Mathematical Applications and Computational Intelligence in Medicine and Biology

Abstract submission deadline

31 January 2027

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31 March 2027

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Topic Information

Dear Colleagues,

Mathematical modeling, triaged in an optimized and controlled manner through applicable computational methods with regard to uncertain phenomena, is pertinent for describing and computing complex behaviors, which entails the viable mathematical formulations and applications of neural dynamics across the temporal and spatial scales in medical and biological systems. Systems based on computational intelligence are capable of learning data, manifesting an evolutionary process based on the alterations in the environment while considering uncertainty, complexities and risks and ensuring the characterization of clinical, medical, synthetic, fragmented, omics, imaging, signal, sensor data, amongst other elements to improve the processing of a multitude of data in healthcare toward the development of timely and intelligent solutions to diagnose, prognose, treat, manage and analyze the course of complex dynamic diseases. Accordingly, computational analyses based on advanced mathematical models and computational intelligence, as biologically inspired computational algorithms, constituting the use of genetic algorithms, fuzzy systems, neural networks, probabilistic methods, and so forth, address the employment of computational techniques, methods and algorithms geared towards voluminous data analysis, control, as well as problem-solving in various realms spanning and progressing across advancing applied sciences, engineering applications and scientific research in which mathematical and computational analyses include computational models, simulations, predictions, numerical analyses, processes, etc.

The theory of mathematics and computational theory constitute the essential foundational structure for comprehending computation and its applications in medicine and biology along with their inherent intricate details to analyze the capabilities concerning computer systems, neural networks and algorithms, with relevant implications ranging across various disciplines including mathematics, natural sciences, life sciences, applied sciences, data science, computer science, engineering, bioengineering, etc.

Based on these considerations, mathematical applications and computational intelligence entail the techniques, algorithms, approaches and methods for customized problems and solutions so that mathematical and computational power can be enhanced to process data and conduct advanced implementations regarding real-world complex problems, diseases, biological, epidemiological, environmental factors and other conceivable elements by means of simulations, experimental and/or computational processes, numerical methods, optimization, control and so forth.

Potential topics include, but are not limited to, the following:

• Stochastic disease dynamics of complex networks
• Neural network complexity
• Computational intelligence in oncology
• Complex feedback circuitry
• Gene regulatory networks
• Advanced biomedical data analysis
• Predictive mathematical modeling in medicine/biology
• Medical / Clinical decision-support systems
• Systems biology and medicine
• Precision medicine
• Applied mathematics modeling in treatment regimens
• Soft computing with advanced applications for clinical purposes
• Fractional calculus and its applications in systems medicine and biology
• Difference and differential equations (PDEs, ODEs, FDEs, SDEs, and so on) with applications for diagnostics
• Multidrug-resistant treatment regiments
• Advanced mathematical methods in intelligence systems
• Mathematical modeling, control systems and optimization methods
• Chaos and nonlinear systems
• Fractal physiology and chaos in medicine/biology
• Image and/or signal processing
• Applied complexity, computational complexity and complex systems
• Applied statistics and probability
• Advances in computational modeling in engineering and science applications
• Application of advanced AI (machine learning, deep learning, quantum, and so forth)
• Artificial Intelligence of Things (AIoT) in medicine/biology

Prof. Dr. Yeliz Karaca
Prof. Dr. Majaz Moonis (MD)
Prof. Dr. Yudong Zhang
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AI ai	6.5	7.3	2020	20.4 Days	CHF 1800	Submit
Algorithms algorithms	2.6	5.4	2008	17.6 Days	CHF 1800	Submit
AppliedMath appliedmath	1.4	1.4	2021	20.4 Days	CHF 1200	Submit
Bioengineering bioengineering	4.4	7.5	2014	16.9 Days	CHF 2700	Submit
Mathematics mathematics	2.3	5.4	2013	17.4 Days	CHF 2600	Submit

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Published Papers (13 papers)

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Open AccessReview

Making Healthcare AI Explainable: A Structured Review of Methods and Clinical Practice

by Razvan-Alexandru Nicu and Nirvana Popescu

AppliedMath 2026, 6(10), 170; https://doi.org/10.3390/appliedmath6100170 - 9 Oct 2026

Abstract

Artificial intelligence is rapidly transforming modern medicine, providing powerful tools to assist clinicians. However, the most accurate models are opaque, and their limited interpretability hinders clinical adoption and raises regulatory concerns. Explainable Artificial Intelligence (XAI) aims to make these models’ decisions comprehensible. Despite [...] Read more.

