Mathematics

27 pages, 498 KB

Open AccessArticle

An Information Theory of Persistent Homology: Entropy, the Data Processing Inequality, and Rate–Distortion Bounds for Topological Features

by Deepalakshmi Perumalsamy, Caleb Gunalan and Rajermani Thinakaran

Mathematics 2026, 14(8), 1385; https://doi.org/10.3390/math14081385 (registering DOI) - 20 Apr 2026

Abstract

Background: Topological Data Analysis (TDA) captures multi-scale geometric features of data as persistence diagrams, yet no principled information-theoretic framework quantifies how much information those features carry, how efficiently they compress, or when they are informationally irreducible. Methods: We construct a measure-theoretic [...] Read more.

Background: Topological Data Analysis (TDA) captures multi-scale geometric features of data as persistence diagrams, yet no principled information-theoretic framework quantifies how much information those features carry, how efficiently they compress, or when they are informationally irreducible. Methods: We construct a measure-theoretic probability space over persistence diagram space using a Poisson-process reference measure, and define topological entropy (H-T), topological mutual information (I-T), and a topological rate–distortion function as the core objects of a new theory. Results: Four theorems with full proofs establish finite stability, axiomatic uniqueness, a Topological Data Processing Inequality, and a Rate–Distortion Theorem with explicit Poisson-model closed-form formula. A Renyi generalization of topological entropy is also established. Computational and practical implementation aspects—including finite-sample estimation, multi-parameter extension, and algorithmic realization—are addressed inline throughout the paper. Conclusions: This framework provides a rigorous measure-theoretic information-theoretic foundation for persistent homology, demonstrated on simulated brain connectivity and point cloud data, with applications to threshold selection, genomic classification bounds, and compressed sensing. Full article

16 pages, 1443 KB

Open AccessArticle

Scalar-on-Function Regression with Replicated Error-Prone Functional Covariates

by Xiyue Cao and Chunzheng Cao

Mathematics 2026, 14(8), 1384; https://doi.org/10.3390/math14081384 (registering DOI) - 20 Apr 2026

Abstract

In this article, we study scalar-on-function regression with functional covariates observed through replicated measurements subject to measurement error. Treating replicated curves as surrogates of an underlying latent process, the proposed framework resolves the identifiability issues commonly encountered in functional measurement error models. Through [...] Read more.

In this article, we study scalar-on-function regression with functional covariates observed through replicated measurements subject to measurement error. Treating replicated curves as surrogates of an underlying latent process, the proposed framework resolves the identifiability issues commonly encountered in functional measurement error models. Through functional principal component analysis, the model is represented as a finite-dimensional hierarchical linear measurement error model. Parameter estimation is carried out using an expectation-maximization algorithm, and alternative correction strategies based on adjusted regression calibration and simulation extrapolation are also considered for comparison. Simulation studies demonstrate the advantages of explicitly accounting for measurement error in terms of bias reduction and estimation stability. An application to soybean yield prediction in Illinois, using meteorological variables contaminated by measurement error, illustrates the practical value of the proposed approach. Full article

(This article belongs to the Special Issue Statistical Learning and Data Science: Methods, Theory, and Applications)

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21 pages, 11108 KB

Open AccessFeature PaperArticle

Using Negative Power Transformation to Model Block Minima

by Thanawan Prahadchai, Piyapatr Busababodhin, Taeyong Kwon and Sanghoo Yoon

Mathematics 2026, 14(8), 1383; https://doi.org/10.3390/math14081383 (registering DOI) - 20 Apr 2026

Abstract

This study proposes a novel transformation method for analyzing block minima using the generalized extreme value distribution (GEVD). The negative power transformation (NPT), which includes a tunable hyperparameter and reduces to the reciprocal transformation (RT) when set to 1, improves the accuracy and [...] Read more.

