A Mathematical Framework for Adaptive Rolling Conformal Quantile Boosting under Temporal Distribution Shift: Application to Hour-Ahead PM2.5 Forecast Intervals

Aiyared Iampan; Said Broumi

doi:https://doi.org/10.54216/PAMDA.050203

International Journal of Neutrosophic Science | 2026

Solution of Intuitionistic Fuzzy System of Linear Volterra Integro-differential Equations by a Novel Hybrid Method

Our study addresses the intuitionistic fuzzy system of linear Volterra-integro-differential equations of the second kind. Intuitionistic fuzzy General Transform (I-F-G-transform) method has been used to find the exact solution of these systems. We present two numerical examples for illustrating the applicability of the Intuitionistic fuzzy General integral transform method.

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Guelfen hanane mail

link https://doi.org/10.54216/IJNS.270227

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

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Fusion: Practice and Applications | 2026

Cryptanalysis In Block Ciphers: A Comprehensive Review and Future Directions

This paper examines the use of cryptography in block ciphers and assesses their security, with a focus on the Advanced Encryption Standards (AES). The study reviews key cryptanalytic techniques, including differential cryptanalysis (8.3%), linear cryptanalysis (4.2%), and integral cryptanalysis (4.2%). They give their share (in percentage) regarding the relative frequency in the cryptanalysis research literature from 2015 to 2024 according to their literature survey. Side-channel attacks showed the highest practical success rates, with some studies showing up to 50.0% effectiveness. Additionally, the study examines more sophisticated attack techniques such as meet-in-the-middle attacks, quantum-related threats, and biclique cryptanalysis (16.0%).The entire round AES is resistant to a wide range of attack techniques thanks to its strong diffusion and confusion mechanisms and reliable key schedule. The study concludes that cryptanalysis is essential for strengthening encryption schemes against emerging threats, particularly those resulting from quantum computing.

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Lama Al-Ghamdi mail -

Mawada Al-Sari mail -

Monir Abdullah mail -

Ghassan Ahmed Ali mail

link https://doi.org/10.54216/FPA.210211

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

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Fusion: Practice and Applications | 2026

Development of an Efficient Cluster-Based Hybrid LEACH+TEEN Protocol for Time-Critical WSN Application

Wireless Sensor Networks (WSNs) play a crucial role in monitoring and data collection for various real-time applications, including environmental surveillance, industrial automation, and smart cities. However, achieving energy efficiency and timely data delivery remains a critical challenge, especially in time-sensitive scenarios. This research presents the development of an efficient cluster-based hybrid routing protocol that combines the strengths of Low-Energy Adaptive Clustering Hierarchy (LEACH) and Threshold-sensitive Energy Efficient Network (TEEN) protocols to address these challenges. The proposed Hybrid LEACH-TEEN protocol dynamically adapts to both periodic and event-driven data transmission needs by integrating LEACH’s randomized cluster-head selection and TEEN’s threshold- based data transmission mechanism. This hybrid approach significantly reduces redundant transmissions and optimizes energy consumption across the network. Extensive simulations were conducted to evaluate the protocol’s performance in terms of network lifetime, stability period, energy consumption, and the number of alive nodes over time. Results demonstrate that the Hybrid protocol outperforms traditional LEACH and TEEN protocols, particularly in time- critical applications, by ensuring prompt response to critical events while maintaining energy-efficient operation. This work contributes to the design of intelligent and adaptive routing strategies for next- generation WSNs.

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Basim Jamil Ali mail -

Mohanad Ali Meteab Al-Obaidi mail

link https://doi.org/10.54216/FPA.210212

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

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Journal of Intelligent Systems and Internet of Things | 2026

A Systematic Review on Classification Techniques of Microorganisms: Challenges and Recommendations – Towards Medical Intelligent Systems

Microorganisms are commonly found in our daily living environments and play a crucial role in environmental pollution control, disease prevention, and treatment, as well as food and drug production. To fully utilize the diverse functions of microorganisms, their analysis is essential using Intelligent Systems. Traditional analysis methods can be labor- intensive and time-consuming. As a result, image analysis using Intelligent Systems i.e. machine learning or deep learning have been introduced to improve efficiency. Deep learning networks algorithms such as CNN contain a stack of multi-layer, the first layer and the last are the input and output layers, between them are the hidden layers to extract and learn many features in images, recurrent network algorithms (RNN) combined with convolution neural network (CNN), these networks allow to process a series of images to extract the crucial information from images and also these algorithms help to minimize the size of images and reduce the redundancy in microrganisms images According to previous studies, these algorithms are the most used to classify the images of microorganisms. However, the classification of microorganism images presents several challenges these include the need for robust algorithms due to varying application contexts, the presence of insignificant features, along various analysis tasks that need to be addressed. The research summarizes significant advancements that tackle these challenges through deep learning and machine learning methods. Current obstacles, gaps in knowledge, unresolved issues, limitations, and difficulties in classification techniques are also discussed.