Artificial intelligence is rapidly transforming modern medicine, providing powerful tools to assist clinicians. However, the most accurate models are opaque, and their limited interpretability hinders clinical adoption and raises regulatory concerns. Explainable Artificial Intelligence (XAI) aims to make these models’ decisions comprehensible. Despite its rapid growth and the many reviews already published, aspects such as the rigor of explanation evaluation, clinician involvement, and the use of large language models to generate explanations appear to have received limited attention. This article is a structured, relevance-prioritized review of XAI applied in healthcare, organized around six research questions covering the XAI techniques used, the data and clinical domains they are paired with, the models they explain, how evaluation is performed, the identified limitations, and the use of large language models. Unlike prior reviews that each address only part of this scope, we bring these dimensions together and quantify how rigorously explanations are evaluated and how often the underlying models are externally validated. We conducted a structured search across four literature sources: IEEE Xplore, PubMed, Google Scholar, and PubMed Central (PMC). We adapted the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) flow by carrying a relevance-prioritized subset forward to full-text eligibility assessment, yielding 64 articles for synthesis. Within this corpus, our review revealed a predominantly image-based, post hoc XAI landscape dominated by a few established methods such as SHapley Additive exPlanations (SHAP), Gradient-weighted Class Activation Mapping (Grad-CAM), and Local Interpretable Model-agnostic Explanations (LIME), mostly paired with convolutional, tree-based, and hybrid models on classification and risk-prediction tasks. Clinicians evaluated the explanations in only a minority of the included studies, and relatively few models were externally validated, with no evidence of large language models in our corpus. We conclude that stronger evaluation practices and closer collaboration with clinicians are needed to produce models that are clinically useful and safe to deploy. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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26 pages, 2253 KB  

Open AccessArticle

Triple-Path Kolmogorov–Arnold Networks with Deep Mutual Learning for Robust Retinal Microvascular Segmentation

by Yu-Lung Chang and Yen-Ching Chang

AI 2026, 7(9), 357; https://doi.org/10.3390/ai7090357 - 10 Sep 2026

Viewed by 436

Abstract

Precise segmentation of the retinal microvasculature is vital for early detection and longitudinal monitoring of systemic cardiovascular and ophthalmic diseases. However, contemporary deep learning models struggle to simultaneously preserve fine-vessel branches and suppress background noise, often leading to severe under-segmentation or false-positive artifacts. [...] Read more.

Precise segmentation of the retinal microvasculature is vital for early detection and longitudinal monitoring of systemic cardiovascular and ophthalmic diseases. However, contemporary deep learning models struggle to simultaneously preserve fine-vessel branches and suppress background noise, often leading to severe under-segmentation or false-positive artifacts. To address this persistent challenge, we propose a novel, highly efficient Triple-Path Kolmogorov–Arnold Network (KAN) optimized via Deep Mutual Learning (DML). First, the proposed architecture synergistically integrates U-Net, HaarNet, and SegNet to explicitly decouple global contextual feature extraction from high-frequency spatial edge detection. Second, we introduce field-of-view spatial constraints to strictly eliminate background interference. Third, traditional linear bottlenecks are replaced with KAN blocks, which leverage dynamic, Chebyshev polynomial-based activation functions to robustly model highly nonlinear, chaotic vascular topologies. Finally, a zero-cost DML strategy is employed during training, maximizing the network’s representational capacity without introducing any computational burden during inference. Extensive evaluations demonstrate that our proposed model successfully overcomes the traditional sensitivity-specificity trade-off. Specifically, it achieves a peak sensitivity of 72.38%, a specificity of 98.66%, and an overall Dice score of 72.48%. While maintaining exceptional computational efficiency, this tightly coupled framework establishes a robust, accurate, and clinically viable solution for automated point-of-care retinal diagnostics. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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21 pages, 759 KB  

Open AccessArticle

Dynamic Behaviors of a Stage-Structured Commensalism Model with Holling Type II Benefits and Birth-Related Allee Effect

by Lu Zou and Qin Yue

AppliedMath 2026, 6(9), 152; https://doi.org/10.3390/appliedmath6090152 - 9 Sep 2026

Viewed by 227

Abstract

Low adult density can suppress recruitment through mate limitation or cooperative reproductive failure, even when a host improves adult survival. Motivated by this ecological tension, we introduce a fecundity-related component Allee effect into a stage-structured commensalism model with a Holling type II host [...] Read more.