This study proposes a novel transformation method for analyzing block minima using the generalized extreme value distribution (GEVD). The negative power transformation (NPT), which includes a tunable hyperparameter and reduces to the reciprocal transformation (RT) when set to 1, improves the accuracy and robustness in estimating long-term return levels (RL). Compared to traditional methods, the NPT-GEVD demonstrates lower bias, standard errors, and root mean square errors in Monte Carlo simulations. Furthermore, the NPT-GEVD provides consistent RL estimates with improved robustness across varying parameterizations and sample sizes, mainly when using L-moments for small datasets. The application of the NPT-GEVD to rainfall data from South Korea revealed that the RLs for detecting hourly cumulative rainfall threshold levels varied from 30 min to over 4 h, depending on the location and threshold. This research underscores the value of advanced transformation techniques in environmental risk management, offering critical insights for flood prediction and mitigation strategies in climate change. Full article

(This article belongs to the Special Issue Extreme Value Theory: Theory, Methodology and Applications)

22 pages, 1490 KB

Open AccessArticle

Analysis and Mitigation of Performance Degradation from Layer Insertions into the Middle of Pre-Trained Language Models

by Gyunyeop Kim and Sangwoo Kang

Mathematics 2026, 14(8), 1382; https://doi.org/10.3390/math14081382 (registering DOI) - 20 Apr 2026

Abstract

Full fine-tuning of pre-trained models sometimes requires inserting trainable layers into the middle of a pre-trained backbone, but such middle-layer insertion can severely degrade downstream performance. We hypothesize that this degradation arises because conventionally inserted layers, when randomly initialized and combined with output-side [...] Read more.

Full fine-tuning of pre-trained models sometimes requires inserting trainable layers into the middle of a pre-trained backbone, but such middle-layer insertion can severely degrade downstream performance. We hypothesize that this degradation arises because conventionally inserted layers, when randomly initialized and combined with output-side activation, perturb intermediate representations before the pre-trained model has adapted. We study this phenomenon across natural language processing and computer vision benchmarks by varying insertion locations, the number of inserted layers, and activation designs. To address this problem, we propose a practical stabilization method for middle-layer insertion under full fine-tuning: a bias-free inserted layer with unit initialization and weight-side activation. This design is intended to remain closer to an identity-like transformation at initialization, thereby reducing initialization-time perturbation rather than claiming exact preservation of the original representations. In the tested DeBERTa-v3, T5-base, and ViT-base settings, the proposed method substantially mitigates the severe degradation caused by naive middle-layer insertion and maintains performance close to the no-added-layer baseline, including settings with up to 24 inserted layers. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

22 pages, 4344 KB

Open AccessArticle

A Hybrid Method for Optimization Modulo Theory of Floating-Point Numbers

by Xu Yang, Liantao Song, Jiaqiang Yao, Zhipan Li and Fan Yu

Mathematics 2026, 14(8), 1381; https://doi.org/10.3390/math14081381 (registering DOI) - 20 Apr 2026

Abstract

Optimization Modulo Theory (OMT) is an important extension of Satisfiability Modulo Theory (SMT), aiming to find models that satisfy constraints while optimizing objective functions. OMT naturally arises in program analysis and formal methods, making OMT solving an important and challenging task. OptiMathSAT is [...] Read more.

Optimization Modulo Theory (OMT) is an important extension of Satisfiability Modulo Theory (SMT), aiming to find models that satisfy constraints while optimizing objective functions. OMT naturally arises in program analysis and formal methods, making OMT solving an important and challenging task. OptiMathSAT is currently the state-of-the-art OMT solver supporting floating-point theories. It incrementally calls an SMT solver to prune the search space step by step until the optimal objective value is found. However, this frequent invocation of the SMT solver is highly inefficient. Therefore, this paper proposes a novel hybrid method consisting of two stages: coarse search and precise search. The coarse search stage quickly finds an approximate optimal model using an optimization search algorithm. The precise search stage then performs an SMT-based binary search starting from the approximate model to find the true optimal model (the OMT solution). Evidently, this hybrid approach reduces computational cost by rapidly shrinking the search space, thereby improving overall solving performance. We evaluated our method on benchmarks derived from SMT-LIB2 and real-world programs. Experimental results show that our method outperforms the current state-of-the-art in both effectiveness and efficiency. Full article

(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)

35 pages, 421 KB

Open AccessFeature PaperArticle

A Three-Dimensional Product-Based Circular Intuitionistic Fuzzy Potential Method for Transportation Problems

by Velichka Traneva and Stoyan Tranev

Mathematics 2026, 14(8), 1380; https://doi.org/10.3390/math14081380 - 20 Apr 2026

Abstract

Transportation problems constitute a fundamental class of optimization models; however, real-world applications involve uncertainty, hesitation, and expert disagreement that cannot be adequately captured by deterministic or classical fuzzy approaches. This paper proposes a three-dimensional circular intuitionistic fuzzy potential method (3D–CIFMODI), which extends the [...] Read more.

