algorithms - the cornerstone of modern Bayesian computation. Scalable MCMC for big datasets and complex models is currently an open research question. Using GPUs provides a promising and largely unexplored avenue for accelerating these algorithms, but is nontrivial, because MCMC is inherently sequential and has traditionally been considered difficult to parallelize. We'll show how Gibbs sampling, a widely used MCMC algorithm, can be effectively parallelized on GPUs for a large class of exchangeable hierarchical Bayesian models. Participants will learn the mathematical and hardware/software challenges in bringing GPUs to the Bayesian community. Background in Bayesian statistics or MCMC is not assumed.  Back

Learn how the world's most powerful quantum computers are simulated and benchmarked using GPU-based Monte Carlo algorithms. We'll introduce D-Wave's quantum annealing platform, describe several Monte Carlo algorithms for their simulation, and compare CPU- and GPU-based implementations of these algorithms. In particular, we'll focus on considerations of memory layout and fast mathematical functions to maximize speed. Finally, we'll present benchmarking results, including CPU-based algorithms, GPU-based algorithms, and D-Wave's latest-generation quantum annealers.  Back

Have you heard about the world's biggest eye ever built? Are you interested in scientific simulations running on NVIDIA DGX-1? Come and learn how combining these powerful computing devices dramatically leaps forward the computational astronomy community in designing major, multimillion-dollar optical instruments for the European Extremely Large Telescope. Starting from the mathematical model up to the high-performance implementation on DGX-1, we'll explain how the resulting matrix computations associated with an efficient task-based programming model help design the next generation of telescope instruments and, eventually, demonstrate a pathfinder for the discovery of new galaxies.  Back

Learn how to use the hidden computation capability of GPU texture units for general purpose computation. We describe GRASSY, a system for stellar spectral synthesis where the core problem is interpolation between pre-computed intensity value. We map these pre-computed tables to the GPU''s texture memory. Interpolation then becomes a texture lookup where the hardware automatically performs the interpolation, albeit at very low precision. Our mathematical framework reasons about the impact of this precision and our performance results show 500X speedups. This work generalizes the GPU texture units as computation engines and opens up new problems for GPU acceleration.

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Have you heard about the world's biggest eye? Learn how GPUs help design major, multimillion-dollar optical instruments for the European Extremely Large Telescope. Starting from the mathematical model up to the high-performance implementation on distributed-memory systems with hardware accelerators, we'll explain how the resulting dense linear algebra operations associated with an efficient task-based programming model help design the next generation of telescope instruments.  Back

Have you heard about the largest ground-based telescope ever built? Are you interested in the newest NVIDIA DGX-1 hardware accelerator? Come and learn how the DGX-1 architecture dramatically leaps forward the computational astronomy community in designing major, multimillion-dollar optical instruments for the European Extremely Large Telescope. Starting from the mathematical model up to the high-performance implementation on distributed-memory systems with hardware accelerators, we'll explain how the resulting matrix computations associated with an efficient task-based programming model help design the next generation of telescope instruments.

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Massive amounts of data is being generated in recent times. Current classification methods are quite accurate but extremely slow on big data. We propose a two-pronged approach a) Treat data vertically instead of conventional horizontal treatment and use our vertical-data specific classification algorithm and b) Exploit GPUs fast mathematical computational speed to process vertical data quickly which significantly benefits from our data structure called P-Tree. Our classification algorithm is O(k) where k is number of attributes and achieves significantly high accuracy.  Back

Topology provides a mathematical framework for applying a complete range of statistical, geometric, and machine learning methods, revealing insights from the geometry of your data. Ayasdi utilizes topological data analysis (TDA) in its advanced analytics software to simplify the analysis of complex, multi-variate datasets. In this poster, we illustrate how GPGPU's can be leveraged to accelerate key operations in TDA by over 14X.  Back

