Mathematics

21 pages, 337 KB

Open AccessArticle

Black Box Optimization for Ergodic Systems in Markov Chains

by Julio B. Clempner

Mathematics 2026, 14(8), 1246; https://doi.org/10.3390/math14081246 - 9 Apr 2026

This paper studies a black-box methodology for optimizing ergodic stochastic systems, focusing on the construction of scalar measures that reliably indicate progress toward optimality. Our starting point is a state-value quantity that inherently exhibits oscillatory behavior and does not converge under standard conditions. [...] Read more.

This paper studies a black-box methodology for optimizing ergodic stochastic systems, focusing on the construction of scalar measures that reliably indicate progress toward optimality. Our starting point is a state-value quantity that inherently exhibits oscillatory behavior and does not converge under standard conditions. We show that, despite its fluctuations, this quantity admits a recursive representation derived from a one-step-ahead fixed-local-optimal policy. The approach relies on identifying a Lyapunov-like function whose evolution reflects the long-run behavior of the system without requiring explicit knowledge of its internal dynamics. Such a function provides a monotonic indicator—non-increasing over time—that remains valid for any initial probability distribution. Whenever an optimal trajectory of the Markov chain exists, the proposed method guarantees convergence to it. We also provide a constructive procedure for obtaining the Lyapunov-like function and validate the methodology through theoretical analysis and numerical simulations. Full article

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17 pages, 834 KB

Open AccessArticle

Improved Data-Driven Shrinkage Estimators for Regression Models Under Severe Multicollinearity

by Ali Rashash R. Alzahrani and Asma Ahmad Alzahrani

Mathematics 2026, 14(8), 1245; https://doi.org/10.3390/math14081245 - 9 Apr 2026

Abstract

Multicollinearity is a critical issue in regression analysis, often resulting in inflated variances and unstable parameter estimates. Ridge regression is a widely adopted solution to address this challenge; however, existing ridge estimators are typically tailored to specific scenarios, limiting their universal applicability. Akhtar [...] Read more.

Multicollinearity is a critical issue in regression analysis, often resulting in inflated variances and unstable parameter estimates. Ridge regression is a widely adopted solution to address this challenge; however, existing ridge estimators are typically tailored to specific scenarios, limiting their universal applicability. Akhtar and Alharthi developed ridge estimators based on condition-adjusted ridge estimators (CAREs) to handle severe multicollinearity issues. However, their approach did not account for the error variances in the estimation process. In this study, we propose improvements to these CAREs by incorporating error variances, resulting in the development of multiscale ridge estimators (

M S R E_{1}

,

M S R E_{2}

,

M S R E_{3}

and

M S R E_{4}

) that more effectively address the challenges posed by severe multicollinearity. We compare the performance of our newly proposed estimators with ordinary least square (OLS) and other existing ridge estimators using both simulation studies and real-life datasets. The evaluation, based on estimated mean squared error (MSE), demonstrates that the proposed estimators consistently outperform existing methods, particularly in scenarios with significant multicollinearity, larger sample sizes, and higher predictor dimensions. Results from three real-life datasets further validate the proposed estimators’ ability to reduce estimation error and improve predictive accuracy across diverse practical applications. Full article

(This article belongs to the Special Issue Statistical Machine Learning: Models and Its Applications)

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11 pages, 276 KB

Open AccessArticle

Boundedness of Rough Multiple Oscillatory Singular Integral Operators on Triebel–Lizorkin Space

by Mohammed Ali and Hussain Al-Qassem

Mathematics 2026, 14(8), 1244; https://doi.org/10.3390/math14081244 - 9 Apr 2026

Abstract

In this article, we investigate oscillatory singular integral operators on product domains. We establish the boundedness of these operators on Triebel–Lizorkin spaces under weak assumptions on the rough kernel functions. Our results extend several known results from the one-parameter setting to the two-parameter [...] Read more.