Transportation problems constitute a fundamental class of optimization models; however, real-world applications involve uncertainty, hesitation, and expert disagreement that cannot be adequately captured by deterministic or classical fuzzy approaches. This paper proposes a three-dimensional circular intuitionistic fuzzy potential method (3D–CIFMODI), which extends the classical MODI framework to Circular Intuitionistic Fuzzy Triples (C-IFTs) through radius-aware operations and indexed matrix representations. Unlike existing circular intuitionistic fuzzy transportation methods, which are primarily feasibility-driven, the proposed approach introduces a dual-based optimality framework based on circular reduced costs, preserving the full structure of uncertainty without reducing it to crisp equivalents. The method retains polynomial-time computational complexity

O (m n (m + n))

, i.e.,

O (n^{3})

for square problems, with only a constant computational overhead due to circular operations. A numerical case study demonstrates the effectiveness and robustness of the proposed framework. Furthermore, a comparative analysis between classical intuitionistic fuzzy (IFS) and circular intuitionistic fuzzy (C-IFS) representations shows that incorporating the radius parameter significantly improves discrimination capability, solution stability, and interpretability. The results confirm that the proposed method provides a unified, interpretable, and computationally efficient framework for solving multi-layer transportation problems under circular intuitionistic fuzzy uncertainty. Full article

(This article belongs to the Special Issue Advanced Intelligent Algorithms for Decision Making Under Uncertainty)

22 pages, 3673 KB

Open AccessArticle

A Novel Gradient-Based Method for Decision Trees Optimizing Arbitrary Differential Loss Functions

by Andrei Konstantinov, Lev Utkin and Vladimir Muliukha

Mathematics 2026, 14(8), 1379; https://doi.org/10.3390/math14081379 - 20 Apr 2026

Abstract

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic splitting rules. Unlike traditional approaches that rely on heuristic splitting rules, the proposed [...] Read more.

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic splitting rules. Unlike traditional approaches that rely on heuristic splitting rules, the proposed method refines predictions using the first and second derivatives of the loss function, enabling the optimization of complex tasks such as classification, regression, and survival analysis. We demonstrate the method’s applicability to classification, regression, and survival analysis tasks, including those with censored data. Numerical experiments on both real and synthetic datasets compare the proposed method with traditional decision tree algorithms such as CART, Extremely Randomized Trees, and SurvTree. The implementation of the method is publicly available, providing a practical tool for researchers and practitioners. This work advances the field of decision tree-based modeling, offering a more flexible and accurate approach for handling structured data and complex tasks. By leveraging gradient-based optimization, the proposed method bridges the gap between traditional decision trees and modern machine learning techniques, paving the way for further innovations in interpretable and high-performing models. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence: Models, Optimization, and Machine Learning, 3rd Edition)

8 pages, 215 KB

Open AccessFeature PaperArticle

Statistics in Weak Ascent Sequences

by Toufik Mansour

Mathematics 2026, 14(8), 1378; https://doi.org/10.3390/math14081378 - 20 Apr 2026

Abstract

Weak ascent sequences are a generalization of ascent sequences that appear in many combinatorial problems. In this paper, we give a method to find generating functions that count how often a given statistic

τ

appears in weak ascent sequences of length n, [...] Read more.