When used as predictive tools in natural disasters such as tsunamis, numerical models require extremely fast computations. Just a few years ago, real-time computing in Tsunami Early Warning Systems (TEWS) was unthinkable. Nevertheless, the EDANYA Group has revolutionized tsunami science paradigms. With the goal of saving lives in the framework of TEWS, our group has developed Tsunami-HySEA, a GPU-based numerical model aimed at producing numerical simulations of tsunami events that are faster than ever. Based on highly efficient, robust mathematical algorithms, together with the computational power of NVIDIA GPUs, Tsunami-HySEA is able to simulate a tsunami event in only a few minutes. Nowadays, one of the main challenges in tsunami science is producing accurate assessments of tsunami wave impacts and just a few minutes after the generating earthquake is triggered. This timely prediction would save many lives in a tsunami scenario. When the response is needed only in a few minutes, the resulting scenario is challenging. The required characteristics are difficult to combine in a single numerical tool: robustness, low-dissipation, large domains, and an extremely fast response  Back

Learn step-by-step procedures to write an explicit CFD solver based on final difference methods with staggered grid allocations and boundary fitted coordinates. We will discuss the derivation of the mathematical model, discretization of the model equations, development of the algorithms, and parallelization and visualization of the computed data using OpenCL and OpenGL. Compares case studies of natural convection, driven cavity, scaling analysis, and magneto-thermal convection computed using CSIRO''s CPU/GPU supercomputer cluster to known analytical and experimental solutions.  Back

Learn about optimization efforts in G4CU, a CUDA Monte Carlo code for radiation therapy. G4CU is based on the core algorithm and physics processes in Geant4, a toolkit for simulating particles traveling through and interacting with matter. The techniques covered will include the use of texture references for look-up tables, device configuration for different simulation components, and scheduling of work for different particle types.  Back

Graphics Processing Units (GPUs) are an increasingly popular platform upon which to deploy lattice quantum chromodynamics calculations. While there has been much progress to date in developing solver algorithms to improve strong scaling on such platforms, there has been less focus on deploying 'mathematically optimal' algorithms. A good example of this are hierarchical solver algorithms such as adaptive multigrid, which are known to solve the Dirac operator with optimal O(N) complexity. We describe progress to date in deploying adaptive multigrid solver algorithms to NVIDIA GPU architectures and discuss in general the suitability of heterogeneous architectures for hierarchical algorithms.  Back

GPU-calculations is modern, effective, and fastest way for "ab-initio" mathematical modeling of nanostructures, and, in particular, a properties of nanostructures. This article consist some results of ab-initio research for hardness properties of several stable binary compounds. It is a combinations of Al, Si, Mg, Cu, and Fe in "fcc", "nacl", "cu2mg", "mgcu2", "zns", "caf2", "cscl", "alfe3", and other structures (B1, B2, B3, C1, C15, A15, D03, L12, ...). We find an equilibrium volumes, elastic moduli, and total energy per atom for most stable compounds and compare this ab-initio simulations and experimental data. Also we estimated a increase of performance coefficient, for GPU-calculations with CUDA technology. All calculations performed on GPAW and Abinit software, based on DFT, and their GPU-versions.  Back

Learn how to build a 3D solver for the groundwater flow equation that is accelerated by the GPU. The underlying mathematical model treats the entire subsurface, both saturated and unsaturated, as a whole. The governing nonlinear, time dependent, parabolic partial differential equation is discretized into 19 million nodes. The resulting K20-based GPU solver is 20 times faster than the original single CPU Fortran code.  Back

This talk will demonstrate an implementation of the Total Lagrangian Explicit Dynamic finite element formulation in CUDA. As this method was originally developed for very soft tissues, it is in full compliance to geometric, material and loading nonlinearities and achieves significant speedups over industry-proven solutions while retaining accuracy. Intricacies of parallel TLED implementation and comparisons to conventional FE codes are provided as well as a short introduction into the background of this numerical tool. Learn the details and benefits of mathematically reformulating an FE problem towards parallelization and subsequently implementing/optimizing the algorithm in CUDA.

