Recent Advances in Mathematical Models and Algorithms for Big Data Analytics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 1930

Special Issue Editors


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Guest Editor
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
Interests: evolutionary computation; machine learning; deep learning
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
International Academic Center of Complex Systems, Beijing Normal University, Beijing, China
Interests: computational intelligence; image processing; pattern recognition; software reliability engineering; optical computing; big astronomical data analysis

Special Issue Information

Dear Colleagues,

Nowadays, mathematical models and information technology in a big data context have become a popular new research topic among academics and the industry. Big data refers to a collection of data sets that are too large or too complex for efficient processing and analysis using traditional database management tools. The development of mathematics models and information technology in a big data context will enhance decision making, insight discovery, and process optimization. However, there are still numerous technical challenges and issues that need to be improved and broadly explored. This Special Issue aims to provide readers with the latest and most innovative research on all theoretical and practical aspects of information technology and mathematical models for big data analytics.

The aim of this Special Issue is to present a collection of high-quality research articles on state-of-the-art mathematical models, information technology, and big data analytics. The topics of interest include, but are not limited to:

Information technology and Computer Science

  • artificial intelligence in big data;
  • computer graphics and image processing;
  • computer networks and security;
  • computer science and engineering;
  • computer simulation and modeling;
  • computer-aided design / manufacturing;
  • database technology and data warehousing;
  • e-commerce and e-government;
  • geographical information systems (GIS);
  • grid computing;
  • image processing and acquisition;
  • information retrieval and information security;
  • Internet and Web applications;
  • knowledge discovery and data mining;
  • management information system;
  • neural networks and evolutionary algorithms;
  • pattern recognition and machine learning;
  • programming languages and techniques;
  • semantic grid and natural language processing;
  • smart city and intelligent transportation;
  • software engineering;
  • system modeling and simulation.

Electronics and Communication Technology

  • antennas design, modeling, and measurement;
  • audio/speech signal processing;
  • bioinformatics;
  • biomedical electronics;
  • channel coding;
  • communication and wireless systems;
  • cryptography;
  • electronic devices in communications;
  • image/video processing and coding;
  • industrial electronics and automations;
  • integrated optics;
  • medical imaging and image analysis;
  • microwave circuits;
  • multimedia communications;
  • optical communications;
  • photonic technologies;
  • radio propagations;
  • signal detection and estimation;
  • signal and informatics processing;
  • telecommunication services and applications;
  • wireless communication and wireless networking;
  • UAV technology.

Big data Analytics

  • mathematical models for big data analytics;
  • mathematics of machine learning and application;
  • machine learning for big data;
  • traditional and emerging methods for big data;
  • privacy preservation for big data;
  • intelligent and unconventional methods for big data;
  • search and optimization for big data;
  • parallel, accelerated, and distributed big data analysis;
    • high-performance computing for big data;
  • novel hardware and software architectures for big data;
  • real-world applications and success stories of big data analysis;
  • mining of unstructured, spatio-temporal, streaming, and multimedia data.

Prof. Dr. Hai-Lin Liu
Prof. Dr. Yuping Wang
Prof. Dr. Ping Guo
Guest Editors

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Published Papers (2 papers)

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Research

20 pages, 2880 KiB  
Article
A Second Examination of Trigonometric Step Sizes and Their Impact on Warm Restart SGD for Non-Smooth and Non-Convex Functions
by Mahsa Soheil Shamaee and Sajad Fathi Hafshejani
Mathematics 2025, 13(5), 829; https://doi.org/10.3390/math13050829 - 1 Mar 2025
Viewed by 440
Abstract
This paper presents a second examination of trigonometric step sizes and their impact on Warm Restart Stochastic Gradient Descent (SGD), an essential optimization technique in deep learning. Building on prior work with cosine-based step sizes, this study introduces three novel trigonometric step sizes [...] Read more.
This paper presents a second examination of trigonometric step sizes and their impact on Warm Restart Stochastic Gradient Descent (SGD), an essential optimization technique in deep learning. Building on prior work with cosine-based step sizes, this study introduces three novel trigonometric step sizes aimed at enhancing warm restart methods. These step sizes are formulated to address the challenges posed by non-smooth and non-convex objective functions, ensuring that the algorithm can converge effectively toward the global minimum. Through rigorous theoretical analysis, we demonstrate that the proposed approach achieves an O1T convergence rate for smooth non-convex functions and extend the analysis to non-smooth and non-convex scenarios. Experimental evaluations on FashionMNIST, CIFAR10, and CIFAR100 datasets reveal significant improvements in test accuracy, including a notable 2.14% increase on CIFAR100 compared to existing warm restart strategies. These results underscore the effectiveness of trigonometric step sizes in enhancing optimization performance for deep learning models. Full article
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22 pages, 3608 KiB  
Article
Scheduling Model and Algorithm for Transportation and Vehicle Charging of Multiple Autonomous Electric Vehicles
by Xiaoli Wang, Zhiyu Zhang, Mengmeng Jiang, Yifan Wang and Yuping Wang
Mathematics 2025, 13(1), 145; https://doi.org/10.3390/math13010145 - 2 Jan 2025
Viewed by 878
Abstract
Autonomous electric vehicle (AEV) services leverage advanced autonomous driving and electric vehicle technologies to provide innovative, driverless transportation solutions. The biggest challenge faced by AEVs is the limited number of charging stations and long charging times. A critical challenge is maximizing passenger travel [...] Read more.
Autonomous electric vehicle (AEV) services leverage advanced autonomous driving and electric vehicle technologies to provide innovative, driverless transportation solutions. The biggest challenge faced by AEVs is the limited number of charging stations and long charging times. A critical challenge is maximizing passenger travel satisfaction while reducing the AEV idle time. This involves coordinating passenger transport and charging tasks via leveraging the information from charging stations, passenger transport, and AEV data. There are four important contributions in this paper. Firstly, we introduce an integrated scheduling model that considers both passenger transport and charging tasks. Secondly, we propose a multi-level differentiated charging threshold strategy, which dynamically adjusts the charging threshold based on both AEV battery levels and the availability of charging stations, reducing competition among vehicles and minimizing waiting times. Thirdly, we develop a rapid strategy to optimize the selection of charging stations by combining geographic and deviation distance. Fourthly, we design a new evolutionary algorithm to solve the proposed model, in which a buffer space is introduced to promote diversity within the population. Finally, experimental results show that compared to the existing state-of-the-art scheduling algorithms, the proposed algorithm shortens the running time of scheduling algorithms by 6.72% and reduces the idle driving time of AEVs by 6.53%, which proves the effectiveness and efficiency of the proposed model and algorithm. Full article
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