Weak ascent sequences are a generalization of ascent sequences that appear in many combinatorial problems. In this paper, we give a method to find generating functions that count how often a given statistic

τ

appears in weak ascent sequences of length n, keeping track of the number of weak ascents, where

τ

is the number of levels, ascents, descents, and weak descents. Full article

(This article belongs to the Special Issue Advances in Combinatorics, Discrete Mathematics and Graph Theory, 2nd Edition)

19 pages, 4280 KB

Open AccessArticle

Adaptive Recursive Model Predictive Current Control for Linear Motor Drives in CNC Machine Tools Based on Cartesian Distance Minimization

by Lin Song, Ziling Nie, Jun Sun, Yangwei Zhou, Jingxin Yuan and Huayu Li

Mathematics 2026, 14(8), 1377; https://doi.org/10.3390/math14081377 - 20 Apr 2026

Abstract

With the increasing demand for high speed and high-precision motion control in CNC machine tools, permanent magnet linear synchronous motors (PMLSMs) have been widely adopted in feed drive systems due to their excellent dynamic performance and positioning accuracy. However, existing model predictive current [...] Read more.

With the increasing demand for high speed and high-precision motion control in CNC machine tools, permanent magnet linear synchronous motors (PMLSMs) have been widely adopted in feed drive systems due to their excellent dynamic performance and positioning accuracy. However, existing model predictive current control (MPCC) variants still face challenges regarding high computational overhead and strong dependency on accurate motor parameters, which limit their industrial applicability. To address these issues, this paper proposes an adaptive recursive MPCC for PMLSM drives based on the Cartesian distance minimization principle. An adaptive recursive prediction scheme that is inspired by the feedback structure of recurrent architectures is first introduced. By cyclically utilizing the previously sampled current to predict the next period’s state, the strategy effectively decouples the control law from inductance variations. The dependence on resistance is further mitigated by analyzing the correlation between the ideal current vector and voltage vector deviations. Second, the selection of the optimal voltage vector is transformed into a geometric problem: minimizing the Cartesian distance between the reference voltage and 19 candidate deviations within a proposed virtual voltage vector hexagon. To minimize the computational burden, the vector space is partitioned into eight regions, allowing the optimal candidate to be selected from only two pre-derived deviations. The experimental results demonstrate that the proposed method significantly outperforms existing MPCC benchmarks. Specifically, the execution time is reduced by 63.6%. Under severe parameter mismatch, the current THD is reduced from 14.82% to 6.35%, and the thrust ripple is improved from 12.06 N to 5.25 N, validating its superior robustness and efficiency. Full article

(This article belongs to the Special Issue Advances in Control Theory and Applications in Energy Systems)

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18 pages, 22311 KB

Open AccessArticle

Optimization of Multi-Scale Feature Extraction and Loss Functions in YOLOv8 for Insulator Defect Detection

by Meng Su, Shuailun Geng, Hong Yu, Shuai Zhou, Lihua Zhou and Jiao Luo

Mathematics 2026, 14(8), 1376; https://doi.org/10.3390/math14081376 - 19 Apr 2026

Abstract

To address the challenges of high miss detection rates and accuracy degradation in UAV-based insulator defect detection—primarily stemming from complex background interference and the loss of fine-grained features—this paper presents an optimized lightweight detection framework based on an improved YOLOv8 model. The integration [...] Read more.

To address the challenges of high miss detection rates and accuracy degradation in UAV-based insulator defect detection—primarily stemming from complex background interference and the loss of fine-grained features—this paper presents an optimized lightweight detection framework based on an improved YOLOv8 model. The integration of a Spatial-to-Depth Convolution (SPDConv) module strengthens the extraction of fine-grained features for microscopic defects, while the incorporation of an SCConv module suppresses computational redundancy, leading to a 2.80% accuracy improvement. This architecture is further enhanced by a Channel and Spatial Reconstruction Attention Module (CSRAM), which dynamically prioritizes target-related regions and mitigates noise from vegetation and infrastructure. To improve regression robustness against low-quality annotations and blurred boundaries, a Focal-WIoU loss function utilizing a dynamic non-monotonic focusing mechanism is introduced. Experimental results on complex insulator datasets demonstrate that the proposed model achieves an mAP@0.5 of 91.75% and an mAP@0.5:0.95 of 59.86%, representing a 4.40% and 5.04% increase over the YOLOv8 baseline, respectively. Notably, while maintaining a lightweight profile with only 11.14 M parameters and 28.66 G FLOPs, the model achieves a high inference speed of 376.56 FPS, effectively enabling precise multi-scale defect recognition under extreme operational conditions. Full article