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The goal of this session is to show how to create geometric shapes in GPUs, by taking advantage of GPU's tessellation feature, using the state of the art spline technique called PSP splines (PSPS). PSPS are simpler than B-splines in its mathematical form, but are much more powerful than NURBS in geometric design. Compared with Bezier, B-spline, NURBS, design a geometric shape using PSPS is much more efficient, flexible and more intuitive. In this session we will describe what PSPS are and demonstrate how to directly implement PSPS in GLSL or HLSL in the tessellation stages to create new geometries.   Back

This work concerns the parallel implementation of 3D mapping algorithm. Several nearest neighborhood search strategies are compared. The accuracy of final 3D mapping is evaluated with geodetic precision. This work can be used in several applications such as mobile robotics and spatial design. Attendees will learn how to choose proper nearest neighbors search strategy for 3D data registration, how to build accurate 3D maps, how to evaluate 3D mapping system with geodetic precision and what the influence of parallel programming is to performance and accuracy.  Back

RISE - Risky Intervention and Surveillance Environment is very de- manding task. In presentation three areas of research are shown such as 3D data registration, robot navigation and 3D cloud of points processing. The approach based on robust KNN nearest neighborhood search applied for improvement of ICP algorithm is shown. The path planning parallel approach based on wave propagation method is shown. On line segmentation of 3D cloud of points based on normal vector computation is given. The set of proposed algorithms where tested on GPGPU NVIDIA CUDA GF 580, the results are satisfying.

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Hausdorff distance is a widely used metric in visual computing for comparing images, finding patterns, and performing registrations. We propose two parallel algorithms for computing the Hausdorff distance using morphological dilations on the GPU. The algorithms require block synchronization and both the CPU-based and GPU-based block synchronizations were evaluated. Furthermore, we compare the efficiency of the proposed algorithms to implementations on the CPU and GPU regarding distinct programming languages, including C++, Java, and the Aparapi library. Experimental results have shown that the CUDA GPU-based synchronized algorithm provided the best results and was approximately 26 and 6630 times faster than the CPU for large binary and grey images, respectively.  Back

Mathematical models describing cellular membranes form the basis of whole tissue models to describe the electrical activity of entire organs, such as the heart. Numerical simulations based on these models are useful for both basic science and increasingly for clinical diagnostic and therapeutic applications such as targeting ablation therapy for atrial arrhythmias, defibrillator design and cardiac resynchronization therapy. A common bottleneck in such simulations arises from solving large stiff systems of ordinary differential equations (ODEs) thousands of times for numerous integration points (representing cells) throughout a three-dimensional tissue or organ model. For some electrophysiology simulations, over 80% of the time is spent solving these systems of ODEs. While a cluster provides the required interactive response time to solve the ODEs, a desktop sized platform would enhance usability of the software in a laboratory setting. The audience will benefit by learning how a real-world, complex, HPC application can directly benefit by the use of CUDA technology. Participants will learn which optimization techniques yielded the best performance results on an actual application. We will also explore the benefits and limits of the use of single precision in certain scientific applications.  Back

Zaxtar is the highest performance video server that will feed up to 4GB/sec of video data to 4K projectors or 4K displays. This performance is accomplished by utilizing CPU, GPU and synchronization of multiple computers. The most important feature is mathematically lossless compression, which can compress video or graphics data at the ratio of 3 to 1 without losing any information. Mathematically lossless compression has been achieved by CPU up until now, but we have ported the algorithm to Quadro FX 5800.

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A fast way of developing, prototyping and deploying numerical algorithms that can take advantage of CUDA capable systems is available in Mathematica 8. Over the past year, educators, scientists, and business users have taken advantage of the benefits that the support of GPU programming in Mathematica. By integrating and implementing CUDA/OpenCL in their programs, users make use of a hybrid approach, combining the speed-up that GPUs offer and a powerful numerical development system. In this presentation several examples describing numerical applications ranging from deconvolution of MRI imaging, linear solvers for FEM, systems of ODEs, line integral convolution visualization are presented.

