The classical cognitive models are often formulated in terms of dynamics with the assumption of decomposability. In this formulation, the mind is considered to be a simple machine processing discrete pieces of information, and the decisions are considered to be linear combinations of these pieces. However, these models are not able to represent the complex nature of human thought. This paper proposes a new collective level quantum dynamics model. To reduce the complexity involved
in massive subject cognition, this paper attempts to develop and simulate a new quantum dynamics model for the non-decomposable collective cognitive decision-making process in a financial setting, where we are concerned with the interaction between two or more agents. This procedure involves specifying the collective state space, specifying a collective Hamiltonian that represents the social interaction, simulating the joint cognitive process, and computing the probabilities of the outcomes. The method specifies the joint decision space as a finite dimensional Hilbert space. The Collective Hamiltonian is comprised of personal preference, intrinsic elements, and macroscopic non-decomposable social interactions. The time-evolution of the collective mental state is modeled by numerically solving the Time Dependent Schr¨odinger Equation. The primary result is the final collective decision probability, which can be determined by applying the Born Rule to calculate the square length of the projection of the time-evolved state vector onto the corresponding basis states for each of the four possible outcomes. This calculation yields the time-dependent probability of the group reaching a particular end-point financial decision. These results are then used in an AI-integrated research protocol with tensor networks and other advanced quantum cognitive AI processes for visualization to produce a Dynamic Probability Profile. Validation is performed using a cross-validation technique by setting aside 30% of the sample space data for validation purposes only after completing the research with the remaining 70%

Reconstructing a 3D solid from its orthographic projections is a classical problem in computational geometry and computer-aided design (CAD). Although humans perform this task intuitively in technical drawing, algorithmic reconstruction is non-trivial due to ambiguity and incomplete spatial information.

This paper presents a semi-constructive computational method for reconstructing 3D polyhedral solids from orthographic projections (front, top, and side views). The approach integrates planar decomposition, graph-based cycle analysis, and a Winged-Edge boundary representation (BRep) structure to ensure geometric and topological consistency. Unlike universal reconstruction algorithms, the proposed method targets structured polyhedral objects and progressively refines candidate 3D edges through topological filtering. The methodology includes DXF parsing, vertex inference, candidate segment generation via planar intersections, cycle-based internal edge elimination, collinearity merging, and final BRep construction. The experimental results demonstrate correct reconstruction for a representative class of polyhedral objects and highlight both strengths and current limitations of the approach.

The method does not aim to solve the universal reconstruction problem but instead focuses on a structured family of polyhedral solids whose faces are predominantly planar and frequently parallel to projection planes.

The main contributions are as follows:

-A pipeline integrating 2D DXF parsing with 3D vertex inference.

-Exhaustive candidate segment generation using planar intersections.

-Graph-based cycle analysis to eliminate internal edges. \item A consistent Winged-Edge BRep construction.

-Export to STL with correct face orientation.

Artificial Intelligence (AI) models rely on loss functions as fundamental optimization tools to quantify the discrepancy between predicted and observed outputs. The mathematical properties of these functions, including convexity, differentiability, and sensitivity to input variations, directly influence model stability, convergence, and robustness. However, loss functions are often selected empirically with limited theoretical justification, which may result in unstable or suboptimal performance. This study investigates the impact of loss function design on AI model stability, focusing on Mean Squared Error (MSE) and Huber Loss. The methodology combines mathematical analysis with simulation-based experiments. The convexity and convergence behavior of MSE were examined through its first and second derivatives, while Huber Loss was analyzed for its piecewise structure and robustness to outliers. Linear regression models were trained on a housing dataset using both loss functions under identical conditions. Model performance was evaluated using multiple metrics, including MSE, MAE, RMSE, prediction variance, and sensitivity to noisy inputs. Experimental results indicate that the MSE-based model achieved lower test error (MSE ≈ 6.56 × 10⁹; RMSE ≈ 81,000) and slightly better overall stability on clean data. In contrast, Huber Loss produced a lower MAE (≈ 58,877), demonstrating greater robustness to absolute deviations and outliers. Variance analysis showed marginally higher prediction variability for the Huber model, while noise perturbation experiments confirmed that both methods experienced performance degradation, with MSE remaining slightly more stable. Overall, the findings demonstrate that the mathematical structure of loss functions significantly affects model behavior. While MSE provides superior accuracy under normal conditions, Huber Loss offers improved robustness in noisy or outlier-prone settings. These insights provide practical guidance for selecting appropriate loss functions to enhance stability and reliability in supervised learning applications.