(This article belongs to the Special Issue Optimization Models and Algorithms in Data Science, 2nd Edition)

36 pages, 16375 KB

Open AccessArticle

An Improved Parrot Optimization Algorithm Applied to Engineering Optimization Problems

by Yueqiao Yang, Mingyuan Li, Minhao Qu, Yang Gao, Liang Zhao and Boni Du

Mathematics 2026, 14(8), 1375; https://doi.org/10.3390/math14081375 - 19 Apr 2026

Abstract

Metaheuristic algorithms have become effective tools for solving complex engineering optimization problems. The Parrot Optimization (PO) algorithm is a recently proposed method with promising performance; however, it still suffers from premature convergence and slow convergence when handling complex tasks. To address these issues, [...] Read more.

Metaheuristic algorithms have become effective tools for solving complex engineering optimization problems. The Parrot Optimization (PO) algorithm is a recently proposed method with promising performance; however, it still suffers from premature convergence and slow convergence when handling complex tasks. To address these issues, this paper proposes an improved variant termed the Elite Cauchy Multi-scale Multi-directional Parrot Optimization algorithm (ECMPO). The proposed ECMPO incorporates three coordinated strategies. First, an elite learning strategy is introduced before the behavioral update phase to guide the population toward promising regions and accelerate convergence. Second, after the behavioral update, individuals are adaptively processed based on their fitness: elite individuals perform a multi-scale multi-directional search to enhance local exploitation. Third, non-elite individuals undergo Cauchy mutation to increase population diversity and strengthen global exploration. These strategies enable ECMPO to achieve a better balance between exploration and exploitation. To evaluate its performance, ECMPO is examined through ablation studies on the CEC2017 benchmark functions and further compared with eleven algorithms on the CEC2020–2022 benchmark suites. Finally, it is applied to six constrained engineering design problems. The results demonstrate that ECMPO exhibits superior performance compared with competitive algorithms. ECMPO shows strong robustness and applicability in practical engineering optimization tasks. Full article

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24 pages, 4624 KB

Open AccessFeature PaperArticle

Regional Coordinated Traffic Signal Control Based on Improved Chaotic Particle Swarm Optimization

by Ke Ji and Jinjun Tang

Mathematics 2026, 14(8), 1374; https://doi.org/10.3390/math14081374 - 19 Apr 2026

Abstract

In urban traffic systems, traditional signal control can no longer meet the increasing traffic demand, and local congestion is severe during peak hours. Fixed detector data is characterized by high deployment density, full sample detection and restorable vehicle paths, providing new data support [...] Read more.

In urban traffic systems, traditional signal control can no longer meet the increasing traffic demand, and local congestion is severe during peak hours. Fixed detector data is characterized by high deployment density, full sample detection and restorable vehicle paths, providing new data support for coordinated signal control. We propose an optimization method for regional coordinated control, with the Changsha road network as the study area. Firstly, based on License Plate Recognition (LPR) data, the road network is divided into sub-networks and combined with the boundary control for regional coordinated control. Then, the critical path is taken as the control object, and the phase coordination rate is introduced as the optimization objective. The particle swarm optimization algorithm improved by the logistic chaotic map is used as the global searcher, and sequential quadratic programming is adopted as the local searcher to solve the optimization strategy for the objective function. Finally, a simulated road network is constructed in VISSIM 6.0 simulation software to verify the effectiveness of the strategy. The results show that the optimization strategy reduces intersection delay and saturation by 20.3% and 19.3% in the critical path coverage area. Road travel time and the average number of vehicle stops are reduced by 21% and 22.1%. This indicates that the regional coordinated control based on the improved particle swarm algorithm can better alleviate the peak hour traffic congestion. Full article

(This article belongs to the Special Issue Application of Mathematical Methods to Transportation: Modeling and Analysis)

28 pages, 80241 KB

Open AccessArticle

A Variational Screened Poisson Reconstruction for Whole-Slide Stain Normalization

by Junlong Xing, Hengli Ni, Qiru Wang and Yijun Jing

Mathematics 2026, 14(8), 1373; https://doi.org/10.3390/math14081373 - 19 Apr 2026

Abstract

Stain variability in digital pathology affects both cross-center diagnostic consistency and the robustness of downstream computational analysis. In this work, we formulate stain normalization as a variational inverse problem and derive a Screened Poisson Normalization (SPN) model from the steady-state reaction–diffusion mechanism underlying [...] Read more.

