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Mathematical Modeling for Parallel and Distributed Processing

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

Deadline for manuscript submissions: closed (1 April 2024) | Viewed by 8701

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Special Issue Editors

Dr. Tian-Yi Li

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Guest Editor

Department of Computer Science, Aalborg University, 9220 Aalborg, Denmark
Interests: spatiotemporal database; distributed optimization; big graph data mining
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Lu Chen

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College of Computer Science, Zhejiang University, Hangzhou 310027, China
Interests: database; big data management; AI interaction with dB technology
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Dr. Peiyuan Guan

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Department of Informatics, University of Oslo, 0316 Oslo, Norway
Interests: edge computing; real-time systems; task scheduling; deep learning; reinforcement learning
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Dr. Lingxiao Yang

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School of Artificial Intelligence, Anhui University, Hefei 230093, China
Interests: deep reinforcement learning; energy management; distributed optimization
Special Issues, Collections and Topics in MDPI journals

Dr. Yushuai Li

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Guest Editor

Department of Informatics, University of Oslo, 0316 Oslo, Norway
Interests: distributed optimization; energy management; machine learning; digitial twin
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Parallel and distributed processing have become increasingly essential for solving computationally intensive tasks. With the exponential growth of data and the increasing availability of CPU cores, efficient parallel and distributed processing solutions have become more desirable. However, despite decades of development, fundamental challenges still exist, such as distributed knowledge discovery for large-scale data, peer-to-peer energy trading under complex system environments, services improvement in intelligent transportation systems, and parallel training in deep learning. Mathematical models can greatly help address these challenges through resource utilization optimization, data mining and analytics, energy consumption minimization, and communication overhead reduction. By incorporating powerful mathematical models into parallel and distributed processing, we can achieve better performance, optimize computation and communication between nodes, and overcome the fundamental challenges that exist in this field.

The main objective of this Special Issue is to showcase innovative research that combines parallel and distributed computing with powerful and smart mathematical methods. We welcome submissions that present the latest developments in distributed optimization, algorithm design, and mathematical modeling, as well as their applications in big data processing, data usability, energy, transportation, aerospace, and 5G/6G. By highlighting the latest advances in these fields, we aim to foster new ideas and collaborations that can address the current challenges and drive further progress in parallel and distributed computing.

Dr. Tian-Yi Li
Prof. Dr. Lu Chen
Dr. Peiyuan Guan
Dr. Lingxiao Yang
Dr. Yushuai Li
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.

Keywords

algebraic digital techniques
distributed computing
parallel processing
algorithm design
mathematical modeling
optimization

Related Special Issue

Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition in Mathematics

Published Papers (10 papers)

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Research

16 pages, 1479 KiB

Open AccessArticle

RNDLP: A Distributed Framework for Supporting Continuous k-Similarity Trajectories Search over Road Network

by Hong Jiang, Sainan Tong, Rui Zhu and Baoze Wei

Mathematics 2024, 12(2), 270; https://doi.org/10.3390/math12020270 - 14 Jan 2024

Viewed by 478

Abstract

Continuous k-similarity trajectories search over a data stream is an important problem in the domain of spatio-temporal databases. Given a set of trajectories

T

and a query trajectory

T_{q}

over road network

G

, the system monitors trajectories within

T

, [...] Read more.

Continuous k-similarity trajectories search over a data stream is an important problem in the domain of spatio-temporal databases. Given a set of trajectories

T

and a query trajectory

T_{q}

over road network

G

, the system monitors trajectories within

T

, reporting k trajectories that are the most similar to

T_{q}

whenever one time unit is passed. Some existing works study k-similarity trajectories search over trajectory data, but they cannot work in a road network environment, especially when the trajectory set scale is large. In this paper, we propose a novel framework named RNDLP (Road Network-based Distance Lower-bound-based Prediction) to support CKTRN over trajectory data. It is a distributed framework based on the following observation. That is, given a trajectory

T_{i}

and the query trajectory

T_{q}

, when we have knowledge of D(

T_{i}

), we can compute the lower-bound and upper-bound distances between

T_{q}

and

T_{i}

, which enables us to predict the scores of trajectories in

T

and employ these predictions to assess the significance of trajectories within

T

. Accordingly, we can form a mathematical model to evaluate the excepted running cost of each trajectory we should spend. Based on the model, we propose a partition algorithm to partition trajectories into a group of servers so as to guarantee that the workload of each server is as the same as possible. In each server, we propose a pair-based algorithm to predict the earliest time

