Universal lossless source coding with the Burrows Wheeler transform

The Burrows Wheeler transform (1994) is a reversible sequence transformation used in a variety of practical lossless source-coding algorithms. In each, the BWT is followed by a lossless source code that attempts to exploit the natural ordering of the BWT coefficients. BWT-based compression schemes are widely touted as low-complexity algorithms giving lossless coding rates better than those of the Ziv-Lempel codes (commonly known as LZ'77 and LZ'78) and almost as good as those achieved by prediction by partial matching (PPM) algorithms. To date, the coding performance claims have been made primarily on the basis of experimental results. This work gives a theoretical evaluation of BWT-based coding. The main results of this theoretical evaluation include: (1) statistical characterizations of the BWT output on both finite strings and sequences of length n → ∞, (2) a variety of very simple new techniques for BWT-based lossless source coding, and (3) proofs of the universality and bounds on the rates of convergence of both new and existing BWT-based codes for finite-memory and stationary ergodic sources. The end result is a theoretical justification and validation of the experimentally derived conclusions: BWT-based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in Ziv-Lempel style codes and, for some BWT-based codes, within a constant factor of the optimal rate of convergence for finite-memory source

Heuristic Spike Sorting Tuner (HSST), a framework to determine optimal parameter selection for a generic spike sorting algorithm

Extracellular microelectrodes frequently record neural activity from more than one neuron in the vicinity of the electrode. The process of labeling each recorded spike waveform with the identity of its source neuron is called spike sorting and is often approached from an abstracted statistical perspective. However, these approaches do not consider neurophysiological realities and may ignore important features that could improve the accuracy of these methods. Further, standard algorithms typically require selection of at least one free parameter, which can have significant effects on the quality of the output. We describe a Heuristic Spike Sorting Tuner (HSST) that determines the optimal choice of the free parameters for a given spike sorting algorithm based on the neurophysiological qualification of unit isolation and signal discrimination. A set of heuristic metrics are used to score the output of a spike sorting algorithm over a range of free parameters resulting in optimal sorting quality. We demonstrate that these metrics can be used to tune parameters in several spike sorting algorithms. The HSST algorithm shows robustness to variations in signal to noise ratio, number and relative size of units per channel. Moreover, the HSST algorithm is computationally efficient, operates unsupervised, and is parallelizable for batch processing

Parallel resampling in the particle filter

Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle filter, or more generally Sequential Monte Carlo (SMC), which are increasingly used in statistical inference. SMC methods carry a set of weighted particles through repeated propagation, weighting and resampling steps. The propagation and weighting steps are straightforward to parallelise, as they require only independent operations on each particle. The resampling step is more difficult, as standard schemes require a collective operation, such as a sum, across particle weights. Focusing on this resampling step, we analyse two alternative schemes that do not involve a collective operation (Metropolis and rejection resamplers), and compare them to standard schemes (multinomial, stratified and systematic resamplers). We find that, in certain circumstances, the alternative resamplers can perform significantly faster on a GPU, and to a lesser extent on a CPU, than the standard approaches. Moreover, in single precision, the standard approaches are numerically biased for upwards of hundreds of thousands of particles, while the alternatives are not. This is particularly important given greater single- than double-precision throughput on modern devices, and the consequent temptation to use single precision with a greater number of particles. Finally, we provide auxiliary functions useful for implementation, such as for the permutation of ancestry vectors to enable in-place propagation.Comment: 21 pages, 6 figure

A sparse octree gravitational N-body code that runs entirely on the GPU processor

We present parallel algorithms for constructing and traversing sparse octrees on graphics processing units (GPUs). The algorithms are based on parallel-scan and sort methods. To test the performance and feasibility, we implemented them in CUDA in the form of a gravitational tree-code which completely runs on the GPU.(The code is publicly available at: http://castle.strw.leidenuniv.nl/software.html) The tree construction and traverse algorithms are portable to many-core devices which have support for CUDA or OpenCL programming languages. The gravitational tree-code outperforms tuned CPU code during the tree-construction and shows a performance improvement of more than a factor 20 overall, resulting in a processing rate of more than 2.8 million particles per second.Comment: Accepted version. Published in Journal of Computational Physics. 35 pages, 12 figures, single colum

Reordering Rows for Better Compression: Beyond the Lexicographic Order

Sorting database tables before compressing them improves the compression rate. Can we do better than the lexicographical order? For minimizing the number of runs in a run-length encoding compression scheme, the best approaches to row-ordering are derived from traveling salesman heuristics, although there is a significant trade-off between running time and compression. A new heuristic, Multiple Lists, which is a variant on Nearest Neighbor that trades off compression for a major running-time speedup, is a good option for very large tables. However, for some compression schemes, it is more important to generate long runs rather than few runs. For this case, another novel heuristic, Vortex, is promising. We find that we can improve run-length encoding up to a factor of 3 whereas we can improve prefix coding by up to 80%: these gains are on top of the gains due to lexicographically sorting the table. We prove that the new row reordering is optimal (within 10%) at minimizing the runs of identical values within columns, in a few cases.Comment: to appear in ACM TOD

Mechanistic modeling of architectural vulnerability factor

Reliability to soft errors is a significant design challenge in modern microprocessors owing to an exponential increase in the number of transistors on chip and the reduction in operating voltages with each process generation. Architectural Vulnerability Factor (AVF) modeling using microarchitectural simulators enables architects to make informed performance, power, and reliability tradeoffs. However, such simulators are time-consuming and do not reveal the microarchitectural mechanisms that influence AVF. In this article, we present an accurate first-order mechanistic analytical model to compute AVF, developed using the first principles of an out-of-order superscalar execution. This model provides insight into the fundamental interactions between the workload and microarchitecture that together influence AVF. We use the model to perform design space exploration, parametric sweeps, and workload characterization for AVF