Stain variability in digital pathology affects both cross-center diagnostic consistency and the robustness of downstream computational analysis. In this work, we formulate stain normalization as a variational inverse problem and derive a Screened Poisson Normalization (SPN) model from the steady-state reaction–diffusion mechanism underlying histological staining. In the CIE

L^{*} a^{*} b^{*}

space, the model couples a gradient-domain fidelity term with a chromatic anchoring term, yielding a screened Poisson equation that preserves tissue morphology while enforcing color consistency. We prove that the corresponding variational problem is well-posed in

H^{1} (Ω)

and stable with respect to perturbations of the input data. We further show that the screening term induces an intrinsic localization length

ℓ_{c} \sim λ_{c}^{- 1 / 2}

, so that boundary perturbations decay exponentially away from tile interfaces. Based on this locality, we develop a non-overlapping tiled DCT-based spectral solver for gigapixel whole-slide images, enabling consistent tile-wise stain normalization and seamless whole-slide reassembly without heuristic boundary blending. Experiments on multi-scanner, multi-protocol, and archival-fading pathology datasets show that SPN achieves stable stain normalization with competitive chromatic alignment and strong preservation of diagnostically relevant microstructure, particularly in full-slide and tiled reconstruction settings. Supplementary experiments on synthetic pathology-like images further support the robustness of SPN under controlled color perturbations and indicate good generalization across diverse staining variations. Full article

(This article belongs to the Special Issue Numerical and Computational Methods in Engineering, 2nd Edition)

17 pages, 744 KB

Open AccessArticle

Efficient Computational Algorithms for Non-Convex Constrained Beamforming in Heterogeneous IoV Backhaul Networks

by Haowen Zheng, Zeyu Wang, Chun Zhu, Haifeng Tang and Xinyi Hui

Mathematics 2026, 14(8), 1372; https://doi.org/10.3390/math14081372 - 19 Apr 2026

Abstract

The rapid expansion of the Internet of Vehicles (IoV) necessitates high-capacity backhaul connectivity, yet the deployment of such networks under strict hardware and power constraints poses significant computational challenges for network optimization. To address this challenge, this paper investigates a joint transmit–receive beamforming [...] Read more.

The rapid expansion of the Internet of Vehicles (IoV) necessitates high-capacity backhaul connectivity, yet the deployment of such networks under strict hardware and power constraints poses significant computational challenges for network optimization. To address this challenge, this paper investigates a joint transmit–receive beamforming optimization problem for narrowband wireless backhaul in IoV networks under constant-modulus constraints. Unlike ideal digital architectures, we focus on cost-effective analog phase shifters, which introduce strictly non-convex constant-modulus constraints, rendering the optimization problem mathematically intractable for standard solvers. Since the resulting problem is highly non-convex, we develop two structured numerical methods: an iterative alternating optimization (AO) method and a joint optimization (JO) method, where AO employs auxiliary WMMSE-guided alternating updates together with constant-modulus projection, while JO jointly updates both beamformers over the constant-modulus feasible set. We compare their achievable sum-rate performance with that of a CDO-based benchmark and analyze their dominant computational costs through representative Big-O complexity expressions. Furthermore, we examine the effect of SVD-based and random feasible initializations on empirical convergence behavior, runtime, and final achievable performance. Simulation results demonstrate that the proposed computational methods significantly improve achievable sum-rate performance compared with the CDO benchmark. Moreover, SVD-based initialization provides a more structured starting point and generally leads to better convergence behavior and lower runtime than random feasible initialization. The empirical timing results further show that AO exhibits faster empirical convergence and requires lower runtime, whereas JO achieves better final sum-rate performance after more iterations. Full article

20 pages, 463 KB

Open AccessArticle

Weighted Approximation by Szász–Mirakyan-Type Operators Preserving Two Exponential Functions

by Gülsüm Ulusoy Ada and Ali Aral

Mathematics 2026, 14(8), 1371; https://doi.org/10.3390/math14081371 - 19 Apr 2026

Abstract

In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval

[0, \infty)

. The operators act on exponential weighted spaces and are analyzed within the framework of [...] Read more.