Low adult density can suppress recruitment through mate limitation or cooperative reproductive failure, even when a host improves adult survival. Motivated by this ecological tension, we introduce a fecundity-related component Allee effect into a stage-structured commensalism model with a Holling type II host benefit. The nonlinear recruitment term is $f\left(x_2\right)=\alpha x_2^2/(x_2+A)$, and the independently growing host converges to its carrying capacity, yielding an asymptotically autonomous commensal subsystem. We obtain a complete analytical classification. If the long-term host benefit D exceeds mature mortality ${\delta }_2$, a unique coexistence equilibrium attracts every nontrivial commensal population. If the benefit is insufficient, fecundity limitation can instead create two positive equilibria: a low-density saddle whose stable set is the basin boundary and a stable high-density coexistence state. Thus, extinction and coexistence are both possible, depending on initial stage composition and host abundance. Stronger fecundity limitation enlarges the extinction region, whereas greater recruitment, maturation or host benefit promotes persistence. At the critical boundary, the positive equilibria merge in a non-degenerate saddle-node bifurcation. Rigorous global arguments and numerical comparisons with the linear-recruitment model show how a component Allee effect can induce strong-Allee-type demographic behavior, including bistability and threshold-mediated extinction. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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44 pages, 1971 KB  

Open AccessArticle

Stochastic Environmental Impacts on Two-Patch Cholera Model: Threshold Analysis and Ergodic Stationary Distribution

by Hassan Ranjbar and Afshin Babaei

Mathematics 2026, 14(13), 2266; https://doi.org/10.3390/math14132266 - 25 Jun 2026

Viewed by 305

Abstract

In-depth analysis of epidemic models, particularly for cholera, is crucial because they serve as significant tools for disease transmission prediction, evaluation of control strategies, and optimization of healthcare resource management. The stochastic models provide increased realism by incorporating environmental uncertainty such as variability [...] Read more.

In-depth analysis of epidemic models, particularly for cholera, is crucial because they serve as significant tools for disease transmission prediction, evaluation of control strategies, and optimization of healthcare resource management. The stochastic models provide increased realism by incorporating environmental uncertainty such as variability in water quality, disparities in access to sanitation, and population mobility. The present work generalizes a deterministic two-patch cholera model to a stochastic framework. We first prove the existence and uniqueness of global solutions, then establish the extinction condition $R_0^{*}<1$ for disease eradication in the long term. A key contribution lies in proving the existence of a unique ergodic stationary distribution when $R_0^{\left(1\right)}>1$ and $R_0^{\left(2\right)}>1$. Furthermore, we derive the stochastic threshold $R_0=\text{max}\{R_0^{\left(1\right)},R_0^{\left(2\right)}\}$, which corresponds to the basic reproduction number ${\mathcal{R}}_0=\text{max}\{{\mathcal{R}}_0^{\left(1\right)},{\mathcal{R}}_0^{\left(2\right)}\}$. Lastly, numerical simulations are employed to confirm theoretical results. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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19 pages, 1946 KB  

Open AccessArticle

Layer-Wise Persistent Entropy of CT Scan Point Clouds for Lung Tumor Classification

by C. Jeeva Jose, Aneesh P. Baiju, Riya Roy, A. Harikrishnan, Rahul Sanju, P. B. Vinod Kumar, K. K. Sherly, Rinku Jacob and G. Sreekumar

AppliedMath 2026, 6(6), 95; https://doi.org/10.3390/appliedmath6060095 - 11 Jun 2026

Viewed by 690

Abstract

In this study, a layer-wise point cloud representation of CT scan images is proposed, from which persistence diagrams are constructed and persistent entropy is computed as a compact topological feature for three-class lung tumor classification. Two parallel approaches are investigated: the direct computation [...] Read more.