In this article, we investigate oscillatory singular integral operators on product domains. We establish the boundedness of these operators on Triebel–Lizorkin spaces under weak assumptions on the rough kernel functions. Our results extend several known results from the one-parameter setting to the two-parameter setting. Full article

37 pages, 1897 KB

Open AccessArticle

A Bayesian Feature Weighting Model with Simplex-Constrained Dirichlet and Contamination-Aware Priors for Noisy Medical Data

by Mehmet Ali Cengiz, Zeynep Öztürk and Abdulmohsen Alharthi

Mathematics 2026, 14(8), 1243; https://doi.org/10.3390/math14081243 - 8 Apr 2026

Abstract

Feature weighting plays a central role in medical classification by enhancing predictive accuracy, interpretability, and clinical trust through the explicit quantification of variable relevance. Despite their widespread use, existing filter-, wrapper-, and embedded-based feature weighting methods are predominantly deterministic and exhibit pronounced sensitivity [...] Read more.

Feature weighting plays a central role in medical classification by enhancing predictive accuracy, interpretability, and clinical trust through the explicit quantification of variable relevance. Despite their widespread use, existing filter-, wrapper-, and embedded-based feature weighting methods are predominantly deterministic and exhibit pronounced sensitivity to label noise and outliers, which are pervasive in real-world medical data. This often results in unstable importance estimates and unreliable clinical interpretations. In this work, we introduce a novel Bayesian feature weighting model that fundamentally departs from existing approaches by jointly integrating simplex-constrained Dirichlet priors for global feature weights, hierarchical shrinkage priors for coefficient regularization, and contamination-aware priors for explicit modeling of label noise within a single coherent probabilistic framework. Unlike conventional Bayesian feature selection or robust classification models, the proposed formulation yields globally interpretable feature weights defined on the probability simplex, while simultaneously providing full posterior uncertainty quantification and robustness to both mislabeled observations and aberrant feature values through principled influence control. Comprehensive simulation studies across diverse contamination scenarios, together with applications to multiple real-world medical datasets, demonstrate that the proposed model consistently outperforms classical and state-of-the-art baselines in terms of discrimination, probabilistic calibration, and stability of feature-importance estimates. These results highlight the practical and methodological significance of the proposed framework as a robust, uncertainty-aware, and interpretable solution for medical decision making under noisy data conditions. Full article

(This article belongs to the Special Issue Statistical Machine Learning: Models and Its Applications)

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55 pages, 1130 KB

Open AccessArticle

Dirichlet–Kernel Methods for Geometric Conditional Quantiles: Bahadur Expansions and Boundary Adaptivity on the d-Simplex

by Abdulghani Alwadeai, Salim Bouzebda and Salah Khardani

Mathematics 2026, 14(8), 1242; https://doi.org/10.3390/math14081242 - 8 Apr 2026

Abstract

This article develops a boundary-adaptive nonparametric methodology for estimating the geometric conditional quantiles of a multivariate response when the conditioning covariate is supported on the simplex—an important case, as it is the natural domain of compositional data. The statistical difficulty addressed here is [...] Read more.

This article develops a boundary-adaptive nonparametric methodology for estimating the geometric conditional quantiles of a multivariate response when the conditioning covariate is supported on the simplex—an important case, as it is the natural domain of compositional data. The statistical difficulty addressed here is twofold. First, geometric conditional quantiles for multivariate responses must be defined and estimated through a genuinely directional and convex framework rather than through any scalar ordering. Second, when the covariate is compositional or otherwise simplex-constrained, conventional symmetric kernel procedures suffer from intrinsic support mismatch and severe boundary distortion, thereby compromising both estimation accuracy and inferential validity near faces and edges of the simplex. The method proposed in this paper is designed precisely to overcome this combined obstacle. Our main innovation consists in embedding the spatial quantile formalism of Chaudhuri within a Dirichlet–Kernel smoothing scheme whose shape parameters depend deterministically on the evaluation point. This produces a convex M-estimator that respects the simplex geometry exactly, automatically adapts its local shape to the position of the target point, and removes the need for artificial boundary corrections. To the best of our knowledge, this is the first contribution to provide a complete asymptotic treatment of geometric conditional quantile estimation under simplex-supported covariates with location-adaptive asymmetric kernels. We establish a Bahadur-type linear representation with an explicit negligible remainder, from which we derive refined asymptotic bias and variance expansions. The variance analysis reveals a distinctive geometric phenomenon: each coordinate direction approaching the simplex boundary induces an additional

b^{- 1 / 2}

inflation factor, so that the variance at a face of codimension

| J |

scales as

n^{- 1} b^{- (s + | J |) / 2}

. We further obtain the asymptotic mean squared error, an explicit optimal bandwidth rate, asymptotic normality under the nonstandard normalization

n^{1 / 2} b^{- s / 4}

, and consistent plug-in covariance estimators yielding valid confidence ellipsoids. Numerical experiments and a real-data illustration based on the GEMAS data confirm the practical merit of the approach, especially in boundary regions where classical methods are known to deteriorate. Full article