In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval

[0, \infty)

. The operators act on exponential weighted spaces and are analyzed within the framework of positive linear operator theory. We first establish their well-definedness and boundedness between suitable weighted spaces. By applying a weighted Korovkin-type theorem, we prove convergence in the corresponding weighted norm. Furthermore, we obtain quantitative estimates in terms of a weighted modulus of continuity and derive an order of convergence result. A Voronovskaya-type asymptotic formula is also established, describing the precise asymptotic behavior of the operators. Numerical examples are included to support the theoretical results. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

25 pages, 8035 KB

Open AccessArticle

Enhancing the Transferability of Generative Targeted Adversarial Attacks via Cosine-Based Logit Alignment

by Tengfei Shi, Shihai Wang and Bin Liu

Mathematics 2026, 14(8), 1370; https://doi.org/10.3390/math14081370 - 19 Apr 2026

Abstract

Adversarial examples reveal critical vulnerabilities in deep neural networks, posing significant risks in real-world deployment. In black-box settings, transferable targeted attacks rely on surrogate models but often suffer from low success rates. We argue that this limitation arises not only from surrogate-boundary overfitting [...] Read more.

Adversarial examples reveal critical vulnerabilities in deep neural networks, posing significant risks in real-world deployment. In black-box settings, transferable targeted attacks rely on surrogate models but often suffer from low success rates. We argue that this limitation arises not only from surrogate-boundary overfitting but also from insufficient alignment with the target semantic space, which restricts the ability of adversarial examples to encode target-specific characteristics. To address this issue, we propose Cosine-Based Logit Alignment (CBLA), a unified framework for transferable targeted attacks. CBLA replaces the conventional cross-entropy loss with a cosine similarity objective to enhance directional alignment in logit space and alleviate gradient saturation. In addition, a semantic-invariant transformation strategy is introduced to improve structural consistency and cross-model generalization. Experiments on the ImageNet validation set demonstrate that CBLA consistently improves targeted attack success rates, achieving an average gain of 4.55% over strong baselines across multiple architectures. Full article

(This article belongs to the Special Issue Advanced Research in Neural Networks, Machine Learning, and Image Processing)

31 pages, 1694 KB

Open AccessArticle

Optimized CNN–LSTM Modeling for Crisis Event Detection in Noisy Social Media Streams

by Mudasir Ahmad Wani

Mathematics 2026, 14(8), 1369; https://doi.org/10.3390/math14081369 - 19 Apr 2026

Abstract

Event detection is crucial for disaster response, public safety, and trend analysis, enabling real-time identification of critical events. Social media platforms provide a vast content source, offering timely and diverse event coverage compared to traditional news reports. However, challenges arise due to the [...] Read more.

Event detection is crucial for disaster response, public safety, and trend analysis, enabling real-time identification of critical events. Social media platforms provide a vast content source, offering timely and diverse event coverage compared to traditional news reports. However, challenges arise due to the informal and noisy nature of the text, along with the limited availability of ground truth data for training models. This study introduces SOCIAL (Social Media Event Classification using Integrated Artificial Learning and Natural Language Processing), a mathematically grounded framework for real-time social media event detection. SOCIAL integrates a formal representation of social media text with a customized CNN–LSTM architecture, combining convolutional operations for local feature extraction with sequential modeling to capture temporal dependencies, thereby enhancing classification accuracy. Generative AI is employed to create synthetic event-related samples, addressing data scarcity and ensuring a balanced dataset, while the design incorporates quantitative principles to guide embedding selection and model optimization. This study systematically evaluates six experimental configurations with TF-IDF and Word2Vec embeddings. The TF-IDF-based CNN–LSTM model achieved top performance with 98.59% accuracy, 98.13% precision, 99.06% recall, and 0.9719 MCC. Additionally, the