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Marwa T. Albayati mail -

Mohd Ezanee Bin Rusli mail -

Moamin A. Mahmoud mail -

Aws A. Abdulsahib mail -

Mohammed F. Alomari mail -

Sallar S. Murad mail

link https://doi.org/10.54216/JISIoT.180224

Volume & Issue

Vol. Volume 18 / Iss. Issue 2

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Prospects for Applied Mathematics and Data Analysis | 2025

Some Special Types of Neutrosophic Domains

The neutrosophic ring cannot be an integral domain, but the pseudo-neutrosophic ring could be an integral domain. The main objective of this paper is to present and study some special types of neutrosophic domains, which has not been studied before, such as integral domains.

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Shawqi Al-lkami mail -

Adel Al-odhari mail

link https://doi.org/10.54216/PAMDA.050103

Volume & Issue

Vol. Volume 5 / Iss. Issue 1

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Prospects for Applied Mathematics and Data Analysis | 2026

Spectrally Matched Fractional Sobolev Tikhonov Regularization for Periodic Deconvolution

Let T = R/Z and Aβ = (I−Δ)−β/2 with β > 0. From data gδ = Aβ f †+η, ∥η∥2 ≤ δ, consider the fractional Sobolev Tikhonov family f δ λ,s = argminf∈Hs(T) Aβ f −gδ 2 2 +λ ∥ f ∥2 Hs, s ≥ 0. Writing μk = (1+4π2k2)1/2 and ρ = s+β, the estimator is diagonal in the Fourier basis, bf δ λ,s(k) = μβ k 1+λ μ2ρ k bgδ (k). If f † ∈ Hr(T) and 0 < r ≤ 2ρ, then f δ λ,s− f † 2 ≤Caδλ−a+CbMrλb, a = β 2ρ , b = r 2ρ , Mr = f † Hr . where Cq = qq(1−q)1−q for 0 < q < 1 and C1 = 1. Direct minimization gives λ∗ ≍ δ2ρ (r+β) and f δ λ∗,s− f † 2 = O δr/(r+β). Thus the pre-saturation exponent is independent of the penalty order s. When r > 2ρ, the bias saturates and the rate becomes O(δ2ρ/(2ρ+β)); hence the least order avoiding saturation is smin = max{0, r/2−β}. The balanced half-power frequency satisfies μc ≍ δ−1/(r+β), whereas its logarithmic roll-off is −ρ/2. The same exponents persist for spectrally equivalent convolution operators c−μ−β k ≤ ak ≤ c+μ−β k . Fourier experiments on N = 2048 modes, using three source regularities, four penalty orders, five noise levels, and 30 perturbations per configuration, reproduce the predicted saturation ordering and transition boundary. For the H6 benchmark at δ = 10−3, the mean L2 error decreases from 1.4013×10−2 for s = 0 to 1.2710×10−3 for s = 2; the latter is the first tested order in the non-saturated regime.

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Takaaki Fujita mail -

Ajoy Kanti Das mail

link https://doi.org/10.54216/PAMDA.060101

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Prospects for Applied Mathematics and Data Analysis | 2026

A Symmetric Discrete-Gradient Finite-Volume Method for Positive Drift–Diffusion Flows

Consider the periodic gradient flow ∂tu = ∂x(m(u)∂xμ) , μ = h′(u)+V, E [u] = Z 1 0 {h(u)+Vu} dx, for strictly positive density u, convex entropy density h, and mobility m > 0. We couple a centered finite-volume flux with a symmetric two-state approximation of the chemical potential. Its entropy component is the divided difference Dh(a,b) = h(a)−h(b) a−b , Dh(a,a) = h′(a), which enforces the discrete chain rule exactly. With midpoint edge mobility and the logarithmic state un+1 i =expzn+1 i , the nonlinear update is self-adjoint and, for every solved algebraic step, satisfies E n+1 h −E n h = −ΔtΣi M n+1/2 i+1/2 (μn+1/2 i+1 −μn+1/2 i )2 Δx ≤ 0. The flux telescopes to conserve mass, the logarithmic parametrization confines finite roots to the positive cone, and states satisfying h′(ui)+Vi = const are fixed points. A midpoint expansion gives second-order consistency in time; the centered flux gives the same order in space. For h(u) = u(logu−1), a manufactured heat-flow calculation gives observed L2 orders 1.998 and 1.999 under coupled refinement. In a confining Fokker–Planck test, the maximum mass defect is 3.20×10−14 and the energy identity is satisfied within 1.42×10−14. Replacing Dh by the midpoint chemical potential in the same one-step problem produces an energy-balance defect 1.60×10−2, isolating the role of the temporal discrete gradient.