This study evaluates the potential of near-term quantum computing for combinatorial optimization, using the Traveling Salesman Problem (TSP) as a canonical benchmark. Using Qiskit, we construct a hybrid quantum-classical workflow based on the Quantum Approximate Optimization Algorithm (QAOA) and then assess its performance on symmetric TSP instances compared to classical exact methods (Gurobi solver). The Miller–Tucker–Zemlin formulation is implemented to create a Quadratic Unconstrained Binary Optimization (QUBO) encoding. Our findings show that conventional branch-and-bound solvers significantly outperform QAOA in both solution quality and runtime on existing hardware, even though QAOA successfully produces feasible tours. On Noisy Intermediate-Scale Quantum (NISQ) devices, the optimality gap for QAOA grows with problem size, demonstrating its sensitivity to hardware noise, penalty scaling, and variational changes in parameters. Among the tested classical optimizers within the QAOA loop, Constrained Optimization BY Linear Approximations (COBYLA) demonstrated the most practical balance between efficiency and noise tolerance. In order to improve near-term quantum heuristics, this paper validates a functional quantum optimization procedure and highlights key factors for optimizer selection, encoding choice, and error mitigation. We conclude that current NISQ technology does not currently provide a quantum advantage for TSP; rather, our work provides a systematic methodology and performance baselines that are essential for the development of future hybrid quantum-classical algorithms.

Urban flooding is a complex phenomenon driven by limitations regarding precipitation and drainage systems. In this sense, a dynamic analysis of the processes allows us to model them by describing water accumulation over time through integrals and analyzing the instantaneous rate of change through derivatives. This approach enables early identification of risk situations before critical levels are reached. Concepts of differential and integral calculus are applied to model water accumulation in urban environments and predict flood risks. The following work proposes using continuous and discrete mathematical modeling to monitor hydrological behavior. The theoretical foundation is based on three pillars: the definition of water accumulation A(t) as the integral of the difference between rainfall intensity R(t) and drainage capacity D(t). Computationally, the discrete model is A(t+delta t)=A(t)+ (R-D); the instantaneous rate of change A'(t)=R(t)-D(t) as the main risk indicator (positive values indicate increasing accumulation, while rates that exceed a critical threshold trigger accelerated risk alerts); and the application of limiting casesto represent extreme behaviors, such as rainfall intensity approaching or tdrainage capacity approaching its physical maximum. Simulations demonstrated that the application identifies critical points A'(t) = 0, and predicts flooding before the level reaches the safety threshold (Ac). Thus, the model demonstrates the effectiveness of applying mathematics for the analysis of environmental problems. Integrating functions, derivatives, and integrals into a modern platform enables the transformation of mathematical models into tools with high social impact.

Introduction: The deployment of artificial intelligence in high-stakes domains increasingly demands systems that combine performance with fundamental interpretability, a requirement formalized by regulations such as the EU AI Act. This paper addresses the computational challenge of approximate inference in LIMEN-AI (Łukasiewicz Interpretable Markov Engine for Neuralized AI), a Small Reasoning Model engine that represents knowledge through weighted first-order logic formulas interpreted under Łukasiewicz fuzzy semantics. While this approach ensures human-readable reasoning steps, efficient inference over continuous interpretation spaces in relational settings remains a critical hurdle.

Methods: We develop a family of sampling-based inference algorithms tailored to the energy-based distribution induced by Łukasiewicz Markov Logic. Our approach includes importance sampling with mixture proposals and power sampling variants operating across multiple temperature levels. To address the saturation problem inherent in fuzzy logic—where truth values at boundaries cause vanishing gradients—we introduce ε-regularized operators that preserve informative gradients throughout the interpretation space. We employ the Metropolis-Adjusted Langevin Algorithm (MALA) to exploit the piecewise smooth gradients of the Łukasiewicz energy manifold, ensuring efficient exploration in high-dimensional spaces while maintaining convergence guarantees.

Results: We provide theoretical complexity bounds and extensive quantitative validation on relational domains containing up to 10⁴ ground atoms. Performance is evaluated through Effective Sample Size (ESS) metrics and comparison with analytical ground truth. Our results demonstrate that gradient-guided sampling maintains reliability where uniform baseline approaches collapse, particularly in high-dimensional settings.

Conclusions: The resulting inference routines preserve interpretability while achieving computational tractability, producing structured explanation traces that satisfy EU AI Act transparency requirements. This work bridges the gap between geometric logic and regulatory compliance, enabling auditable decision support in critical applications.

Heatwaves have become more common and severe due to climate change, especially rising temperatures, posing a serious public health problem in tropical countries. In this paper, a modified version of the Heat–SEIR model is developed to investigate the influence of seasonal temperature changes and long-term warming on population health. This model was developed by incorporating temperature-related parameters in the classical SEIR model. Seasonal and long-term temperature changes were modeled as a bounded sinusoidal function using average temperature data for Bangladesh from 2000 to 2024. Firstly, the mathematical properties of the proposed model were investigated, and its positivity and boundedness were proved. Then the disease-free equilibrium and the basic reproduction number R₀ were derived. From the local stability analysis of the proposed model, the disease-free equilibrium was stable if R₀ < 1 and unstable if R₀ > 1. However, the existence of the endemic equilibrium when R₀ > 1 was been proved.