F_{0.5}

,

F_{1}

, and

F_{2}

scores were 98.31%, 98.59%, and 98.87%, respectively, confirming the model’s strong predictive capabilities. TF-IDF integration enhanced event-specific term recognition, reducing misclassifications and improving reliability. These results demonstrate that SOCIAL is not only a fast, accurate, and scalable tool for crisis event detection, but also a formally principled framework for modeling and analyzing social media signals. Full article

(This article belongs to the Special Issue Deep Representation Learning for Social Network Analysis)

20 pages, 1413 KB

Open AccessArticle

Finite-Time Neural Adaptive Control of Electro-Hydraulic Servo Systems with Minimal Input Delay and Parametric Uncertainty via Padé Approximation

by Shuai Li, Ke Yan, Yuanlun Xie, Qishui Zhong, Jin Yang and Daixi Liao

Mathematics 2026, 14(8), 1368; https://doi.org/10.3390/math14081368 - 19 Apr 2026

Abstract

Physical coupling, nonlinearity and uncertainty degrade the dynamic performance of electro-hydraulic servo systems, particularly under conditions involving input delays, leading to reduced trajectory tracking accuracy or even system instability. These factors often fail to meet the high-precision requirements of engineering applications. To effectively [...] Read more.

Physical coupling, nonlinearity and uncertainty degrade the dynamic performance of electro-hydraulic servo systems, particularly under conditions involving input delays, leading to reduced trajectory tracking accuracy or even system instability. These factors often fail to meet the high-precision requirements of engineering applications. To effectively address these difficulties, this paper proposes a novel adaptive control protocol for networked electro-hydraulic servo systems. For the minimal communication delay problem of networked electro-hydraulic servo systems, Laplace transform algorithm together with Padé approximation is adopted in this study to remove the delay term from the mathematical system model. Moreover, the matched modeling parametric uncertainty of systems is estimated and compensated by the neural network adaptive method to improve the dynamical performance of the system during the steady state. The controller is designed on the basis of recursive backstepping strategy and the finite-time stability theorem, which can handle system nonlinearity and guarantee transient response. The validity of the proposed theoretical results is proved by Lyapunov stability and the feasibility and superiority are verified via physical simulation. Full article

(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems and Robotics with Applications)

29 pages, 1345 KB

Open AccessFeature PaperArticle

From Cell-Specific Heuristics to Transferable Structural Search for Ramsey Graph Construction

by Sorin Liviu Jurj

Mathematics 2026, 14(8), 1367; https://doi.org/10.3390/math14081367 - 19 Apr 2026

Abstract

Recent automated search methods have improved lower bounds for several Ramsey numbers, but the strongest gains often depend on structured seeding and cell-specific heuristic discovery. This leaves open a more fundamental question: Can a useful search structure be transferred across related Ramsey cells [...] Read more.

Recent automated search methods have improved lower bounds for several Ramsey numbers, but the strongest gains often depend on structured seeding and cell-specific heuristic discovery. This leaves open a more fundamental question: Can a useful search structure be transferred across related Ramsey cells rather than rediscovered independently for each target instance? This work proposes a teacher–student framework for transferable structural search in Ramsey graph construction, inspired by the structure-distillation logic of Physics Structure-Informed Neural Networks (Ψ-NNs). The framework builds compressed structural representations from teacher witnesses and search traces, extracts reusable motifs and relations, and reconstructs transfer candidates. These are refined by balanced search and, for weak R(3, s) cells, by exact small-cell supervision. The framework is evaluated as a proof of concept across five Ramsey cells under transfer, matched-compute, search, ablation, and interpretability settings, including a proportional shift-scaling baseline and a greedy triangle-closing baseline that probe the structure-validity frontier from complementary directions. Supplementary experiments cover seed robustness, budget sensitivity, transfer-neighborhood variation, structural-resolution changes, stronger exact supervision, cross-r teacher pooling, single-teacher configurations, and scaling behavior across graph sizes. The results show that the portfolio version of the framework is the strongest balanced transfer method in the current study, while a structure-dominant oracle achieves stronger witness-shape agreement but worse Ramsey-valid construction. These findings reveal a clear structure-validity frontier and suggest that transferable Ramsey search should be evaluated by how well structural priors survive the validity constraints of new cells. Full article

(This article belongs to the Special Issue Advances in Graph Labelings and Ramsey Theory in Discrete Structures)

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