T_{i}

could become a query result, and use the predicted result to organize these trajectories. Our proposed algorithm helps us support query processing via accessing a few points of a small number of trajectories whenever trajectories are updated. Finally, we conduct extensive performance studies on large, real, and synthetic datasets, which demonstrate that our new framework could efficiently support CKST over a data stream. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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23 pages, 1546 KiB

Open AccessArticle

Parallel Prediction Method of Knowledge Proficiency Based on Bloom’s Cognitive Theory

by Tiancheng Zhang, Hanyu Mao, Hengyu Liu, Yingjie Liu, Minghe Yu, Wenhui Wu, Ge Yu, Baoze Wei and Yajuan Guan

Mathematics 2023, 11(24), 5002; https://doi.org/10.3390/math11245002 - 18 Dec 2023

Viewed by 613

Abstract

Knowledge proficiency refers to the extent to which students master knowledge and reflects their cognitive status. To accurately assess knowledge proficiency, various pedagogical theories have emerged. Bloom’s cognitive theory, proposed in 1956 as one of the classic theories, follows the cognitive progression from foundational to advanced levels, categorizing cognition into multiple tiers including “knowing”, “understanding”, and “application”, thereby constructing a hierarchical cognitive structure. This theory is predominantly employed to frame the design of teaching objectives and guide the implementation of teaching activities. Additionally, due to the large number of students in real-world online education systems, the time required to calculate knowledge proficiency is significantly high and unacceptable. To ensure the applicability of this method in large-scale systems, there is a substantial demand for the design of a parallel prediction model to assess knowledge proficiency. The research in this paper is grounded in Bloom’s Cognitive theory, and a Bloom Cognitive Diagnosis Parallel Model (BloomCDM) for calculating knowledge proficiency is designed based on this theory. The model is founded on the concept of matrix decomposition. In the theoretical modeling phase, hierarchical and inter-hierarchical assumptions are initially established, leading to the abstraction of the mathematical model. Subsequently, subject features are mapped onto the three-tier cognitive space of “knowing”, “understanding”, and “applying” to derive the posterior distribution of the target parameters. Upon determining the objective function of the model, both student and topic characteristic parameters are computed to ascertain students’ knowledge proficiency. During the modeling process, in order to formalize the mathematical expressions of “understanding” and “application”, the notions of “knowledge group” and “higher-order knowledge group” are introduced, along with a parallel method for identifying the structure of higher-order knowledge groups. Finally, the experiments in this paper validate that the model can accurately diagnose students’ knowledge proficiency, affirming the scientific and meaningful integration of Bloom’s cognitive hierarchy in knowledge proficiency assessment. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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18 pages, 98620 KiB

Open AccessArticle

Enhancing Dropout Prediction in Distributed Educational Data Using Learning Pattern Awareness: A Federated Learning Approach

by Tiancheng Zhang, Hengyu Liu, Jiale Tao, Yuyang Wang, Minghe Yu, Hui Chen and Ge Yu

Mathematics 2023, 11(24), 4977; https://doi.org/10.3390/math11244977 - 16 Dec 2023

Viewed by 912

Abstract

Learning patterns are crucial for predicting student dropout in educational settings, providing insights into students’ behaviors and motivations. However, existing mainstream dropout prediction models have limitations in effectively mining these learning patterns and cannot mine these learning patterns in large-scale, distributed educational datasets. In this study, we analyze the representations of mainstream models and identify their inability to capture students’ distinct learning patterns and personalized variations across courses. Addressing these challenges, our study adopts a federated learning approach, tailoring the analysis to leverage distributed data while maintaining privacy and decentralization. We introduce the Federated Learning Pattern Aware Dropout Prediction Model (FLPADPM), which utilizes a one-dimensional convolutional neural network (CNN) and a bidirectional long short-term memory (LSTM) layer within a federated learning framework. This model is designed to effectively capture nuanced learning patterns and adapt to variations across diverse educational settings. To evaluate the performance of LPADPM, we conduct an empirical evaluation using the KDD Cup 2015 and XuetangX datasets. Our results demonstrate that LPADPM outperforms state-of-the-art models in accurately predicting student dropout behavior. Furthermore, we visualize the representations generated by LPADPM, which confirm its ability to effectively mine learning patterns in different courses. Our results showcase the model’s ability to capture and analyze learning patterns across various courses and institutions within a federated learning context. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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13 pages, 795 KiB