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Mathematical methods based on the use of the Laplace transform are a standard component of undergraduate education. Real world problems however often yield Laplace space solutions which are too complex to be analytically inverted to expressions in physically meaningful variables. A robust numerical inversion approach is thus desirable. In this talk, I present one of the approaches to compute an approximate inverse, the Weeks method. I will also discuss the difficulties in performing numerical inversion. Finally, I will show how we have been able to utilize Jacket from AccelerEyes in MATLAB to more efficiently and robustly implement the Weeks method.

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We present an investigation into the emergent mathematical behavior of computational operations which are performed efficiently on massively multi-core architectures. This novel perspective for computationally solving mathematical equations is designed from the ground up for efficient implementation on massively multi-core architectures. In this session, we present one of our alogithms which randomly generates a large number of sparse domain discretizations of a Partial Differential Equation. The statistical moments of the ultra-sparse-grid solutions suggest optimal locations for gridpoints. We will apply this algorithm to Poisson and Hamilton-Jacobi steady state equations and provide preliminary analytical results.

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Learn about the fast multipole method (FMM) and its optimization on NVIDIA GPUs. The FMM is a well-known algorithm with a variety of applications in areas like galaxy simulation, electrostatic potential calculations, boundary element methods, integral equations, dislocations dynamics, etc. The FMM offers several difficulties when running on parallel heterogeneous platforms such as multicore processors with GPUs. Some parts of the calculation suffer from limited concurrency, and load-balancing can be very uneven for certain distributions of particles. We will present a new API and runtime system, called StarPU, that allows expressing a calculation as a graph of tasks, with dependencies, and contains a runtime system that can optimally schedule those tasks on a parallel machine. StarPU supports conventional multicore processors as well as NVIDIA GPUs. Authors: Emmanuel Agullo, Bérenger Bramas, Olivier Coulaud, Matthias Messner, (INRIA Bordeaux - Sud-Ouest / LaBRI, Talence, France). Eric Darve, (Stanford Institute for Computational and Mathematical Engineering). Toru Takahashi, (Department of Mechanical Science and Engineering, Nagoya University, Nagoya, Japan).

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Learn how to perform efficient dense rectangular matrix transposition in place on the GPU. Transposition (full and tiled) has been an important building block in many GPU-accelerated algorithms for better memory access patterns. However, out-of-place transposition, while simple in nature, may be prohibitive due to large spatial overhead for applications with large datasets. This talk presents the techniques on in-place matrix transposition, and the audience will also learn how to use our in-place transposition library with examples given in CUDA, MATLAB, and Mathematica CUDA bindings.

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Learn how to mitigate rounding errors that can hamper result reproducibility when concurrent executions burst and workflow determinism vanishes. This talk unveils the power of mathematical methods to model rounding-errors in scientific applications and illustrates how these methods can mitigate error drifting on new generation, many-core GPUs. We will discuss performance and accuracy issues for a diverse set of scientific applications that rely on floating point arithmetic. In particular, our experimental study will cover the following exploration space: floating point format and precision (e.g., single, double, and composite precision), numerical range used by the computation, degree of multi-threading, thread scheduling scheme, and algorithmic variant.  Back

GPUs can push teraflops of mathematical power, but feeding the SMs with data can often be harder than optimising your algorithm. A well-designed program must take into account both access of data from within the GPU as well as allocation and transfer of data between CPU and GPU. This talk will cover techniques including sub-allocation, shared memory management, and parallel memory structures such as stacks, queues and ring-buffers which can greatly improve the throughput of your algorithms. 75% of programs are limited by memory bandwidth and not compute power, so careful memory management is critical to a high-performance program.  Back

Mathematica is widely used in scientific, engineering, mathematical fields and education. In this session, new tools for general GPU programming in the next release of Mathematica are presented. These tools build on top of Mathematica's technology which provides a simple, yet powerful, interface to the large base of compiling tools. Applications of CUDA and OpenCL from within Mathematica will be presented. These examples will provide a general overview of the powerful development environment for GPU programming that Mathematica can offer not just for researchers but for anybody with basic knowledge of Mathematica and GPU programming.  Back