(This article belongs to the Section D1: Probability and Statistics)

24 pages, 1282 KB

Open AccessArticle

Estimating Network Causal Effects with Misclassified Outcomes: Evidence from Karnataka

by Yaqin Liao and Ming Lin

Mathematics 2026, 14(8), 1241; https://doi.org/10.3390/math14081241 - 8 Apr 2026

Abstract

Misclassification of binary outcomes in network settings may bias the estimates of causal effects, including spillover effects that arise from social interactions, and may generate spurious causal effects. To address this issue, we develop a parametric framework that jointly estimates misclassification probabilities and [...] Read more.

Misclassification of binary outcomes in network settings may bias the estimates of causal effects, including spillover effects that arise from social interactions, and may generate spurious causal effects. To address this issue, we develop a parametric framework that jointly estimates misclassification probabilities and causal effect parameters within a binary choice model with neighborhood exposure mappings. Monte Carlo simulations show that ignoring outcome misclassification or network-related variables leads to substantial bias, whereas the proposed method achieves a smaller bias and RMSE. By applying the method to microfinance and social network data from Karnataka, we find that under binary exposure, ignoring outcome misclassification yields statistically significant spillover and overall effects, whereas these effects become statistically insignificant once outcome misclassification is corrected for. Furthermore, omitting network-related variables overstates the direct effect. These results underscore the importance of jointly correcting for outcome misclassification and accounting for network-related variables to obtain credible causal inference. Full article

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28 pages, 2486 KB

Open AccessArticle

Sharpness Estimation of Hankel Determinants and Logarithmic Coefficients for a Family of Analytic Functions Related to a Lung-Shaped Domain

by Mohamed A. Mamon, Shams Alyusof, Rabab Alyusof and Alaa H. El-Qadeem

Mathematics 2026, 14(8), 1240; https://doi.org/10.3390/math14081240 - 8 Apr 2026

Abstract

This investigation introduces a novel family of univalent analytic functions subordinate to lung-shaped domains within the open unit disk. Through rigorous application of subordination theory and systematic analysis, we establish coefficient bounds for the initial five coefficients, derive estimates for Hankel determinants of [...] Read more.

This investigation introduces a novel family of univalent analytic functions subordinate to lung-shaped domains within the open unit disk. Through rigorous application of subordination theory and systematic analysis, we establish coefficient bounds for the initial five coefficients, derive estimates for Hankel determinants of orders two and three, determine bounds for the first four logarithmic coefficients, and derive the bounds of some Zalcman functionals. The lung-shaped domain is characterized by the subordination condition involving a secant-based function, which maps the unit disk onto a geometrically distinctive region exhibiting bilateral symmetry. All obtained bounds are demonstrated to be sharp through the construction of specific extreme functions. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions, 2nd Edition)

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30 pages, 800 KB

Open AccessFeature PaperArticle

Symmetry-Resolved Phase Transitions of Electromagnetic Degrees of Freedom Under RIS Control

by Carlos Bousoño-Calzón

Mathematics 2026, 14(8), 1239; https://doi.org/10.3390/math14081239 - 8 Apr 2026

Abstract

The theory of physical degrees of freedom (DoF) developed by Franceschetti–Migliore–Minero (FMM) establishes a fundamental phase transition in the singular-value spectrum of electromagnetic radiation operators under maximal rotational symmetry. In this work, we revisit this result from a symmetry-explicit operator-theoretic perspective and extend [...] Read more.