In this study, a layer-wise point cloud representation of CT scan images is proposed, from which persistence diagrams are constructed and persistent entropy is computed as a compact topological feature for three-class lung tumor classification. Two parallel approaches are investigated: the direct computation of persistence diagrams from CT images, and computation from subsampled point clouds derived from image intensity layers. The proposed method is evaluated on the publicly available IQ-OTH/NCCD lung cancer dataset, comprising 1097 CT scan images from 110 individuals, annotated by expert oncologists and radiologists. Classification is performed using K-Nearest Neighbors (KNN), Random Forest, Support Vector Machine, and eXtreme Gradient Boosting, and compared against Convolutional Neural Network (CNN) and traditional image feature-based methods. The persistent entropy approach applied to layer-wise subsampled point clouds achieves 97.67% accuracy, a Precision–Recall AUC of 96.63%, and a ROC-AUC of 99.46% using KNN, outperforming direct image-based analysis (95.91%) and achieving comparable accuracy to the CNN method (97.21%) with a computational speedup of approximately $478\times$. These results demonstrate that persistent homology applied to subsampled point clouds provides an accurate, mathematically interpretable, and computationally efficient alternative to deep learning for lung tumor classification. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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12 pages, 8070 KB  

Open AccessArticle

A Parametric Model of the Mitral Valve for Finite Element Patient-Specific Simulations

by Alicia Menéndez Hurtado and Sergejus Borodinas

Bioengineering 2026, 13(6), 676; https://doi.org/10.3390/bioengineering13060676 - 10 Jun 2026

Viewed by 538

Abstract

Finite element models of the mitral valve can be useful tools for physicians as a predictive tool for surgical planning, teaching, or observation. In order to seamlessly implement these tools in a clinical setting, the process for the creation of the models needs [...] Read more.

Finite element models of the mitral valve can be useful tools for physicians as a predictive tool for surgical planning, teaching, or observation. In order to seamlessly implement these tools in a clinical setting, the process for the creation of the models needs to take into account the diagnostic procedures and tools available to physicians. In this study, a rapid patient-specific model for clinical applications is developed, creating a parametric geometry from measurements routinely taken during the diagnostic process and maintaining a low computational cost through simplifications in material and boundary conditions. The healthy valve model is then validated against ultrasound images from peak diastole to peak systole, finding a good conformity despite simplifications. These results can serve as a stepping stone towards the development of a clinical digital twin of the mitral valve that combines engineering knowledge and medical process. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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17 pages, 14891 KB  

Open AccessArticle

Data-Driven Modeling and Classification of Brain Blood-Flow Pathologies

by Irem Topal, Alexander Cherevko, Yuriy Bugai, Maxim Shishlenin, Jean Barbier, Deniz Eroglu, Édgar Roldán and Roman Belousov

AI 2026, 7(3), 105; https://doi.org/10.3390/ai7030105 - 11 Mar 2026

Viewed by 1450

Abstract

Cerebral aneurysms and arteriovenous malformations are life-threatening hemodynamic pathologies of the brain. While surgical intervention is often essential to prevent fatal outcomes, it carries significant risks both during the procedure and in the postoperative period, making the management of these conditions highly challenging. [...] Read more.

Cerebral aneurysms and arteriovenous malformations are life-threatening hemodynamic pathologies of the brain. While surgical intervention is often essential to prevent fatal outcomes, it carries significant risks both during the procedure and in the postoperative period, making the management of these conditions highly challenging. Parameters of cerebral blood flow, routinely monitored during medical interventions or with modern noninvasive high-resolution imaging methods, could potentially be utilized in machine-learning-assisted protocols for risk assessment and therapeutic prognosis. To this end, we developed a linear oscillatory model of blood velocity and pressure for clinical data acquired from neurosurgical operations. Using the method of Sparse Identification of Nonlinear Dynamics (SINDy), the parameters of our model can be reconstructed online within milliseconds from a short time series of the hemodynamic variables. The identified parameter values enable automated classification of the blood-flow pathologies by means of logistic regression, achieving a balanced accuracy of 74%. Our results demonstrate the potential of this model for both diagnostic and prognostic applications, providing a robust and interpretable framework for assessing cerebral blood vessel conditions. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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26 pages, 5240 KB  

Open AccessArticle

Enhanced Assumption-Aware Linear Discriminant Analysis for the Wisconsin Breast Cancer Dataset: A Guide to Dimensionality Reduction and Prediction with Performance Comparable to Machine Learning Methods

by Vasiliki Pantoula, Vasileios Mandikas and Tryfon Daras

AppliedMath 2026, 6(2), 20; https://doi.org/10.3390/appliedmath6020020 - 3 Feb 2026

Cited by 2 | Viewed by 1374

Abstract

The analysis of multivariate data is a central issue in biomedical research, where the accurate classification of patients and the extraction of reliable conclusions are of critical importance. Linear Discriminant Analysis (LDA) remains one of the most established methods for both dimensionality reduction [...] Read more.