As GPU hardware becomes more prevalent in both research and commercial institutions, software that takes advantage of this specialized hardware is growing in demand. In many cases, it is infeasible or impossible to rewrite an existing program to run entirely on the GPU, so the goal is often to offload as much work as possible. As the IMSL Library team at Rogue Wave Software considers how best to tackle the GPU realm with a general mathematical library, the IMSL Fortran Library takes an initial step where the CUDA BLAS library is utilized to offload CPU work to GPU hardware. This presentation will discuss the approach and architecture of the solution. Benchmark results will show where success has been found. Plans for future products will also be covered.  Back

Mathematica comes with many extremely optimized numerical libraries integrated into the application, but they don''t yet take advantage of the GPU. Thankfully, Mathematica provides an easy to use API for communicating between a large variety of external resources, called MathLink. This tutorial will provide a hands-on introduction to start using CUDA within Mathematica, an introduction to the cuda mathematica plugin, as well as the different issues one has to keep in mind when writing MathLink applications using the CUDA Toolkit. Finally we will showcase a few real-world examples.

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Since version 8, Mathematica offers advanced support for GPU acceleration with optimized CUDA functions and a built-in framework for developing scientific CUDA kernel code. In this session, the Wolfram development team will share their experience developing their next-generation CUDA support in Mathematica. From the unique ability of Parallel Nsight to attach its CUDA debugger to a running process, the new parallel Warp Watch for warp-wide variable views and expression evaluation, to the latest runtime CUDA profiling experiments; they will demonstrate how they were able to take advantage of Parallel Nsight to get the most out of CUDA and the GPU.

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This work presents 3D mapping algorithm implemented on Tegra K1 device. The data processing pipeline is implemented in parallel using CUDA. The performance and accuracy of the final model were compared to the mobile and desktop GPU results. This work shows how to replace traditional CUDA-enabled laptops with embedded Tegra K1. Attendees will learn about the problems and challenges of embedding parallel 3D mapping algorithm and how to improve its speed.  Back

Visuvi develops targeted visual search engine solutions for a wide range of vertical applications in medicine, ecommerce and general-purpose visual search and maintains an index of images on the Internet. Visuvi has patent pending technology fort it's search engine that examines the content and patterns within an image, categorizes that information via mathematical indexing and delivers search results based on the image itself - no text or meta-tags required. Visuvi Inc. is a privately held company based in Redwood City, CA and is managed by a seasoned executive team consisting of Christopher Boone, President and CEO, Alexander Valenica, Chief Scientist and Co-Founder, Florian Brody, VP Marketing and Yuri Drozd, VP Product Management.

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With the introduction of GPU support in version 8, Mathematica has become an excellent environment for integrating CUDA with high level code for interpretation or visualization. In this presentation, we will show the usefulness of Mathematica in the venue of computational finance. In addition to demonstrating the GPU-accelerated financial computations which can be readily performed within Mathematica, we will show that these calculations can easily be integrated with third-party data sources including Microsoft Excel and databases. Furthermore, we will cover the UnRisk Mathematica package written by MathConsult, which seamlessly adds GPU-accelerated complex model calibration algorithms to Mathematica's repertoire.

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Learn how a rapidly growing mid-sized financial company incorporated GPU computing into its quantitative finance models. Our quantitative development team faced two major obstacles in adopting GPU computing. The first obstacle is the large cost of switching away from our mature .NET development process. The other obstacle arises from the difficulty of synchronizing a slow hardware purchasing cycle with a fast software delivery cycle. We addressed these concerns by creating a hybrid linear algebra library in .NET that dynamically switches to GPU computing when CUDA hardware is available. This library allows our developers to code in .NET and focus on the mathematical and financial models without worrying about CUDA syntax. In this session we will describe how we built the library in .NET using CUBLAS, CURAND, and CUDA Runtime libraries. We will also show the performance gains from switching to GPU computing in pricing Bermudan swaptions using the Libor Market Model.  Back