The theory of physical degrees of freedom (DoF) developed by Franceschetti–Migliore–Minero (FMM) establishes a fundamental phase transition in the singular-value spectrum of electromagnetic radiation operators under maximal rotational symmetry. In this work, we revisit this result from a symmetry-explicit operator-theoretic perspective and extend it to scenarios with reduced and controllable symmetries, with particular emphasis on reconfigurable intelligent surfaces (RISs). We model the radiation process as a compact operator acting between admissible source and observation spaces and characterize its symmetry through group equivariance. This formulation enables a systematic decomposition of the operator into irreducible representation sectors associated with the effective symmetry group, defined as the intersection of symmetries supported jointly by the source architecture, RIS geometry and programmability, receiver configuration, and propagation environment. We show that the FMM phase transition persists within each symmetry sector and that the total DoF budget is redistributed across sectors according to symmetry constraints. A key outcome of this analysis is the distinction between physical and effective degrees of freedom. While breaking the maximal

SO (2)

symmetry does not increase the total number of electromagnetic DoF dictated by physics, symmetry reduction modifies their allocation across sectors, potentially lifting degeneracies and increasing the number of degrees of freedom that can be effectively addressed by a given excitation, RIS control, and measurement architecture, even when the total number of physical DoF remains fixed by fundamental limits. This clarifies the role of controlled symmetry breaking as a design mechanism rather than a means to surpass fundamental limits. The proposed framework bridges electromagnetic operator theory, representation theory, and RIS-enabled system design, providing both rigorous symmetry-resolved DoF accounting and actionable insights for excitation, surface programmability, and measurement strategies under practical architectural constraints. Full article

(This article belongs to the Section E: Applied Mathematics)

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15 pages, 311 KB

Open AccessReview

Some Remarks on Fourth-Order Tensor Fields on Space-Times

by Graham Hall

Mathematics 2026, 14(8), 1238; https://doi.org/10.3390/math14081238 - 8 Apr 2026

Abstract

This paper is a contribution to Einstein’s general relativity theory and is mostly a review of known work. It concentrates attention on four fourth-order tensors which arise on the space-time manifold describing this theory and which are very useful. These are the (Riemann) [...] Read more.

This paper is a contribution to Einstein’s general relativity theory and is mostly a review of known work. It concentrates attention on four fourth-order tensors which arise on the space-time manifold describing this theory and which are very useful. These are the (Riemann) curvature tensor, the Weyl conformal tensor, the “E” tensor and the Weyl projective tensor. The first of these, the curvature tensor, plays an important role in the formulation and interpretation of Einstein’s theory. Next, the Weyl conformal tensor is introduced and its conformal properties described and with it, the Petrov classification of gravitational fields which arises from this tensor. This, in turn, gives rise to the Bel criteria for distinguishing Petrov types at a point by an alignment of certain null directions at that point. The third of these tensors, the “E” tensor, is an important tensor in calculations due to its close connection to the Ricci tensor. The fourth tensor, the Weyl projective tensor, is then described together with its properties relating to the geodesic structure of space-time. As examples of the combined usefulness of these tensors, pp-waves and generalised pp-waves are discussed and related, and a review of the geodesic structure of vacuum metrics is given. Full article

(This article belongs to the Section B: Geometry and Topology)

24 pages, 2425 KB

Open AccessFeature PaperArticle

ReDyGait: Representation Disentanglement with Gated Attention for Invariant-Contextual Transfer in Stance Detection

by Yanzhou Ma, Yun Luo and Mingyang Peng

Mathematics 2026, 14(7), 1237; https://doi.org/10.3390/math14071237 - 7 Apr 2026

Abstract

Cross-topic stance detection degrades when encoders entangle stance signals with topic-specific vocabulary, causing representations that fail to transfer to unseen targets. Existing methods commit to either topic-invariant or topic-aware representations and apply the same strategy uniformly to every input, sacrificing complementary information. We [...] Read more.

Cross-topic stance detection degrades when encoders entangle stance signals with topic-specific vocabulary, causing representations that fail to transfer to unseen targets. Existing methods commit to either topic-invariant or topic-aware representations and apply the same strategy uniformly to every input, sacrificing complementary information. We propose ReDyGait, a three-stage framework that disentangles these two types of signals through dedicated contrastive pre-training and recombines them adaptively at inference time. Stage 1 trains a topic-invariant encoder with supervised contrastive loss over cross-topic positives. Stage 2 trains a topic-contextual encoder with bidirectional pair contrastive loss over within-topic positives; both stages employ topic-aware hard negative mining to prevent shortcut learning. Stage 3 freezes the two contrastive encoders and learns a gating network that produces per-instance weights over invariant, contextual, and base-encoder pathways. On VAST, ReDyGait achieves a macro-averaged F1 of 0.782 in the zero-shot setting and 0.752 in the few-shot setting, improving over the strongest baseline by 1.1 points in both; on SEM16t6 in a leave-one-target-out setup, ReDyGait reaches an average F1 of 0.612. Analysis of the learned gate weights shows that the model shifts toward the invariant pathway for unfamiliar topics and toward the contextual pathway when topic-specific patterns are available, confirming that the disentanglement operates as intended. Full article

