Advances in Mathematical Methods and Applications for High-Performance Computing

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (20 May 2024) | Viewed by 3715

Special Issue Editor


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Guest Editor
School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Interests: cloud computing; edge computing; Internet of Things; cyber–physical systems; optimization

Special Issue Information

Dear Colleagues,

High-performance computing (HPC) in general refers to the practice of processing large-scale data and performing complex calculations with high computational efficiency. This term is most commonly associated with computing as used for scientific research or computational science. High-performance computing has also found applications in business such as in data warehouses, line-of-business applications, and transaction processing. The aim of this Special Issue is to explore the connections between mathematical modeling, computational methods, and high-performance computing, and how recent developments in these areas can help to solve complex problems in scientific and engineering applications. This Special Issue is expected to provide a platform for researchers and practitioners from academia and industry to present their state-of-the-art research results covering the design, implementation, and evaluation of advanced mathematical methods for a variety of high-performance computing platforms.

We invite researchers working in this area of the field to submit papers related to mathematical methods and applications for high-performance computing. Potential topics of interest include, but are not limited to: the application of mathematical methods in high-performance computing technologies, such as multicore, graphics processing units, field-programmable gate array, as well as clouds, clusters, and grids; advanced optimization methods and applications for exploiting the capacity of high-performance computing; the modification of well-known mathematical methods on HPC platforms to reduce computational complexity.

Prof. Dr. Jin Sun
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • high-performance computing
  • compute-intensive applications
  • cloud and edge computing
  • cluster and grid computing
  • multicore computing
  • GPU computing
  • heterogeneous computing

Published Papers (3 papers)

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Research

11 pages, 799 KiB  
Article
Interpretable Model-Agnostic Explanations Based on Feature Relationships for High-Performance Computing
by Zhouyuan Chen, Zhichao Lian and Zhe Xu
Axioms 2023, 12(10), 997; https://doi.org/10.3390/axioms12100997 - 23 Oct 2023
Viewed by 971
Abstract
In the explainable artificial intelligence (XAI) field, an algorithm or a tool can help people understand how a model makes a decision. And this can help to select important features to reduce computational costs to realize high-performance computing. But existing methods are usually [...] Read more.
In the explainable artificial intelligence (XAI) field, an algorithm or a tool can help people understand how a model makes a decision. And this can help to select important features to reduce computational costs to realize high-performance computing. But existing methods are usually used to visualize important features or highlight active neurons, and few of them show the importance of relationships between features. In recent years, some methods based on a white-box approach have taken relationships between features into account, but most of them can only work on some specific models. Although methods based on a black-box approach can solve the above problems, most of them can only be applied to tabular data or text data instead of image data. To solve these problems, we propose a local interpretable model-agnostic explanation approach based on feature relationships. This approach combines the relationships between features into the interpretation process and then visualizes the interpretation results. Finally, this paper conducts a lot of experiments to evaluate the correctness of relationships between features and evaluates this XAI method in terms of accuracy, fidelity, and consistency. Full article
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15 pages, 2696 KiB  
Article
A Sketch-Based Fine-Grained Proportional Integral Queue Management Method
by Haiting Zhu, Hu Sun, Yixin Jiang, Gaofeng He, Lu Zhang and Yin Lu
Axioms 2023, 12(9), 814; https://doi.org/10.3390/axioms12090814 - 24 Aug 2023
Cited by 1 | Viewed by 803
Abstract
The phenomenon “bufferbloat” occurs when the buffers of the network intermediary nodes fill up, causing long queuing delays. This has a significant negative impact on the quality of service of network applications, particularly those that are sensitive to time delay. Many active queue [...] Read more.
The phenomenon “bufferbloat” occurs when the buffers of the network intermediary nodes fill up, causing long queuing delays. This has a significant negative impact on the quality of service of network applications, particularly those that are sensitive to time delay. Many active queue management (AQM) algorithms have been proposed to overcome this problem. Those AQMs attempt to maintain minimal queuing delays and good throughput by purposefully dropping packets at network intermediary nodes. However, the existing AQM algorithms mostly drop packets randomly based on a certain metric such as queue length or queuing delay, which fails to achieve fine-grained differentiation of data streams. In this paper, we propose a fine-grained sketch-based proportional integral queue management algorithm S-PIE, which uses an additional measurement structure Sketch for packet frequency share judgment based on the existing PIE algorithm for the fine-grained differentiation between data streams and adjust the drop policy for a differentiated packet drop. Experimental results on the NS-3 simulation platform show that the S-PIE algorithm achieves lower average queue length and RTT and higher fairness than PIE, RED, and CoDel algorithms while maintaining a similar throughput performance, maintaining network availability and stability, and improving network quality of service. Full article
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18 pages, 853 KiB  
Article
Application of Polling Scheduling in Mobile Edge Computing
by Xiong Wang, Zhijun Yang and Hongwei Ding
Axioms 2023, 12(7), 709; https://doi.org/10.3390/axioms12070709 - 21 Jul 2023
Cited by 4 | Viewed by 1285
Abstract
With the Internet of Things (IoT) development, there is an increasing demand for multi-service scheduling for Mobile Edge Computing (MEC). We propose using polling for scheduling in edge computing to accommodate multi-service scheduling methods better. Given the complexity of asymmetric polling systems, we [...] Read more.
With the Internet of Things (IoT) development, there is an increasing demand for multi-service scheduling for Mobile Edge Computing (MEC). We propose using polling for scheduling in edge computing to accommodate multi-service scheduling methods better. Given the complexity of asymmetric polling systems, we have used an information-theoretic approach to analyse the model. Firstly, we propose an asymmetric two-level scheduling approach with priority based on a polling scheduling approach. Secondly, the mathematical model of the system in the continuous time state is established by using the embedded Markov chain theory and the probability-generating function. By solving for the probability-generating function’s first-order partial and second-order partial derivatives, we calculate the exact expressions of the average queue length, the average polling period, and the average delay with an approximate analysis of periodic query way. Finally, we design a simulation experiment to verify that our derived parameters are correct. Our proposed model can better differentiate priorities in MEC scheduling and meet the needs of IoT multi-service scheduling. Full article
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