The analysis of multivariate data is a central issue in biomedical research, where the accurate classification of patients and the extraction of reliable conclusions are of critical importance. Linear Discriminant Analysis (LDA) remains one of the most established methods for both dimensionality reduction and classification of data. In this paper, we examine in detail the theoretical foundations, assumptions, and statistical properties of LDA, and apply the method step by step to real data from the Breast Cancer Wisconsin (Diagnostic) database, which includes cellular features from breast biopsy samples with the aim of distinguishing benign from malignant tumors. Emphasis is placed on the importance of the method’s assumptions, such as multivariate normality, equality of covariance matrices, and absence of multicollinearity, demonstrating that their fulfillment leads to significant improvements in model performance. Specifically, careful preprocessing and strict adherence to these assumptions increase classification accuracy from $95.6\%$ ($94.7\%$ cross-validated) to $97.8\%$ ($97.4\%$ cross-validated). To our knowledge, this study is the first to demonstrate the dual use of LDA as both a dimensionality-reduction tool and a predictive classification model for this medical database within the same biomedical analysis framework. Moreover, we provide, for the first time, a systematic comparison between our assumption-aware LDA model and related studies employing the most accurate machine-learning classifiers reported in the literature for this dataset, showing that classical LDA achieves accuracy comparable to these more complex methods. The resulting discriminant model, which uses 13 variables out of the original 30, can be applied easily by clinical researchers to classify new cases as benign or malignant, while simultaneously providing interpretable coefficients that reveal the underlying relationships among variables. The implementation is carried out in the SPSS environment, following the theoretical steps described in the paper, thus offering a user-friendly and reproducible framework for reliable application. In addition, the study establishes a structured and transparent workflow for the proper application of LDA in biomedical research by explicitly linking assumption verification, preprocessing, dimensionality reduction, and classification. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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23 pages, 5052 KB  

Open AccessArticle

Exploratory Study on Hybrid Systems Performance: A First Approach to Hybrid ML Models in Breast Cancer Classification

by Francisco J. Rojas-Pérez, José R. Conde-Sánchez, Alejandra Morlett-Paredes, Fernando Moreno-Barbosa, Julio C. Ramos-Fernández, José Luna-Muñoz, Genaro Vargas-Hernández, Blanca E. Jaramillo-Loranca, Juan M. Xicotencatl-Pérez and Eucario G. Pérez-Pérez

AI 2026, 7(1), 29; https://doi.org/10.3390/ai7010029 - 15 Jan 2026

Viewed by 1075

Abstract

The classification of breast cancer using machine learning techniques has become a critical tool in modern medical diagnostics. This study analyzes the performance of hybrid models that combine traditional machine learning algorithms (TMLAs) with a convolutional neural network (CNN)-based VGG16 model for feature [...] Read more.

The classification of breast cancer using machine learning techniques has become a critical tool in modern medical diagnostics. This study analyzes the performance of hybrid models that combine traditional machine learning algorithms (TMLAs) with a convolutional neural network (CNN)-based VGG16 model for feature extraction to improve accuracy for classifying eight breast cancer subtypes (BCS). The methodology consists of three steps. First, image preprocessing is performed on the BreakHis dataset at 400× magnification, which contains 1820 histopathological images classified into eight BCS. Second, the CNN VGG16 is modified to function as a feature extractor that converts images into representative vectors. These vectors constitute the training set for TMLAs, such as Random Forest (RF), Support Vector Machine (SVM), K-Nearest Neighbors (KNN), and Naive Bayes (NB), leveraging VGG16’s ability to capture relevant features. Third, k-fold cross-validation is applied to evaluate the model’s performance by averaging the metrics obtained across all folds. The results reveal that hybrid models leveraging a CNN-based VGG16 model for feature extraction, followed by TMLAs, achieve accuracy outstanding experimental accuracy. The KNN-based hybrid model stood out with a precision of 0.97, accuracy of 0.96, sensitivity of 0.96, specificity of 0.99, F1-score of 0.96, and ROC-AUC of 0.97. These findings suggest that, with an appropriate methodology, hybrid models based on TMLA have strong potential in classification tasks, offering a balance between performance and predictive capability. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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29 pages, 4462 KB  