(This article belongs to the Special Issue Machine Learning and Graph Neural Networks)

29 pages, 8022 KB

Open AccessArticle

Quantum-Inspired Variational Inference for Non-Convex Stochastic Optimization: A Unified Mathematical Framework with Convergence Guarantees and Applications to Machine Learning in Communication Networks

by Abrar S. Alhazmi

Mathematics 2026, 14(7), 1236; https://doi.org/10.3390/math14071236 - 7 Apr 2026

Abstract

Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational [...] Read more.

Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational Inference (QIVI) framework, which systematically integrates quantum mechanical principles (superposition, entanglement, and measurement operators) into classical variational inference through rigorous mathematical formulations grounded in Hilbert space theory and operator algebras. We develop a unified optimization framework that encodes classical parameters as quantum-inspired states within finite-dimensional complex Hilbert spaces, employing unitary evolution operators and adaptive basis selection governed by gradient covariance eigendecomposition. The core mathematical contribution establishes that QIVI achieves a convergence rate of

O ({log}^{2} T / T^{1 / 2})

for

σ

-strongly non-convex functions, provably improving upon the classical

O (T^{- 1 / 4})

rate, yielding a theoretical speedup factor of

1.85

–

1.96 \times

. Comprehensive experiments across synthetic benchmarks, Bayesian neural networks, and real-world applications in network optimization and financial portfolio management demonstrate 23–

47 %

faster convergence, 15–

35 %

superior objective values, and 28–

46 %

improved uncertainty calibration. The principal contributions include: (i) a rigorous Hilbert space-based mathematical framework for quantum-inspired variational inference grounded in operator algebras, (ii) a novel hybrid quantum–classical algorithm (QIVI) with adaptive basis selection via gradient covariance eigendecomposition, (iii) formal convergence proofs establishing provable improvement over classical methods, (iv) comprehensive empirical validation across diverse problem domains relevant to machine learning and network optimization, and (v) demonstration of the framework’s applicability to optimization problems arising in wireless networks, data center resource allocation, and network system design. Statistical validation using the Friedman test (

χ^{2} = 847.3

,

p < 0.001

) and post hoc Wilcoxon signed-rank tests with Holm–Bonferroni correction confirm that QIVI’s improvements over all baseline methods are statistically significant at the

α = 0.05

level across all benchmark categories. The framework discovers

18.1

out of 20 true modes in multimodal distributions versus

9.1

for classical methods, demonstrating the potential of quantum-inspired optimization approaches for challenging stochastic problems arising in machine learning, wireless communication, and network optimization. Full article

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23 pages, 9838 KB

Open AccessArticle

Bimodal Image Fusion and Brightness Piecewise Linear Enhancement for Crack Segmentation

by Yong Li, Nian Ji, Fuzhe Zhao, Huaiwen Zhang, Zeqi Liu, Laxmisha Rai and Zhaopeng Deng

Mathematics 2026, 14(7), 1235; https://doi.org/10.3390/math14071235 - 7 Apr 2026

Abstract

Accurate segmentation of structural cracks is a core prerequisite for quantifying crack parameters, assessing damage severity, and providing early warning of structural safety. However, different types of structures exhibit significant individual variations in features such as color, texture, and brightness. Consequently, commonly used [...] Read more.

Accurate segmentation of structural cracks is a core prerequisite for quantifying crack parameters, assessing damage severity, and providing early warning of structural safety. However, different types of structures exhibit significant individual variations in features such as color, texture, and brightness. Consequently, commonly used image segmentation algorithms struggle to establish a universal mathematical model, making it challenging to robustly identify and precisely segment crack targets amidst multi-feature disparities. To address the issue, this paper proposes a crack-segmentation algorithm based on bimodal image fusion and brightness piecewise linear enhancement (CSA-BB), and further enables parameter extraction and crack monitoring. The algorithm utilizes the complementary properties of visible-light and pseudo-color images for bimodal image fusion, thereby enhancing the detailed features of cracks. Furthermore, a brightness piecewise linear function has been devised that automatically selects appropriate parameters for image enhancement of structural cracks across varying background brightness. Subsequently, the crack region is effectively segmented using the bottom-hat transform and the OTSU algorithm. Ultimately, the crack’s safety level is determined from the acquired crack parameters, thereby enabling effective monitoring and assessment of the crack development process. In this paper, the proposed method achieves the best segmentation performance with a Dice coefficient of 0.4511 and a Jaccard index of 0.2981. Compared to the second-best algorithm, it yields significant improvements of 26.9% and 34.5%, respectively, demonstrating higher consistency with the ground truth. Moreover, superior computational efficiency and robustness are achieved, fulfilling the operational demands of real-world engineering environments. Full article