Furthermore, the influence of temperature change was investigated using the Pearson correlation coefficient between the maximum temperature and other climate-related parameters. Sensitivity analysis was also conducted using normalized sensitivity indices and partial rank correlation coefficients to identify the parameters that most influence the proposed model. From the sensitivity analysis, the transmission and recovery rates were identified, as well as the most influential parameters, while heat-related mortality and temperature-sensitivity parameters were also found to influence the proposed model to a certain extent. Conducting a simulation to demonstrate the effects of seasonal heatwaves and long-term warming on population health, this study provides a clear, data-driven modeling framework for understanding heat-related health risks and could inform future public health planning.

Agriculture production is inherently affected by uncertainty arising from climate variability, input availability, market fluctuations, and management practices. Conventional statistical and time series forecasting models often fail to effectively capture the vagueness and imprecision associated with such agriculture data. To address this issue, the present study proposes a fuzzy multi-criteria decision-making framework based on the Fuzzy Multi-Attribute Technique for Order Preference by Similarity to Ideal Solution (FM-TOPSIS) for the comparative evaluation of crop production performance using year-wise agricultural data. In the proposed approach, each agricultural year is treated as an independent alternative, while multiple production-related factors such as yield, rainfall adequacy, cost cultivation, pest incidence, soil fertility status, and market stability are considered as evaluation criteria under a fuzzy environment. Linguistic assessments provided by domain experts and farmers are converted into triangular fuzzy numbers to construct the fuzzy decision matrix. FM TOPSIS is then applied to determine the relative closeness of each year to the ideal agriculture performance scenario. Furthermore, a two-stage hybrid evaluation strategy is employed, wherein yearwise rankings obtained through FM-TOPSIS are aggregated to derive an overall performance assessment across multiple years. This hybrid framework enhances robustness and enables consistent comparative analysis of agricultural performance under uncertainty. The results demonstrate that the proposed FM-TOPSIS-based methodology provides a reliable and practical decision support tool for evaluating crop production trends and supporting sustainable agricultural planning.

For better quantification of static and dynamic texture features and visual analysis within videos and animations, the combination of geometry, probabilistic formulation, and the latest machine learning and artificial intelligence mechanisms has become essential. Due to the potential and capability in image generation and dimensionality reduction, this study unites the mathematical underpinnings of Variational AutoEncoder (VAE) models for producing video frames with the geometric and algebraic framework of Lie group manifolds for dynamic video texture classification via Support Vector Machines (SVMs). Using VAE models, theoretical foundations of variational inference in autoencoding and decoding processes, the decomposition of the VAE loss function into latent KL divergence, and reconstructing loss for regularizing latent space distribution and preserving input feature fidelity will be explored. Case studies generating new interfaces and validating the effectiveness of data clustering mechanisms with the MNIST database will be used for performance assessments.

Despite VAE’s effectiveness in latent variable disentanglement and categorizing latent spaces, it is necessary to classify the dynamic texture of videos due to their continuous moving nature. Thus, a geometric approach combining an autoregressive moving average (ARMA) model, Lie group manifold, and matrix shape of Gaussian (SOG) descriptors was adopted to formalize video dynamic textures; then, a kernel function based on the Riemannian distance in the Lie group manifold was incorporated into the traditional SVM model to capture non-Euclidean manifold structure and implement the Lie-SVM multi-classifier with rigorous geometric regularization. Empirical validation based on sequences of images from a dynamic video confirms that our proposed algorithm yields superior classification performance, while preserving geometric invariants of manifold in kernel space.

The synergy of these mathematical and artificial intelligence methodologies can effectively handle and analyze both static generative visual content and dynamic texture videos, eventually bridging the gap between latent space design and discriminative manifold-aware feature classification for interactive user interface applications in the future.

The diagnoses of cardiac diseases using medical imaging has always been one of the major applications in the medical field, and tools such as machine learning methods have been heavily invested in this application; however, it often requires large, high-quality datasets that are difficult to obtain due to ethical, cost, and variability constraints. To tackle this challenge, we present this study, which explores the integration of classic matrix factorization techniques with deep learning for enhanced cardiac disease classification.

We adapt the matrix factorization approach and principal component analysis to identify dominant modes of variation that capture key features across five cardiac conditions: healthy, diabetic cardiomyopathy, myocardial infarction, obesity, and TAC-induced hypertension in mice. Echocardiography videos were processed into image datasets from long-axis (LAX) and short-axis (SAX) views, reshaped into vectors, and arranged in separate matrices (one matrix per cardiac condition), mean-subtracted, and decomposed using the matrix factorization tool, the singular value decomposition (SVD), to generate a principal components basis for each cardiac condition. These bases are used to represent the original images using projection. The new SVD-generated data is then used to train a convolutional neural network (CNN) classifier.

Compared to training the CNN on original echocardiography images, the SVD-based preprocessing significantly improved performance. Classification accuracy increased substantially across training, testing, and unseen (prediction) datasets, demonstrating about a ~50 % enhancement when using SVD-derived representations.

These results indicate that combining matrix factorization with deep learning can effectively overcome data scarcity issues and improve generalization in medical image classification. The proposed hybrid methodology provides a promising tool for cardiac disease diagnosis, suggesting broader applicability to other medical imaging problems where data limitations hinder machine learning performance.