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Mathematics
Special Issues
Securing Software Through Mathematics and Domain-Specific Knowledge: Innovations and Applications
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Securing Software Through Mathematics and Domain-Specific Knowledge: Innovations and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 15 November 2026 | Viewed by 2244

Special Issue Editors

Dr. Wei Zheng

E-Mail Website
Guest Editor
School of Software, Northwestern Polytechnical University, Xi'an, China
Interests: software security; formal verification; intelligent software testing; vulnerability analysis; AI security; AI-assisted software security; vulnerability evolution
Dr. Xiaoxue Wu

E-Mail Website
Guest Editor
School of Information Engineering, Yangzhou University, Yangzhou 225000, China
Interests: domain knowledge graph; software quality assurance; software security

Special Issue Information

Dear Colleagues,

Software security and domain knowledge are critical pillars in modern computing, driving innovation across industries such as healthcare, finance, and critical infrastructure. As systems become increasingly complex, the integration of domain-specific knowledge and robust security measures is essential to address emerging threats and ensure reliability.

We invite you to contribute original research articles focusing on mathematical innovations and challenges in software security and domain knowledge engineering. This Special Issue aims to showcase cutting-edge research that bridges theoretical foundations with practical applications, fostering interdisciplinary collaboration.

Broad Topics

The scope of this Special Issue includes, but is not limited to, the following:

  • Mathematical Innovations in Domain Knowledge Engineering:Software security related knowledge representation, reasoning, and integration in complex systems.
  • Mathematical Methods in Software Security: Vulnerability analysis, penetration testing, secure coding practices, and threat modeling.
  • AI-Driven Security: Machine learning for anomaly detection, automated threat response, and adversarial attacks.
  • Formal Methods:Model checking, theorem proving, and verification for secure software design.
  • Cybersecurity in Emerging Technologies: IoT security, blockchain vulnerabilities, and quantum-resistant cryptography.

Dr. Wei Zheng
Dr. Xiaoxue Wu
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 250 words) can be sent to the Editorial Office for assessment.

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

  • domain knowledge graph
  • software security
  • vulnerability analysis
  • security testing
  • formal methods
  • AI in cybersecurity
  • LLMS for software security
  • LLM security
  • IoT security
  • blockchain security
  • adversarial machine learning

