Extensional and Intensional Semantics of Bounded and Unbounded Nondeterminism

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that these extensional and intensional representations are equivalent, by showing how to construct the unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may-testing and must-testing denotational semantics for sequential functional languages with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may-testing and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped {\lambda}-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract.

Coherent Parallelization of Universal Classical Computation

Previously, higher-order Hamiltonians (HoH) had been shown to offer an advantage in both metrology and quantum energy storage. Here, we axiomatize a model of computation that allows us to consider such Hamiltonians for the purposes of computation. From this axiomatic model, we formally prove that an HoH-based algorithm can gain up to a quadratic speed-up over classical sequential algorithms—for any possible classical computation. We show how our axiomatic model is grounded in the same physics as that used in HoH-based quantum advantage for metrology and battery charging. Thus we argue that any advance in implementing HoH-based quantum advantage in those scenarios can be co-opted for the purpose of speeding up computation.

Theoretical Investigation of Unconditionally Stable Sequential Algorithms of Coupled Flow and Geomechanics for Hydraulically Fractured Systems

We investigate unconditionally stable sequential algorithms for coupled hydraulically fractured geomechanics and flow systems, which can account for poromechanics behavior within the fractures. We focus on modifying the concepts of the fixed stress and undrained sequential methods properly for the coupled systems by taking appropriate stabilization terms for stability and convergence with energy analyses. Specifically, an apparent fracture stiffness is used for for numerical stabilization. Because this fracture stiffness depends on the fracture length, the stabilization term needs to be updated dynamically, different from the drained bulk modulus used for typical poromechanics problems. For numerical tests, we take the extended finite element method for geomechanics while the piecewise constant finite element method is used for flow within an existing hydraulic fracture. The numerical results support a priori stability analyses.

Parallelism exploration in sequential algorithms via animation tool

Different high performance techniques, such as profiling, tracing, and instrumentation, have been used to tune and enhance the performance of parallel applications. However, these techniques do not show how to explore the potential of parallelism in a given application. Animating and visualizing the execution process of a sequential algorithm provide a thorough understanding of its usage and functionality. In this work, an interactive web-based educational animation tool was developed to assist users in analyzing sequential algorithms to detect parallel regions regardless of the used parallel programming model. The tool simplifies algorithms’ learning, and helps students to analyze programs efficiently. Our statistical t-test study on a sample of students showed a significant improvement in their perception of the mechanism and parallelism of applications and an increase in their willingness to learn algorithms and parallel programming.

Practical Wavelet Tree Construction

We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves. Most of our algorithms are also adapted to the wavelet matrix , a variant that is particularly suited for large alphabets.

A Strategy of Parallel Seed-Based Image Segmentation Algorithms for Handling Massive Image Tiles over the Spark Platform

The volume of remote sensing images continues to grow as image sources become more diversified and with increasing spatial and spectral resolution. The handling of such large-volume datasets, which exceed available CPU memory, in a timely and efficient manner is becoming a challenge for single machines. The distributed cluster provides an effective solution with strong calculation power. There has been an increasing number of big data technologies that have been adopted to deal with large images using mature parallel technology. However, since most commercial big data platforms are not specifically developed for the remote sensing field, two main issues exist in processing large images with big data platforms using a distributed cluster. On the one hand, the quantities and categories of official algorithms used to process remote sensing images in big data platforms are limited compared to large amounts of sequential algorithms. On the other hand, the sequential algorithms employed directly to process large images in parallel over a distributed cluster may lead to incomplete objects in the tile edges and the generation of large communication volumes at the shuffle stage. It is, therefore, necessary to explore the distributed strategy and adapt the sequential algorithms over the distributed cluster. In this research, we employed two seed-based image segmentation algorithms to construct a distributed strategy based on the Spark platform. The proposed strategy focuses on modifying the incomplete objects by processing border areas and reducing the communication volume to a reasonable size by limiting the auxiliary bands and the buffer size to a small range during the shuffle stage. We calculated the F-measure and execution time to evaluate the accuracy and execution efficiency. The statistical data reveal that both segmentation algorithms maintained high accuracy, as achieved in the reference image segmented in the sequential way. Moreover, generally the strategy took less execution time compared to significantly larger auxiliary bands and buffer sizes. The proposed strategy can modify incomplete objects, with execution time being twice as fast as the strategies that do not employ communication volume reduction in the distributed cluster.

Comparison of Extragraft Bone Formation after Anterior Cervical Discectomy and Fusion Using Simultaneous and Sequential Algorithms

Extragraft bone formation is crucial for obtaining a successful outcome after spinal fusion surgery. However, the cause of bone formation is not well investigated. In this study, it was hypothesised that extragraft bone formation is generated by mechanical stimuli. A preoperative plan for anterior cervical discectomy and fusion was applied to the finite element model of the C5–C6 motion segment. Extragraft bone formations posterior to the interbody cage were simulated using simultaneous and sequential algorithms. While the simultaneous algorithm predicted the formation of extragraft bone bridging under flexion and extension, the bridge was generated only under extension with the sequential algorithm. This was caused by an ill-defined design space in cases where the simultaneous algorithm was used. Our results using the sequential algorithm show how the progress of extragraft bone formation affects spine mechanics, and our results support the hypothesis that a mechanical stimulus is a major factor influencing extragraft bone formation.

A Behavioural Theory of Recursive Algorithms

“What is an algorithm?” is a fundamental question of computer science. Gurevich’s behavioural theory of sequential algorithms (aka the sequential ASM thesis) gives a partial answer by defining (non-deterministic) sequential algorithms axiomatically, without referring to a particular machine model or programming language, and showing that they are captured by (nondeterministic) sequential Abstract State Machines (nd-seq ASMs). However, recursive algorithms such as mergesort are not covered by this theory, as has been pointed out by Moschovakis, who had independently developed a different framework to mathematically characterize the concept of (in particular recursive) algorithm. In this article we propose an axiomatic definition of the notion of sequential recursive algorithm which extends Gurevich’s axioms for sequential algorithms by a Recursion Postulate and allows us to prove that sequential recursive algorithms are captured by recursive Abstract State Machines, an extension of nd-seq ASMs by a CALL rule. Applying this recursive ASM thesis yields a characterization of sequential recursive algorithms as finitely composed concurrent algorithms all of whose concurrent runs are partial-order runs.

Analisis Kinerja Algoritma Quick Double Merge Sort Paralel Menggunakan openMP

Processor technology currently tends to increase the number of cores more than increasing the clock speed. This development is very useful and becomes an opportunity to improve the performance of sequential algorithms that are only done by one core. This paper discusses the sorting algorithm that is executed in parallel by several logical CPUs or cores using the openMP library. This algorithm is named QDM Sort which is a combination of sequential quick sort algorithm and double merge algorithm. This study uses a data parallelism approach to design parallel algorithms from sequential algorithms. The data used in this study are the data that have not been sorted and also the data that has been sorted is integer type which is stored in advance in a file. The parameter measured to determine the performance of the QDM Sort algorithm is speedup. In a condition where a large amount of data is above 4096 and the number of threads in QDM Sort is the same as the number of logical CPUs, the QDM Sort algorithm has a better speedup compared to the other parallel sorting algorithms discussed in this study. For small amounts of data it is still better to use sequential sorting algorithm.