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35 pages, 474 KB

Open AccessReview

Developments in Modular Space Fixed Point Theory

by Wojciech M. Kozlowski

Mathematics 2026, 14(7), 1234; https://doi.org/10.3390/math14071234 - 7 Apr 2026

Abstract

This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that satisfy pointwise asymptotic nonexpansive and contractive conditions in the [...] Read more.

This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that satisfy pointwise asymptotic nonexpansive and contractive conditions in the modular sense, and the results can also be applied directly to Banach spaces. Utilizing the framework of regular and super-regular modular spaces, our research generalizes several established results concerning fixed points of nonlinear operators, applicable to both Banach spaces and modular function spaces. The study seeks to identify and discuss current challenges, knowledge gaps, and unresolved questions, providing insights into the potential of future research opportunities. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)

21 pages, 586 KB

Open AccessArticle

Analysing Digital Government Performance Indicators Using a Clustering Technique-Embedded Fuzzy Decision-Making Framework

by Mehmet Erdem, Akın Özdemir, Hatice Yalman Kosunalp and Bozhana Stoycheva

Mathematics 2026, 14(7), 1233; https://doi.org/10.3390/math14071233 - 7 Apr 2026

Abstract

Digital transformation is reshaping societies by promoting the adoption of advanced technologies. Moreover, the digitization of public services has become an important focus for governments. In this paper, digital government performance indicators are analyzed to improve the efficiency of digitizing public services. Based [...] Read more.

Digital transformation is reshaping societies by promoting the adoption of advanced technologies. Moreover, the digitization of public services has become an important focus for governments. In this paper, digital government performance indicators are analyzed to improve the efficiency of digitizing public services. Based on this awareness, the seven main criteria and twenty-one sub-criteria are determined. Then, a fuzzy decision-making framework is proposed to evaluate digital government performance across 165 countries as alternatives. To the best of our knowledge, limited studies have investigated an integrated clustering-based fuzzy decision-making framework for evaluating digital government performance. The intuitionistic trapezoidal fuzzy number-based analytical hierarchy process (ITFNAHP), a part of the introduced framework, is developed to find the weights of the main criteria and sub-criteria. Digital technologies, innovation, and the economy are the most significant criteria for digital government operations. The k-means clustering method is then employed to group the alternatives. The four clusters are obtained from the clustering technique. Next, the technique of order preference similarity to ideal solution (TOPSIS) is introduced to rank the digital governments of each cluster. Switzerland, Rwanda, North Macedonia, and Eswatini are the top choices among others in each cluster, respectively. Additionally, a sensitivity analysis is conducted considering the ten different situations. In addition, the managerial and policy implications are discussed, including the achievement of Sustainable Development Goals (SDGs). Full article

(This article belongs to the Special Issue Advances in Multiple-Criteria Decision Making: New Trends and Applications)

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27 pages, 3039 KB

Open AccessArticle

Dynamic Fee Markets at Sub-Second Timescales: Adapting EIP-1559 for High-Throughput Blockchains

by Petar Zhivkov and Eric Chen

Mathematics 2026, 14(7), 1232; https://doi.org/10.3390/math14071232 - 7 Apr 2026

Abstract

Dynamic fee market mechanisms, exemplified by EIP-1559, have been extensively studied for Ethereum’s 12 s block environment but remain uncharacterized at sub-second timescales. We present an agent-based simulation study of an EIP-1559 adaptation for Injective, a Layer 1 blockchain combining native EVM compatibility [...] Read more.