Open AccessArticle

Adaptive Variable-Damping Impedance Control for Unknown Interaction Environment

by Dawei Gong, Yaru Song, Minglei Zhu, Yunlong Teng, Jinmao Jiang and Shiliang Zhang

Mathematics 2023, 11(24), 4961; https://doi.org/10.3390/math11244961 - 14 Dec 2023

Viewed by 678

Abstract

Aiming at the force-tracking error phenomenon of impedance control in an unknown surface environment, an adaptive variable-damping impedance control algorithm is proposed, and the stability and convergence of the algorithm are deduced. An adaptive-law selection rule is proposed to aim at the phenomenon that the adaptive parameters are too large to cause the system oscillation and overshoot and too small to cause the adaptive line variation in the curved surface environment. Finally, experiments conclude that the impedance control based on the adaptive variable-damping algorithm has a better force-tracking effect than the ordinary impedance control in the curved surface environment where the contact surface between the end-effector of the manipulator and the atmosphere is unknown. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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22 pages, 19527 KiB

Open AccessArticle

Research on the Attack Strategy of Multifunctional Market Trading Oriented to Price

by Jiaqi Tian, Bonan Huang, Zewen Shi, Lu Liu, Lihong Feng and Guoxiu Jing

Mathematics 2023, 11(23), 4728; https://doi.org/10.3390/math11234728 - 22 Nov 2023

Viewed by 521

Abstract

In the context of energy transformation and power market system reform, it is crucial to address the network risks associated with enhancing the integration of the “Energy–Information–Market” paradigm. This necessitates research on multi-energy market trading modes and the corresponding offensive and defensive technologies. This paper proposes a novel approach centered around a node-local Energy Hub (EH) that represents large industrial users with diverse energy demands. To facilitate multi-energy two-way trading, a price-oriented Transactive Energy (TE) market clearing strategy is developed. Building upon this transaction network framework, a data-driven attack strategy targeting the state estimator of the Transmission System Operator (TSO) is introduced and implemented in two stages, encompassing real-time topology estimation and False Data Injection attacks. By leveraging Matrix Transfer Entropy (MTE), the optimal attack target is identified to disrupt the economic stability of the system and the profit of the attacker increases significantly. The proposed attack strategy is validated through simulations conducted on a 30-node system, yielding conclusive evidence of its effectiveness while offering vital insights for system defense. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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13 pages, 1943 KiB

Open AccessArticle

Distributed Fixed-Time Energy Management for Port Microgrid Considering Transmissive Efficiency

by Zixiao Ban, Fei Teng, Huifeng Zhang, Shuo Li, Geyang Xiao and Yajuan Guan

Mathematics 2023, 11(17), 3674; https://doi.org/10.3390/math11173674 - 25 Aug 2023

Viewed by 618

Abstract

To enhance the efficiency of a port microgrid, this paper proposes an energy management method and a topology construction mechanism considering the convergence rate and information transmission distances, respectively. Firstly, a distributed fixed-time energy management method is proposed to solve an energy management problem in a known time and guarantee the efficiency of the port microgrid. Secondly, to address the challenge of heterogeneous devices with multiple communication protocols, information exchange between different devices is facilitated through a polymorphic network. To obtain a connected communication topology that can ensure the implementation of the distributed energy management method, a connected networking mechanism is proposed. This mechanism minimizes the total communication distance to reduce the effect of the information transmission distance on communication effectiveness. Finally, the effectiveness of both algorithms is demonstrated by simulation, and the advantages of the distributed fixed-time energy management method on the convergence rate are reflected through a comparison with other methods. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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22 pages, 5062 KiB

Open AccessArticle

Algebraic-Connectivity-Based Multi-USV Distributed Formation Method via Adding a Reverse Edge

by Jingchen Wang, Qihe Shan, Jun Zhu, Xiaofeng Cheng and Baoze Wei

Mathematics 2023, 11(13), 2942; https://doi.org/10.3390/math11132942 - 30 Jun 2023

Cited by 1 | Viewed by 695

Abstract

This paper concerns the formation problem in multi-USV cluster formation containment tracking tasks with a special topology. A topology reconstruction method was proposed that enables the followers’ formation to be dispersed while achieving the fastest convergence rate for the system. This topology structure is based on tree topology and DAG (directed acyclic graph) local structure stem as prototypes, using the principle of adding reverse edges on the stem to reduce algebraic connectivity. By adding a reverse edge to obtain a more dispersed formation, a method for selecting appropriate reverse edges was achieved. Through relevant theoretical quantitative and qualitative analysis, it was demonstrated that adding this reverse edge can enable the system to achieve the fastest convergence rate. Finally, through simulation experiments, it was verified that the selected reverse edge can optimize the formation of followers and achieve the fastest convergence rate. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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16 pages, 1168 KiB