Open AccessArticle

Integrating Machine Learning and Fractional-Order Dynamics for Enhanced Psoriasis Prediction and Clinical Decision Support

by David Amilo, Khadijeh Sadri, Evren Hincal and Mohamed Hafez

AppliedMath 2025, 5(4), 143; https://doi.org/10.3390/appliedmath5040143 - 15 Oct 2025

Cited by 4 | Viewed by 1775

Abstract

This study introduces a novel hybrid framework that integrates machine learning (ML) with fractional-order differential equations (FDE) to enhance the prediction and clinical management of psoriasis, leveraging real-world data from the UCI Dermatology Dataset. By optimizing ML models, particularly the Voting Ensemble, to [...] Read more.

This study introduces a novel hybrid framework that integrates machine learning (ML) with fractional-order differential equations (FDE) to enhance the prediction and clinical management of psoriasis, leveraging real-world data from the UCI Dermatology Dataset. By optimizing ML models, particularly the Voting Ensemble, to inform FDE parameters, and developing a user-friendly graphical user interface (GUI) for real-time diagnostics, the approach bridges computational efficiency with physiological realism, capturing memory-dependent disease progression beyond traditional integer-order models. Key findings reveal that the Voting Ensemble achieves a precision of 0.986 ± 0.007 and an AUC of 0.992 ± 0.005. At the same time, the fractional-order model, with an optimized order of 0.6781 and a mean square error (MSE) of 0.0031, accurately simulates disease trajectories, closely aligning with empirical trends for features such as Age and SawToothRete. The GUI effectively translates these insights into clinical tools, demonstrating probabilities ranging from 0% to 100% based on input features, supporting early detection and personalized planning. The framework’s robustness and potential for broader application to chronic conditions highlight its significance in advancing healthcare. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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18 pages, 382 KB  

Open AccessArticle

Self-Organized Criticality and Quantum Coherence in Tubulin Networks Under the Orch-OR Theory

by José Luis Díaz Palencia

AppliedMath 2025, 5(4), 132; https://doi.org/10.3390/appliedmath5040132 - 2 Oct 2025

Cited by 2 | Viewed by 9542

Abstract

We present a theoretical model to explain how tubulin dimers in neuronal microtubules might achieve collective quantum coherence, resulting in wavefunction collapses that manifest as avalanches within a self-organized criticality (SOC) framework. Using the Orchestrated Objective Reduction (Orch-OR) theory as inspiration, we propose [...] Read more.

We present a theoretical model to explain how tubulin dimers in neuronal microtubules might achieve collective quantum coherence, resulting in wavefunction collapses that manifest as avalanches within a self-organized criticality (SOC) framework. Using the Orchestrated Objective Reduction (Orch-OR) theory as inspiration, we propose that microtubule subunits (tubulins) become transiently entangled via dipole–dipole couplings, forming coherent domains susceptible to sudden self-collapse. We model a network of tubulin-like nodes with scale-free (Barabási–Albert) connectivity, each evolving via local coupling and stochastic noise. Near criticality, the system exhibits power-law avalanches—abrupt collective state changes that we identify with instantaneous quantum wavefunction collapse events. Using the Diósi–Penrose gravitational self-energy formula, we estimate objective reduction times $T_{\mathrm{OR}}=\hslash /E_g$ for these events in the 10–200 ms range, consistent with the Orch-OR conscious moment timescale. Our results demonstrate that quantum coherence at the tubulin level can be amplified by scale-free critical dynamics, providing a possible bridge between sub-neuronal quantum processes and large-scale neural activity. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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19 pages, 2030 KB  

Open AccessArticle

Non-Linear Synthetic Time Series Generation for Electroencephalogram Data Using Long Short-Term Memory Models

by Bakr Rashid Alqaysi, Manuel Rosa-Zurera and Ali Abdulameer Aldujaili

AI 2025, 6(5), 89; https://doi.org/10.3390/ai6050089 - 25 Apr 2025

Cited by 2 | Viewed by 2561

Abstract

Background/Objectives: The implementation of artificial intelligence-based systems for disease detection using biomedical signals is challenging due to the limited availability of training data. This paper deals with the generation of synthetic EEG signals using deep learning-based models, to be used in future research [...] Read more.