This work concerns the development of training and support system for SAR missions based on NVIDIA GRID technology. The architecture of cloud system will be discussed. This system can be deployed in the disaster zone as Mobile Data Centre and in typical Data Centre. We developed software tools for registration and gathering robotic data (3D cloud of points) into the common coordinate system. The rendering of 3D data is accessible via SaaS (Software as a Service) model. This software is dedicated for SAR teams working with modern UAV (Unmanned Aerial Vehicles) and UGV (Unmanned Ground Vehicles). GRID technology helps with integration of many data sources and visualisation over Ethernet. Training system is using these 3D maps as reference training area for rigid body simulation of robots.  Back

Get the latest development in Next Generation Knowledge Based Engineering (KBE) software which provides real results over the traditional design approach. Today there exist numerous KBE applications in the field of vehicle ergonomics, suspension, NVH, safety, regulations etc which deal with huge number of iterations and mathematical algorithm. With GPU computing and CUDA the KBE kernel is restructured to incorporate parallel programming model which helps the applications run faster and achieving time reduction from hours to seconds. KBE geometry kernel also gets benefited by enabling CUDA in topology based operations which take lot of time when performed on CPU.

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In our current work, we present the first massively parallel, GPU accelerated implementation of the Cube Calculus operations for multivalued and binary logic, also called Cube Calculus Machine (CCM). Substantial speedups upto the order of 85x are achieved using the CUDA enabled nVIDIA Tesla GPU compared to the CPU implementation on a sequential processor.CC is a very efficient and convenient mathematical formalism for representation, processing and synthesis of binary and multivalued logic which has significant applications in logic synthesis, image processing and machine learning. Thus, massive speedups achieved using GPUs are very encouraging to build future parallel VLSI EDA systems   Back

This talk describes the recent simulation of ~18,000 proteins in suspension, reproducing the crowding conditions of the cell interior. The simulations were obtained with MUPHY, a computational platform for multi-scale simulations of real-life biofluidic problems. The same software has been used in the past to simulate blood flows through the human coronary arteries and DNA translocation across nanopores. The simulations were performed on the Titan system at the Oak Ridge National Laboratory, and exhibits excellent scalability up to 18, 000 K20X NVIDIA GPUs, reaching 20 Petaflops of aggregate sustained performance with a peak performance of 27.5 Petaflops for the most intensive computing component. In this talk I will describe how the combination of novel mathematical models, computational algorithms, hardware technology and parallelization techniques allowed reproducing for the first time such a massive amount of proteins.  

 

ACM Gordon Bell Finalist

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Learn how GPUs help design major, multimillion-dollar optical instruments for the European Extremely Large Telescope. From the mathematical model up to the high-performance implementation on distributed-memory systems with hardware accelerators, this talk will explain how the resulting dense linear algebra operations associated with an efficient task-based programming model help design the next generation of telescope instruments. 

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What do we need to achieve artificial general intelligence? How do we distribute intelligence over the internet-of-things? We'll dive deep into the heart of the matter, which is machine reasoning. Following recent advances in mathematical foundations and homotopy-type theory, we conclude that the crux is to formally separate intents from implementations. We can teach neural networks to understand these intents and to use a divide-and-conquer method for compiling these intents into implementations. Our goal is to outline a distributed strategy for accomplishing this moonshot.  Back

This session will concentrate on the topic of mission planning for search hand rescue personnel and how CUDA can help in this task. Urban Search and Rescue is a challenging and important activity in current society. The ICARUS project (Integrated Components for Assisted Rescue and Unmanned Search operations) concentrates on aiding these efforts by providing robotic components for rescue teams. Adding mobile robots into the tray rises the need for additional planning effort, which would consume a lot of time using classical approach. We will present how this can be prevented by using CUDA based mission planners for solving tasks like path planning, patrol communication relay location etc. A number of CUDA-implemented algorithms will be shown along with example results.  Back

