Embedding emergent parts in shape grammars is computationally challenging. The first challenge is the representation of shapes, which needs to enable reinterpretation of parts regardless of the creation history of the shapes. The second challenge is the relevant part searching algorithm that provides an extensive exploration of the design space–time efficiently. In this work, we propose a novel method to solve both problems; we treat shapes as they are and use a parallel particle swarm optimization-based algorithm to compute emergent parts. The execution time of the proposed method is improved substantially by dividing the search space into small parts and carrying out searches in each part concurrently using a graphics processing unit. The experiments show that the proposed implementation detects emergent parts accurately and time efficiently.

Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action functional. Due to the high number of degrees of freedom in multi-dimensional fluid flows, traditional global minimization techniques quickly become prohibitive in their memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamical system is a non-gradient, non-linear partial differential equation, and the forcing is restricted to a limited length scale. We demonstrate the efficiency of the algorithm in terms of performance and memory by computing high resolution instanton field configurations corresponding to viscous shocks for 1D and 2D compressible flows.

The lattice Boltzmann method (LBM) can gain a great amount of performance benefit by taking advantage of graphics processing unit (GPU) computing, and thus, the GPU, or multi-GPU based LBM can be considered as a promising and competent candidate in the study of large-scale fluid flows. However, the multi-GPU based lattice Boltzmann algorithm has not been studied extensively, especially for simulations of flow in complex geometries. In this paper, through coupling with the message passing interface (MPI) technique, we present an implementation of multi-GPU based LBM for fluid flow through porous media as well as some optimization strategies based on the data structure and layout, which can apparently reduce memory access and completely hide the communication time consumption. Then the performance of the algorithm is tested on a one-node cluster equipped with four Tesla C1060 GPU cards where up to 1732 MFLUPS is achieved for the Poiseuille flow and a nearly linear speedup with the number of GPUs is also observed.

With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This paper presents differential equations and solution methods for the functions of the form Q(x) = F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish–Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish–Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of sample space. The avoidance of branching statements is of use in optimal graphics processing unit (GPU) computations as it avoids the effect of branch divergence. We give a branch-free normal quantile that offers performance improvements in a GPU environment while retaining the best precision characteristics of well-known methods. We also offer models with low probability branch divergence. Comparisons of new and existing forms are made on Nvidia GeForce GTX Titan and Tesla C2050 GPUs. We argue that in both single- and double-precisions, the change-of-variables approach offers the most GPU-optimal Gaussian quantile yet, working faster than the Cuda 5.5 built-in function.

Structured illumination fluorescence microscopy is a powerful super-resolution method that is capable of achieving a resolution below 100 nm. Each super-resolution image is computationally constructed from a set of differentially illuminated images. However, real-time application of structured illumination microscopy (SIM) has generally been limited due to the computational overhead needed to generate super-resolution images. Here, we have developed a real-time SIM system that incorporates graphic processing unit (GPU) based in-line parallel processing of raw/differentially illuminated images. By using GPU processing, the system has achieved a 90-fold increase in processing speed compared to performing equivalent operations on a multiprocessor computer—the total throughput of the system is limited by data acquisition speed, but not by image processing. Overall, more than 350 raw images (16-bit depth, 512 × 512 pixels) can be processed per second, resulting in a maximum frame rate of 39 super-resolution images per second. This ultrafast processing capability is used to provide immediate feedback of super-resolution images for real-time display. These developments are increasing the potential for sophisticated super-resolution imaging applications.