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

13 pages, 3260 KB  
Article
Efficient Deep Image Prior with Spatial-Channel Attention Transformer
by Weiwei Lin, Zeqing Zhang, Jin Lin and Ying You
Mathematics 2026, 14(7), 1185; https://doi.org/10.3390/math14071185 - 1 Apr 2026
Viewed by 423
Abstract
The deep image prior (DIP) suggests that it is possible to train a randomly initialized network with a suitable architecture to solve inverse imaging problems by simply optimizing its parameters to reconstruct a single degraded image. However, the prior knowledge exploited by vanilla [...] Read more.
The deep image prior (DIP) suggests that it is possible to train a randomly initialized network with a suitable architecture to solve inverse imaging problems by simply optimizing its parameters to reconstruct a single degraded image. However, the prior knowledge exploited by vanilla DIP relies on basic local convolutions, which inevitably limits the performance of inverse imaging tasks to the generative capacity of the model. Furthermore, image information is often not only related to neighboring pixels but also dependent on global color features and spatial distribution. Simple local convolutions used in inverse imaging cannot capture precise fine-grained details. Moreover, DIP is an unsupervised process but requires iterations to learn inverse imaging, consuming computational power and limiting the adaptation of global attention. To solve these problems, this article explores an efficient global prior module—a tri-directional multi-head self-attention mechanism—aiming to learn pixel-wise correlations along three directions: horizontal, vertical, and channel-wise. Our observations found that global learning can effectively enhance the detail information of edge pixels, making images more vivid and textures clearer. In addition, tri-directional multi-head self-attention can efficiently replace the global perception ability of pixel-level self-attention. Finally, we demonstrate that global learning can effectively improve the imaging effect of inverse imaging problems and enhance the information of texture edge pixels. Moreover, tri-directional multi-head self-attention can effectively alleviate the computation redundancy of pixel-level self-attention, thus achieving efficient and high-quality inverse imaging tasks. The principle of this method lies in global feature capture and efficient attention modeling, striking a balance between detail fidelity and computational practicality. Full article
(This article belongs to the Special Issue Securing Software Through Mathematics and Domain-Specific Knowledge: Innovations and Applications)
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17 pages, 1362 KB  
Article
CFGuide-Fuzz: Dynamic Fuzz Testing Framework Based on Control Flow Features
by Yajun Gao, Wei Zheng and Xiaoxue Wu
Mathematics 2026, 14(3), 452; https://doi.org/10.3390/math14030452 - 28 Jan 2026
Viewed by 491
Abstract
RTL-level fuzz testing is critical for identifying vulnerabilities in hardware designs. However, existing hardware fuzz testing methods suffer from slow coverage improvement and blind exploration due to the lack of fine-grained control flow guidance. To address this gap, this article proposes the CFGuide-Fuzz [...] Read more.
RTL-level fuzz testing is critical for identifying vulnerabilities in hardware designs. However, existing hardware fuzz testing methods suffer from slow coverage improvement and blind exploration due to the lack of fine-grained control flow guidance. To address this gap, this article proposes the CFGuide-Fuzz framework, which includes control node extraction and compression techniques based on FIRRTL instrument and a hardware fuzz engine driven by feature feedback. This research introduces a fine-grained control flow feedback mechanism for hardware fuzz testing, enabling a pivotal shift from blind exploration to targeted testing. Experimental results demonstrate that compared to the DiFuzzRTL baseline, the proposed CFGuide-Fuzz framework enhances register state coverage by 9.4% under identical iteration counts and testing environments. Additionally, it doubles the number of effective inputs that trigger mismatched differential test results. These findings fully validate the framework’s dual advantages: deeper hardware control flow exploration and higher semantic vulnerability triggering efficiency. Full article
(This article belongs to the Special Issue Securing Software Through Mathematics and Domain-Specific Knowledge: Innovations and Applications)
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19 pages, 5377 KB  
Article
LEMSOFT: Leveraging Extraction Method and Soft Voting for Android Malware Detection
by Qiang Han, Zhichao Shi, Yao Li and Tao Zhang
Mathematics 2025, 13(21), 3569; https://doi.org/10.3390/math13213569 - 6 Nov 2025
Viewed by 627
Abstract
The pervasive spread of Android malware poses significant threats to users and systems worldwide. In most existing studies, differences in feature importance are often overlooked, and the calculation of feature weights is conducted independently of the classification model. In this paper, we propose [...] Read more.
The pervasive spread of Android malware poses significant threats to users and systems worldwide. In most existing studies, differences in feature importance are often overlooked, and the calculation of feature weights is conducted independently of the classification model. In this paper, we propose an Android malware detection method, Leveraging Extraction Method and Soft Voting classification (LEMSOFT). This approach includes a novel preprocessing module, lexical occurrence ratio-based filtering (LORF), and an improved Soft Voting mechanism optimized through genetic algorithms. We introduce LORF to evaluate and enhance the significance of permissions, API calls, and opcodes. Each type of feature is then independently classified using tailored machine learning models. To integrate the outputs of these classifiers, this paper proposes an innovative soft voting mechanism that improves prediction accuracy for encountered applications by assigning weights through a genetic algorithm. Our solution outperforms the baseline methods we studied, as evidenced by the evaluation of 5560 malicious and 8340 benign applications, with an average accuracy of 99.89%. The efficacy of our methodology is demonstrated through extensive experiments, showcasing significant improvements in detection rates compared to state-of-the-art (SOTA) methods. Full article
(This article belongs to the Special Issue Securing Software Through Mathematics and Domain-Specific Knowledge: Innovations and Applications)
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