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Mathematics
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Supercomputing and Mathematics
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Supercomputing and Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 May 2020) | Viewed by 22625

Special Issue Editors

Prof. Dr. Jordi Garcia

E-Mail Website
Guest Editor
Advanced Network Architectures Lab (CRAAX), Department of Computer Architecture, Universitat Politècnica de Catalunya (UPC BarcelonaTech), 08800 Vilanova i la Geltrú, Spain
Interests: smart cities; smart scenarios; cloud computing; edge computing; resources management; data management
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ramon Canal

E-Mail Website
Guest Editor
Departament d'Arquitectura de Computadors,Universitat Politècnica de Catalunyac/ Jordi Girona 1-3, Mòdul C6-107 08034 Barcelona, Spain
Interests: variation-aware architectures; low-power single/multicore architectures

Special Issue Information

Dear Colleagues,

The journal of Mathematics provides a forum to discuss recent research in the areas of pure and applied mathematics. With this Special Issue, the journal recognizes the importance of mathematics in the development of supercomputing systems, as well as the importance of supercomputing in the advancement of mathematical sciences.

Supercomputing is the science of efficiently solving extremely complex and computing intensive applications. Supercomputers enable high performance problem solving and deep data analysis, which are not feasible with standard computing technology, and can be useful for tackling big scientific problems, engineering simulations, and artificial intelligence algorithms.

This Special Issue gives an opportunity to researchers and developers from academia and industry involved in the areas of high performance and supercomputing systems, and where mathematics contributes in a significant way, to communicate their ideas and advances in this rapidly changing interdisciplinary field.

We invite you to submit papers in the research areas, including, but not limited to, the following topics:

  • Supercomputing applications
  • Mathematical complex models solving
  • Parallel algorithms for simulation
  • Big data processing merging with supercomputing
  • Machine learning and machine intelligence
  • Optimization models and systems
  • Models for performance evaluation and performance estimation
  • Numerical solutions to complex systems
  • Any other topic that combines the use of mathematics with the supercomputing

Prof. Dr. Jordi Garcia
Prof. Ramon Canal
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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.

Published Papers (7 papers)