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Sergey Drominko mail -

Erina Kovachiskaya mail

link https://doi.org/10.54216/PAMDA.060103

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Prospects for Applied Mathematics and Data Analysis | 2026

Heat-Semigroup Persistence on Data Graphs: A Multiscale Extension of Normalized Cut for Class-Separability Analysis

Let G = (V,W) be a weighted data graph with symmetric normalized Laplacian L = I−D−1/2WD−1/2, and let u denote the degree-balanced signal associated with a binary partition C∪ ¯C =V. Instead of reducing the partition geometry to the single Rayleigh quotient u⊤Lu/∥u∥22 , we study the heat-semigroup persistence Pu(t) = ∥e−tLu∥22 ∥u∥22 , HT (u) = 1 T Z T 0 Pu(t)dt. Writing Lφj = λjφj and ωj = |⟨u,φj⟩|2/∥u∥22 yields Pu(t) = Σj ωje−2tλj , so the complete curve is the Laplace transform of the label spectral measure νu = Σj ωjδλj . We prove four identities that give this construction a cut-theoretic interpretation. First, Pu is completely monotone. Second, −P′u(0)/2 = Ncut(C, ¯C). Third, for the instantaneous leakage rate κu(t) = −12 d logPu(t)/dt, one has κu(0) = Ncut and κ′u (t) = −2Varνu,t (λ) ≤ 0 under the exponentially tilted spectral measure. Fourth, when u ⊥ kerL, R ∞ 0 Pu(t)dt = u⊤L†u/(2∥u∥22). Hence normalized cut is only the zero-time slope of a multiscale diffusion object whose higher derivatives recover all spectral moments. A perturbation bound |HT (L)−HT (eL)| ≤ T∥L−eL∥2 is also established for a fixed partition signal. Numerical evaluation on a 1,797-sample, 64-variable handwritten-digit benchmark uses all 45 class pairs and ten repeated stratified train/test splits. With graphs formed exclusively from training observations, mean H1 has Spearman correlation −0.924 with held-out pairwise error (95% bootstrap interval [−0.957,−0.850]); normalized cut gives 0.927, and the second spectral central moment gives 0.930. The comparable predictive rankings are material: the proposed functional is not presented as a replacement for normalized cut, but as its multiscale completion, retaining spectral information that a first moment necessarily discards.

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Nader Taffach mail -

Mohammad Al-Shiekh mail

link https://doi.org/10.54216/PAMDA.060102

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

Comparative Study of Two Optimization Algorithms for Solving Nonlinear Differential Equations: A Performance Analysis

The purpose of this work was to benchmark three population-based metaheuristic optimizers—Particle Swarm Optimization, Differential Evolution, and Grey Wolf Optimizer—when used to solve nonlinear ordinary differential equations within the Neural Network Trial Solution methodology. Problems used for testing were the Riccati initial value problem, the nonlinear pendulum IVP, the Bratu boundary value problem, and the Lane-Emden equation with index five. All problems were implemented such that their boundary/initial conditions were satisfied exactly through analytical construction while their residuals at collocation points were minimized through unconstrained optimization. Thirty Monte Carlo runs of each algorithm were performed with same underlying settings to facilitate statistical comparisons between algorithms. Metrics used for comparisons were mean absolute error (MAE), root mean square error (RMSE), maximum error at any point, and rate of convergence. All significant testing was performed with the Wilcoxon signed-rank test. PSO is shown to consistently provide the smallest mean absolute error across three of the four problems, with an MAE as small as 2.78×10−5 on the Bratu BVP, while GWO was shown to stagnate prematurely when solving boundary value problems.

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Qasim Tayyeh mail

link https://doi.org/10.54216/PMTCS.060201

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

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Prospects for Applied Mathematics and Data Analysis | 2025

A Mathematical Framework for Adaptive Rolling Conformal Quantile Boosting under Temporal Distribution Shift: Application to Hour-Ahead PM2.5 Forecast Intervals

Prediction intervals for temporally dependent data require both conditional quantile estimation and a calibration mechanism capable of responding to distribution shift. An adaptive rolling conformal quantile boosting (ARCQB) formulation is developed in which boosted quantile functions provide a nonlinear base interval and a sequential state variable controls the empirical conformal quantile. For target miscoverage 𝛼, the calibration state follows a projected stochastic recurrence, 𝛼𝑡+1 = ΠA{𝛼𝑡 + 𝛾(𝛼 − 𝑒𝑡 )}, where 𝑒𝑡 is the realized miss indicator. A telescoping identity links the time-averaged miss frequency to the state displacement and projection residuals; in the unprojected bounded case, the calibration error is 𝑂(𝑇−1). The interval width admits the exact decomposition 𝑤𝑡 = 𝑤(0) 𝑡 + 2𝑞𝑡 , separating predictive sharpness from conformal inflation. Numerical evaluation uses a strictly chronological one-hour-ahead design on hourly Beijing air-quality measurements. For nominal 90% coverage, raw boosted quantiles attain 83.18%, static conformal calibration 87.40%, and rolling conformal calibration 89.87%. ARCQB attains 90.05% with mean width 47.14 𝜇gm−3 and the lowest interval score, 72.86. Its maximum seasonal coverage deviation is 0.38 percentage points, compared with 7.99 points for the uncalibrated interval. The numerical behavior is therefore consistent with the feedback relation predicted by the calibration dynamics, while high-pollution regimes remain the principal source of conditional under-coverage.

groups

Aiyared Iampan mail -

Said Broumi mail

link https://doi.org/10.54216/PAMDA.050203

Volume & Issue

Vol. Volume 5 / Iss. Issue 2

Details open_in_new