Dynamic fee market mechanisms, exemplified by EIP-1559, have been extensively studied for Ethereum’s 12 s block environment but remain uncharacterized at sub-second timescales. We present an agent-based simulation study of an EIP-1559 adaptation for Injective, a Layer 1 blockchain combining native EVM compatibility with CometBFT consensus, operating at 600 ms block times. Across twelve simulation runs (four parameter configurations × three demand scenarios), our analysis yields three findings: (1) temporal smoothing mechanisms (MA-25, 25-block trailing average) produce mixed effects in sub-second environments with up to 47% basefee overshoot during spam attacks and slight smoothing elsewhere, making per-block mechanisms preferable for consistent performance; (2) transitioning from 150M (66.66% target) to 300M (50% target) configuration reduces peak fees by 31% during variable demand; during spam attacks, the 300M configuration peaks 32% higher but recovers faster with block capacity as the primary driver for spam throughput; and (3) per-block mechanisms establish initial spam barriers within 17–32 s versus Ethereum’s 4–6 min, economically justifying lower minimum fees. We provide the first systematic sub-second EIP-1559 analysis and a parameter optimization framework for high-throughput chains. With proper tuning, dynamic fee mechanisms are compatible with high-throughput architectures. Full article

(This article belongs to the Special Issue Mathematical Foundations of Blockchain Technology)

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68 pages, 7738 KB

Open AccessReview

An Overview of Complex Time Series Analysis

by Alejandro Ramírez-Rojas, Leonardo Di G. Sigalotti, Luciano Telesca and Fidel Cruz

Mathematics 2026, 14(7), 1231; https://doi.org/10.3390/math14071231 - 7 Apr 2026

Abstract

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including [...] Read more.

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including seismicity and climatic processes. The study of these complex systems is commonly based on the analysis of the signals they generate, using mathematical tools to extract relevant information. A broad spectrum of mathematical disciplines converges in this context, including stochastic, probability and statistical theory, entropic and informational measures, fractal and multifractal analysis, natural time analysis, modeling of non-linearity and recurrence methods, generalized entropies, non-extensive systems, machine learning, and high-dimensional and multivariate complexity. Research in this area is largely focused on the characterization of complex systems, providing indicators of determinism or stochasticity, distinguishing between regularity, chaos, and noise, and identifying topological as well as disorder-regularity features. In addition, short- and long-term forecasting, together with the identification of short- and long-range correlations, play a central role in such characterization. To address these objectives, numerous mathematical tools have been developed for the analysis of time series and point processes, each designed to capture specific signal properties. In this work, many of the most important tools used in time series analysis are compiled and reviewed, highlighting their main characteristics and the different types of complex systems to which they have been applied. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis, 2nd Edition)

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21 pages, 3856 KB

Open AccessArticle

Metal Artifact Reduction in CT Based on a Nonlinear Weighted Anisotropic TV Regularization

by Shuangyang Liu, Haiyang Wang and Yizhuang Song

Mathematics 2026, 14(7), 1230; https://doi.org/10.3390/math14071230 - 7 Apr 2026

Abstract

Metal artifact reduction (MAR) remains a long-standing challenge in computed tomography (CT) reconstruction. Metallic implants introduce inconsistencies between the acquired projection data and the ideal Radon transform, resulting in severe streaking artifacts in images reconstructed using the conventional filtered back projection (FBP) algorithm. [...] Read more.

Metal artifact reduction (MAR) remains a long-standing challenge in computed tomography (CT) reconstruction. Metallic implants introduce inconsistencies between the acquired projection data and the ideal Radon transform, resulting in severe streaking artifacts in images reconstructed using the conventional filtered back projection (FBP) algorithm. In this work, we propose a nonlinear weighted anisotropic total variation (NWATV) regularization method to mitigate metal artifacts and improve CT image quality. The effectiveness of the NWATV method is evaluated through three experiments, and the results demonstrate that it achieves superior reconstruction performance compared to the conventional linear interpolation method, the normalized metal artifact reduction method and the anisotropic total variation (TV) regularization method. Full article

(This article belongs to the Special Issue Inverse Problems in Science and Engineering)

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30 pages, 2308 KB

Open AccessArticle

Early Detection of Virtual Machine Failures in Cloud Computing Using Quantum-Enhanced Support Vector Machine

by Bhargavi Krishnamurthy, Saikat Das and Sajjan G. Shiva

Mathematics 2026, 14(7), 1229; https://doi.org/10.3390/math14071229 - 7 Apr 2026

Abstract

Cloud computing is one of the essential computing platforms for modern enterprises. A total of 84 percent of large businesses use cloud computing services in 2025 to enable remote working and higher flexibility of operation with reduction in the cost of operation. Cloud [...] Read more.