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Research

21 pages, 3006 KiB  
Article
On the Use of Probabilistic Worst-Case Execution Time Estimation for Parallel Applications in High Performance Systems
by Matteo Fusi, Fabio Mazzocchetti, Albert Farres, Leonidas Kosmidis, Ramon Canal, Francisco J. Cazorla and Jaume Abella
Mathematics 2020, 8(3), 314; https://0-doi-org.brum.beds.ac.uk/10.3390/math8030314 - 1 Mar 2020
Cited by 4 | Viewed by 2874
Abstract
Some high performance computing (HPC) applications exhibit increasing real-time requirements, which call for effective means to predict their high execution times distribution. This is a new challenge for HPC applications but a well-known problem for real-time embedded applications where solutions already exist, although [...] Read more.
Some high performance computing (HPC) applications exhibit increasing real-time requirements, which call for effective means to predict their high execution times distribution. This is a new challenge for HPC applications but a well-known problem for real-time embedded applications where solutions already exist, although they target low-performance systems running single-threaded applications. In this paper, we show how some performance validation and measurement-based practices for real-time execution time prediction can be leveraged in the context of HPC applications on high-performance platforms, thus enabling reliable means to obtain real-time guarantees for those applications. In particular, the proposed methodology uses coordinately techniques that randomly explore potential timing behavior of the application together with Extreme Value Theory (EVT) to predict rare (and high) execution times to, eventually, derive probabilistic Worst-Case Execution Time (pWCET) curves. We demonstrate the effectiveness of this approach for an acoustic wave inversion application used for geophysical exploration. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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14 pages, 588 KiB  
Article
Detecting the Proportion of Traders in the Stock Market: An Agent-Based Approach
by Minh Tran, Thanh Duong, Duc Pham-Hi and Marc Bui
Mathematics 2020, 8(2), 198; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020198 - 5 Feb 2020
Cited by 3 | Viewed by 2798
Abstract
In this research, an agent-based model (ABM) of the stock market is constructed to detect the proportion of different types of traders. We model a simple stock market which has three different types of traders: noise traders, fundamental traders, and technical traders, trading [...] Read more.
In this research, an agent-based model (ABM) of the stock market is constructed to detect the proportion of different types of traders. We model a simple stock market which has three different types of traders: noise traders, fundamental traders, and technical traders, trading a single asset. Bayesian optimization is used to tune the hyperparameters of the strategies of traders as well as of the stock market. The experimental results on Bayesian calibration with the Kolmogorov–Smirnov (KS) test demonstrated that the proposed separate calibrations reduced simulation error, with plausible estimated parameters. With empirical data of the Dow Jones Industrial Average (DJIA) index, we found that fundamental traders account for 9%–11% of all traders in the stock market. The statistical analysis of simulated data can produce the important stylized facts in real stock markets, such as the leptokurtosis, the heavy tail of the returns, and volatility clustering. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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12 pages, 981 KiB  
Article
Truth-Teller–Liar Puzzles with Self-Reference
by Laith Alzboon and Benedek Nagy
Mathematics 2020, 8(2), 190; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020190 - 4 Feb 2020
Cited by 4 | Viewed by 5634
Abstract
In this paper, we use commonsense reasoning and graph representation to study logical puzzles with three types of people. Strong Truth-Tellers say only true atomic statements, Strong Liars say only false atomic statements, and Strong Crazy people say only self-contradicting statements. Self-contradicting statements [...] Read more.
In this paper, we use commonsense reasoning and graph representation to study logical puzzles with three types of people. Strong Truth-Tellers say only true atomic statements, Strong Liars say only false atomic statements, and Strong Crazy people say only self-contradicting statements. Self-contradicting statements are connected to the Liar paradox, i.e., no Truth-Teller or a Liar could say “I am a Liar”. A puzzle is clear if it only contains its given statements to solve it, and a puzzle is good if it has exactly one solution. It is known that there is no clear and good Strong Truth-Teller–Strong Liar (also called SS) puzzle. However, as we prove here, there are good and clear Strong Truth-Teller, Strong Liar and Strong Crazy puzzles (SSS-puzzles). The newly investigated type ‘Crazy’ drastically changes the scenario. Some properties of the new types of puzzles are analyzed, and some statistics are also given. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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23 pages, 688 KiB  
Article
Ideal and Predictable Hit Ratio for Matrix Transposition in Data Caches
by Alba Pedro-Zapater, Clemente Rodríguez, Juan Segarra, Rubén Gran Tejero and Víctor Viñals-Yúfera
Mathematics 2020, 8(2), 184; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020184 - 3 Feb 2020
Cited by 3 | Viewed by 3411
Abstract
Matrix transposition is a fundamental operation, but it may present a very low and hardly predictable data cache hit ratio for large matrices. Safe (worst-case) hit ratio predictability is required in real-time systems. In this paper, we obtain the relations among the cache [...] Read more.