Background/Objectives: The implementation of artificial intelligence-based systems for disease detection using biomedical signals is challenging due to the limited availability of training data. This paper deals with the generation of synthetic EEG signals using deep learning-based models, to be used in future research for training Parkinson’s disease detection systems. Methods: Linear models, such as AR, MA, and ARMA, are often inadequate due to the inherent non-linearity of time series. To overcome this drawback, long short-term memory (LSTM) networks are proposed to learn long-term dependencies in non-linear EEG time series and subsequently generate synthetic signals to enhance the training of detection systems. To learn the forward and backward time dependencies in the EEG signals, a Bidirectional LSTM model has been implemented. The LSTM model was trained on the UC San Diego Resting State EEG Dataset, which includes samples from two groups: individuals with Parkinson’s disease and a healthy control group. Results: To determine the optimal number of cells in the model, we evaluated the mean squared error (MSE) and cross-correlation between the original and synthetic signals. This method was also applied to select the length of the hidden state vector. The number of hidden cells was set to 14, and the length of the hidden state vector for each cell was fixed at 4. Increasing these values did not improve MSE or cross-correlation and unnecessarily increased computational complexity. The proposed model’s performance was evaluated using the mean-squared error (MSE), Pearson’s correlation coefficient, and the power spectra of the synthetic and original signals, demonstrating the suitability of the proposed method for this application. Conclusions: The proposed model was compared to Autoregressive Moving Average (ARMA) models, demonstrating superior performance. This confirms that deep learning-based models, such as LSTM, are strong alternatives to statistical models like ARMA for handling non-linear, multifrequency, and non-stationary signals. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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27 pages, 2859 KB  

Open AccessArticle

A New Multidimensional Computerized Testing Approach: On-the-Fly Assembled Multistage Adaptive Testing Based on Multidimensional Item Response Theory

by Jingwen Li, Jianan Sun, Mingyu Shao, Yinghui Lai and Chen Chen

Mathematics 2025, 13(4), 594; https://doi.org/10.3390/math13040594 - 11 Feb 2025

Cited by 2 | Viewed by 2753

Abstract

Unidimensional on-the-fly assembled multistage adaptive testing (OMST), a flexible testing method, integrates the strengths of the adaptive test assembly of computerized adaptive testing (CAT) and the modular test administration of multistage adaptive testing (MST). Since numerous latent trait structures in practical applications are [...] Read more.

Unidimensional on-the-fly assembled multistage adaptive testing (OMST), a flexible testing method, integrates the strengths of the adaptive test assembly of computerized adaptive testing (CAT) and the modular test administration of multistage adaptive testing (MST). Since numerous latent trait structures in practical applications are inherently multidimensional, extending the realm from unidimensional to multidimensional is necessary. Multidimensional item response theory (MIRT), a branch of mathematical and statistical latent variable modeling research, has an important position in the international testing field. Based on MIRT, this study proposes an approach of multidimensional OMST (OMST-M), and on-the-fly automated test assembly algorithms are proposed based on point estimation and confidence ellipsoid, respectively. OMST-M can effectively and flexibly measure multidimensional latent traits through stage-by-stage adaptive testing. The simulation results indicated that under different settings of latent trait structures, module lengths, and module contents, the OMST-M approach demonstrated good performance in terms of ability estimation accuracy and item exposure control. The empirical research revealed that the OMST-M approach was comparable to both multidimensional MST and CAT in ability estimation accuracy and exhibited remarkable flexibility in adjusting the length and content across its test stages. In summary, the proposed OMST-M features relatively high measurement accuracy, efficiency, convenient implementation, and practical feasibility. Full article

(This article belongs to the Topic Mathematical Applications and Computational Intelligence in Medicine and Biology)

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