Cloud computing is one of the essential computing platforms for modern enterprises. A total of 84 percent of large businesses use cloud computing services in 2025 to enable remote working and higher flexibility of operation with reduction in the cost of operation. Cloud environments are dynamic and multitenant, often demanding high computational resources for real-time processing. However, the cloud system’s behavior is subjected to various kinds of anomalies in which patterns of data deviate from the normal traffic. The varieties of anomalies that exist are performance anomalies, security anomalies, resource anomalies, and network anomalies. These anomalies disrupt the normal operation of cloud systems by increasing the latency, reducing throughput, frequently violating service level agreements (SLAs), and experiencing the failure of virtual machines. Among all anomalies, virtual machine failures are one of the potential anomalies in which the normal operation of the virtual machine is interrupted, resulting in the degradation of services. Virtual machine failure happens because of resource exhaustion, malware access, packet loss, Distributed Denial of Service attacks, etc. Hence, there is a need to detect the chances of virtual machine failures and prevent it through proactive measures. Traditional machine learning techniques often struggle with high-dimensional data and nonlinear correlations, ending up with poor real-time adaptation. Hence, quantum machine learning is found to be a promising solution which effectively deals with combinatorially complex and high-dimensional data. In this paper, a novel quantum-enhanced support vector machine (QSVM) is designed as an optimized binary classifier which combines the principles of both quantum computing and support vector machine. It encodes the classical data into quantum states. Feature mapping is performed to transform the data into the high-dimensional form of Hilbert space. Quantum kernel evaluation is performed to evaluate similarities. Through effective optimization, optimal hyperplanes are designed to detect the anomalous behavior of virtual machines. This results in the exponential speed-up of operation and prevents the local minima through entanglement and superposition operation. The performance of the proposed QSVM is analyzed using the QuCloudSim 1.0 simulator and further validated using expected value analysis methodology. Full article

(This article belongs to the Special Issue Emerging Applications of Artificial Intelligence Algorithms in Computer and Network Security)

34 pages, 1260 KB

Open AccessArticle

Conformally Compactified Minkowski Space: A Re-Examination with Emphasis on the Double Cover and Conformal Infinity

by Arkadiusz Jadczyk

Mathematics 2026, 14(7), 1228; https://doi.org/10.3390/math14071228 - 7 Apr 2026

Abstract

This paper presents a detailed re-examination of the conformalcompactification

\bar{M}

of Minkowski space

M

, constructed as the projective null cone of the six-dimensional space

R^{4, 2}

. We provide an explicit and basis-independent formulation, emphasizing geometric clarity. A central [...] Read more.

This paper presents a detailed re-examination of the conformalcompactification

\bar{M}

of Minkowski space

M

, constructed as the projective null cone of the six-dimensional space

R^{4, 2}

. We provide an explicit and basis-independent formulation, emphasizing geometric clarity. A central result is the explicit identification of

\bar{M}

with the unitary group

U (2)

via a diffeomorphism, offering a clear matrix representation for points in the compactified space. We then systematically construct and analyze the action of the full conformal group

O (4, 2)

and its connected component

{SO}_{0} (4, 2)

on this manifold. A key contribution is the detailed study of the double cover,

\tilde{M}

, which is shown to be diffeomorphic to

S^{3} \times S^{1}

. This construction resolves the non-effectiveness of the

SO (4, 2)

action on

\bar{M}

, yielding an effective group action on the covering space. A significant portion of our analysis is devoted to a precise and novel geometric characterization of the conformal infinity. Moving beyond the often-misrepresented “double cone” description, we demonstrate that the infinity of the double cover,

{\tilde{M}}_{\infty}

, is a squeezed torus (specifically, a horn cyclide), while the simple infinity,

{\bar{M}}_{\infty}

, is a needle cyclide. We provide explicit parametrizations and graphical representations of these structures. Finally, we explore the embedding of five-dimensional constant-curvature spaces, whose boundary is the compactified Minkowski space. The paper aims to clarify long-standing misconceptions in the literature and provides a robust, coordinate-free geometric foundation for conformal compactification, with potential implications for cosmology and conformal field theory. Full article

(This article belongs to the Section E4: Mathematical Physics)

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