Open AccessArticle

An RNN-Based Performance Identification Model for Multi-Agent Containment Control Systems

by Wei Liu, Fei Teng, Xiaotian Fang, Yuan Liang and Shiliang Zhang

Mathematics 2023, 11(12), 2760; https://doi.org/10.3390/math11122760 - 18 Jun 2023

Cited by 2 | Viewed by 828

Abstract

In the containment control problem of multi-agent systems (MASs), the convergence of followers is always a potential threat to the security of system operations. From the perspective of system topology, the inherently non-linear properties of the algebraic connectivity of the follower2follower (F2F) network, combined with the influence of the leader2follower (L2F) topology on the system, make it difficult to design the convergence positions of the followers through mere mathematical analysis. Therefore, in the background of temporary networking tasks for large-scale systems, to achieve the goal of forecasting the performance of the whole system when networking is only completed with local information, this paper investigates the application and effectiveness of recurrent neural networks (RNNs) in the containment control system performance identification, thus improving the efficiency of system networking while ensuring system security. Two types of identification models based on two types of neural networks (NNs), MLP and standard RNN are developed, according to the range of information required for performance identification. Evaluation of the models is carried out by means of the coefficient of determination (

R^{2}

) as well as the root-mean-square error (RMSE). The results show that each model may produce a better forecasting accuracy than the other models in specific cases, with models based on the standard RNN possessing smaller errors. With the proposed method, model identification can be achieved, but in-depth development of the model in further studies is still necessary to the extent the accuracy of the model. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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19 pages, 1986 KiB

Open AccessArticle

Distributed Finite-Time Cooperative Economic Dispatch Strategy for Smart Grid under DOS Attack

by Zhenghang Song, Xiang Wang, Baoze Wei, Zhengyu Shan and Peiyuan Guan

Mathematics 2023, 11(9), 2103; https://doi.org/10.3390/math11092103 - 28 Apr 2023

Cited by 1 | Viewed by 845

Abstract

This paper proposes an energy management strategy that can resist DOS attacks for solving the Economic Dispatch Problem (EDP) of the smart grid. We use the concept of energy agent, which acts as a hub for the smart grid, and each EA is an integrated energy unit that converts, stores, and utilizes its local energy resources. This approach takes into account the coupling relationship between energy agents (EA) and utilizes the Lyapunov function technique to achieve finite-time solutions for optimization problems. We incorporate strategies to resist DOS attacks when analyzing finite-time convergence using the Lyapunov technique. Based on this, a finite convergence time related to DOS attack time is derived. The integral sliding mode control strategy is adopted and the Lyapunov method is used to analyze it, so that the algorithm can resist DOS attacks and resist external disturbances. Through theoretical analysis, it is shown that the strategy is capable of converging to the global optimal solution in finite time even if it is attacked by DOS. We conducted case studies of six-EA and ten-EA systems to verify the effectiveness of this strategy. The proposed strategy has potential for deployment in distributed energy management systems that require resilience against DOS attacks. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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19 pages, 1793 KiB

Open AccessArticle

Learned-Index-Based Semantic Keyword Query on Blockchain

by Zhongming Yao, Junchang Xin, Kun Hao, Zhiqiong Wang and Wancheng Zhu

Mathematics 2023, 11(9), 2055; https://doi.org/10.3390/math11092055 - 26 Apr 2023

Viewed by 1302

Abstract

Blockchain has become increasingly popular for data management in recent years. However, the existing blockchain systems lack efficient semantic queries, particularly keyword queries. To address this issue, we propose a learned-index-based semantic keyword query architecture on blockchain. First, our architecture records data semantics information to support semantic keyword queries. Second, we establish the lookup table index for semantic information among blocks and the block-level recursive model index for blocks to improve the query efficiency. We store the lookup table in the extended block headers to maintain the result’s completeness, and we store recursive model indexes off chain to optimize the maintenance efficiency. Third, we propose a verifiable query algorithm based on our proposed architecture to maintain the result’s correctness. Finally, the experimental results show that combining the lookup table and the learned index effectively improves the query efficiency on blockchain. Full article

(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing)

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