Matrix transposition is a fundamental operation, but it may present a very low and hardly predictable data cache hit ratio for large matrices. Safe (worst-case) hit ratio predictability is required in real-time systems. In this paper, we obtain the relations among the cache parameters that guarantee the ideal (predictable) data hit ratio assuming a Least-Recently-Used (LRU) data cache. Considering our analytical assessments, we compare a tiling matrix transposition to a cache oblivious algorithm, modified with phantom padding to improve its data hit ratio. Our results show that, with an adequate tile size, the tiling version results in an equal or better data hit ratio. We also analyze the energy consumption and execution time of matrix transposition on real hardware with pseudo-LRU (PLRU) caches. Our analytical hit/miss assessment enables the usage of a data cache for matrix transposition in real-time systems, since the number of misses in the worst case is bound. In general and high-performance computation, our analysis enables us to restrict the cache resources devoted to matrix transposition with no negative impact, in order to reduce both the energy consumption and the pollution to other computations. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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16 pages, 396 KiB  
Article
Algorithms for Instance Retrieval and Realization in Fuzzy Ontologies
by Ignacio Huitzil, Jorge Bernad and Fernando Bobillo
Mathematics 2020, 8(2), 154; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020154 - 22 Jan 2020
Cited by 3 | Viewed by 1936
Abstract
Fuzzy description logics, the formalism behind fuzzy ontologies, are an important mathematical method with applications in many artificial intelligence scenarios. This paper proposes the first specific algorithms to solve two reasoning tasks with respect to a fuzzy ontology: the instance retrieval and the [...] Read more.
Fuzzy description logics, the formalism behind fuzzy ontologies, are an important mathematical method with applications in many artificial intelligence scenarios. This paper proposes the first specific algorithms to solve two reasoning tasks with respect to a fuzzy ontology: the instance retrieval and the realization problem. Our algorithms are based on a reduction of the number of optimization problems to solve by merging some of them. Our experimental evaluation shows that the novel algorithm to solve the instance retrieval outperforms the previous algorithm, and that in practice it is common to be able to solve a single optimization problem. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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7 pages, 389 KiB  
Article
A New Record of Graph Enumeration Enabled by Parallel Processing
by Zhipeng Xu, Xiaolong Huang, Fabian Jimenez and Yuefan Deng
Mathematics 2019, 7(12), 1214; https://0-doi-org.brum.beds.ac.uk/10.3390/math7121214 - 10 Dec 2019
Cited by 7 | Viewed by 2676
Abstract
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in the Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular graphs of order 23 as 429,668,180,677,439, [...] Read more.
Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in the Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular graphs of order 23 as 429,668,180,677,439, while discovering several regular graphs with minimum average shortest path lengths (ASPL) that can be used as interconnection networks for parallel computers. The enumeration of 4-regular graphs and the discovery of minimal-ASPL graphs are extremely time consuming. We accomplish them by adapting GENREG, a classical regular graph generator, to three supercomputers with thousands of processor cores. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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18 pages, 891 KiB  
Article
Non-Stationary Acceleration Strategies for PageRank Computing
by Héctor Migallón, Violeta Migallón and José Penadés
Mathematics 2019, 7(10), 911; https://0-doi-org.brum.beds.ac.uk/10.3390/math7100911 - 1 Oct 2019
Cited by 1 | Viewed by 2115
Abstract
In this work, a non-stationary technique based on the Power method for accelerating the parallel computation of the PageRank vector is proposed and its theoretical convergence analyzed. This iterative non-stationary model, which uses the eigenvector formulation of the PageRank problem, reduces the needed [...] Read more.
In this work, a non-stationary technique based on the Power method for accelerating the parallel computation of the PageRank vector is proposed and its theoretical convergence analyzed. This iterative non-stationary model, which uses the eigenvector formulation of the PageRank problem, reduces the needed computations for obtaining the PageRank vector by eliminating synchronization points among processes, in such a way that, at each iteration of the Power method, the block of iterate vector assigned to each process can be locally updated more than once, before performing a global synchronization. The parallel implementation of several strategies combining this novel non-stationary approach and the extrapolation methods has been developed using hybrid MPI/OpenMP programming. The experiments have been carried out on a cluster made up of 12 nodes, each one equipped with two Intel Xeon hexacore processors. The behaviour of the proposed parallel algorithms has been studied with realistic datasets, highlighting their performance compared with other parallel techniques for solving the PageRank problem. Concretely, the experimental results show a time reduction of up to 58.4 % in relation to the parallel Power method, when a small number of local updates is performed before each global synchronization, outperforming both the two-stage algorithms and the extrapolation algorithms, more sharply as the number of processes increases. Full article
(This article belongs to the Special Issue Supercomputing and Mathematics)
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