JPEG2000 is state-of-the-art video compression adopted by all digital cinemas. Besides that, it has become the format of choice for longterm archiving mainly because it significantly saves disk space, provides superior image quality, and it allows for mathematically lossless compression. The recent development in standardization of master video formats (IMF) makes JPEG2000 the emerging video compression for 4K delivery and because of the very high image quality it is being used for broadcast contribution as well. The talk will cover various applications of JPEG2000 in digital video production workflows and it will explain how NVIDIA GPUs enable such workflows with speed sufficient for 4K video processing.  Back

We present BLINK, a language and framework for developing image processing algorithms across a range of computation devices. BLINK-based algorithms are automatically translated to optimised code for both GPUs and CPUs. This "write-once" approach enables us to target both existing and new GPU hardware with minimal extra effort. Many algorithms produce visibly different results if mathematical operations are allowed to differ across platforms. Therefore BLINK has been designed to ensure numerically identical results between NVIDIA GPUs and CPUs. BLINK is at the heart of a number of key Foundry plug-ins and applications. An overview of this work and performance profiles will be presented, highlighting the speed gains achieved by using NVIDIA GPUs.  Back

We implement 3D conebeam computed tomography on a GPU. The implementation takes slices of the target, weighs the projection data and then filters the weighted data to backproject the data and create the final three dimensional construction. This is implemented on a CPU using either Matlab or C and on a heterogeneous system combining CPU and GPU. The relative performance of backprojection is tested and evaluated on a mathematical phantom as well as on mouse data. Speedups of over thirty times using the GPU are seen for phantom data and close to fifty times for the larger mouse datasets.   Back

Learn how to unleash the full power of GPUs on one of the more difficult problems -- preconditioning in sparse solvers -- by using fast N-body methods as a preconditioner. Fast N-body methods have been able to achieve high percentage of the peak performance since the early days of GPU computing. However, its successful applications have been limited to astrophysics and molecular dynamics, where the physics itself is naturally described by a collection of discrete points. Mathematically, there is nothing that prevents the use of fast N-body methods as a solver for a more general class of PDEs. This would not have been a good idea back when Flops were expensive, since it essentially turns the sparse matrix into a dense matrix of the same size, before hierarchically grouping the off-diagonal blocks. But now that Flops are becoming comparatively cheap, the notion of a "compute-bound preconditioner" sounds attractive more than ever. We will demonstrate how competitive such a preconditioner actually is on Kepler.  Back

The goal of this lab is to give a guided tour through the essentials of CUDA parallelization in mathematical finance. We consider pricing a bullet option under LV (Local Volatility) model using either MC (Monte Carlo) or an implicit discretization scheme for PDE (Partial Differential Equation). The considered example is close to a real banking application with an LV model derived from the implicit SVI model of Gatheral & Jacquier using the Andersen & Brotherton-Ratcliffe expression based on Dupire equation. Several optimizations are studied like the judicious memory storage in shared and registers for two discretization scales in MC. Thanks to a simple trick proposed in Abbas-Turki & Graillat, we see also the use of PCR (Parallel Cyclic Reduction) to solve tridiagonal systems of any size.  Back

Visualization on today's GPU technology and at extreme scale requires massive concurrency. The Dax Toolkit is a development framework for designing and using such devices. Learn how to use Dax to execute classic visualization and analysis algorithms on a variety of mesh data structures and adapt the templated toolkit to your own data structures. Also design your own massively-threaded visualization algorithms in a simplified development environment that allows you to focus on the mathematical and algorithmic design. Dax's automatic concept and scheduling mechanisms automatically build parallel scheduling and communication code from signatures using C++.  Back

The analysis of structure in three-dimensional images is increasingly important for biomedical research and computational science. In this poster, we outline ongoing work developing Diderot, a parallel domain-specific language for three-dimensional image visualization and analysis algorithms, such as volume rendering, fiber tractography, and particle systems. Diderot supports a high-level mathematical computation model coupled with a batch-synchronous parallelism model. The poster further describes Diderots GPU implementation and its high performance measurements on GPUs versus other sequential and parallel platforms.

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